curtipot - pka calculator

Version 3.3.2 (2008) for MS-Excel® 1997 - 2007

Copyright © 1992 - 2008Prof. Ivano G.R. Gutz

[email protected]

http://www2.iq.usp.br/docente/gutz/Curtipot_.html

pH and Acid-Base Titration Curves:

Analysis and Simulation

Instituto de Química - Universidade de São Paulo, São Paulo, SP, Brazil

Head of the Chemistry Department of IQ-USP (2004-2006; 2006-2008)

Member of the Editorial Boards of Talanta (2005-2007) and Electrochemistry Communications (2005 -->)

Honored with the National Order of Scientific Merit, Brazil, 2007

Fellow of International Union of Pure and Applied Chemistry

Research interests:

CV, Publications, see: www2.iq.usp.br/docente/gutz

Dr. Ivano Gebhardt Rolf Gutz - Full Professor (since 1992)

This freeware is a courtesy of

F40

Gutz: a) Invention, development, miniaturization, automation and application of analytical devices, systems and methods, with preference for electroanalytical, electrophoretic and spectroeletroanalytical flow systems, including microfluidic ones. b) Research in environmental chemistry with emphasis on the liquid phase and related chemistry of the atmosphere in the São Paulo megacity – the largest “laboratory” of ethanol use as fuel; development of sampling, speciation and determination methods.

» generation of curves with equally spaced data in pH or volume

» simulation of experimental random errors in pH and volume

» overlay of multiple simulated curves for comparison

Read the License first (place mouse on red dot at left); if you agree with all terms, you can use CurTiPot in educational and non-commercial applications

The Regression module becomes operational after activation of the Solver supplement; you can do this later

Regularly check for updated releases at the author’s site www2.iq.usp.br/docente/gutz (University of São Paulo, Brasil)

Experimental pH values are assumed free of calibration, junction potential and alkaline errors of the sensor (to be corrected previously for most accurate results)

The author reserves the right not to be responsible for the correctness, completeness, accuracy and bug-free operation of the freeware CurTiPot

Please report errors and incompatibilities of Curtipot (developed for Excel 9 and 10) to the author;

Read local instructions in comment boxes by placing the mouse on cells with red marks (like in Q2, Q13, Q15 and Q21 in this page);

Save your data, settings and results in Curtipot_anyname.xls files to preserve the original software (optionally deleting unused spreadsheets, but not the this first one);

Some features and uses of CurTiPot (hover on red mark at Q2 to read about the name and origins of the program)

• pH calculation of aqueous solutions (>30 species in equilibrium)

• Simulation of simple and complex acid-base titration curves - Virtual Titrator

• Data analysis of real and simulated curves

» Evaluation of curves by interpolation, smoothing and automatic endpoint detection

» determination of concentrations and refinement pKas by non-linear regression

• Distribution of species and protonation of bases vs. pH and vs. volume

Configure Microsoft Excel to medium security (Tools/Macro/Security/Security level/Medium), open the curtipot_.xls file and activate the macros

Ionic strength and activity coefficient corrections available only in the pH calc module

Click on the pH_calc tab, at the botton of the page; If you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H21;

Click on Calculate pH; clear all concentrations and check the pH of water; test various solutions with one ore more species of the preloaded acid-base systems;

Switch to the preloaded Simulation of the titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

Find endpoints of your real or simulated curves with Evaluation. There are buttons to load the last titration curve from Simulation;

Play and learn with the Distribution module; enjoy the Graphs before you advance to the less simple but more powerful Regression to fit concentrations and pKas;

Version 3.3.2 (2008) for MS-Excel® 1997 - 2007

Applications

Installation

Remarks

Fast Start

http://www2.iq.usp.br/docente/gutz/Curtipot_.html

pH and Acid-Base Titration Curves:

Analysis and Simulation

Q2

The acronym CurTiPot means Potentiometric Titration Curves (in reversed order). Originally written in Turbo Basic for DOS and first demonstrated and distributed during the 15th Annual Meeting of the Brazilian Chemical Society (1992) versions 1 and 2 (not translated do English) became widely diffused in Brazil. The Excel version was launched in 2006 and presents extra features, like the powerful Regression module and a separated pH calculation module, that takes activity coefficients and ionic strength in account. Sitemeter tracks over one thousand downloads of the freeware monthly to one hundred countries from my website http://www2.iq.usp.br/docente/gutz/Curtipot_.html. Many more copies of CurTiPot are downloaded from over 200 sowtware distribution sites. Feedback by e-mail with criticism and suggestions is welcomed (and answered when I find time). If you are really satisfied with CurTiPot, please link to http://www2.iq.usp.br/docente/gutz/Curtipot_.html from your homepage, Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

Q13

End user license agreement Thank you for your interest in the CurTiPot version 3 freeware, a workbook of spreadsheets for Excel (proprietary software of Microsoft), authored by Dr. Ivano G. R. Gutz, Professor of the Institute of Chemistry of the University of São Paulo, São Paulo, Brazil, now on referred as Author of CurTiPot. Please examine the License Agreement before you start using CurTiPot. Personal or Educational Use Only The Author grants you a non-exclusive and non-transferable freeware license of CurTiPot for your personal or educational use at home, in classroom or in academic laboratories. If you intend to make commercial use of CurTiPot, including but not limited to any profitable non-educational activity or selling or distributing CurTiPot for payment, you must obtain a written permission from the Author in advance. Restrictions You may introduce modifications in the spreadsheets to suit your needs, but you are not allowed to remove the original notices about the intellectual property of the workbook and macros, in special but not only from the front page. You shall not distribute copies of modified versions without approval by the Author of the clearly identified changes. Distribution You may share unmodified copies of CurTiPot with students and colleagues that do not have access to the Internet, if they agree to be bound to these Terms and Conditions and as long as you take all reasonable precautions to avoid exposure of your copy to viruses. To minimize risks, it is highly advisable, to use only updated copies obtained from the Author’s download page. Changes to Terms and Conditions The author reserves the right to update CurTiPot and to modify these Terms and Conditions at its sole discretion, without notice or liability to you. You agree to be bound by these Terms and Conditions, as modified. Please download updated versions of CurTiPot from time to time and review the Terms and Conditions. Disclaimer of Warranties The Author disclaims any responsibility for any harm resulting from your use (or use by your colleagues or students) of CurTiPot and third party software used in conjunction with it. CurTiPot is provided "AS IS," with no warranties whatsoever, express, implied, and statutory, including, without limitation, the warranties of merchantability, fitness for a particular purpose, and non-infringement of proprietary rights. The author also disclaims any warranties regarding the security, reliability, accuracy, stability, convergence and performance of CurTiPot. You understand and agree that you download and/or use CurTiPot at your own discretion and risk and that you will be solely responsible for any consequences of incorrect information or results obtained with CurTiPot. This license does not entitle the Licensee to receive from the Author any extra documentation not contained in the program file, support or assistance by any means, or enhancements or updates of CurTiPot other than those made available for download at the Author’s site. Limitation of Liability Under no circumstances shall the Author or his employer be liable to any user on account its use or misuse of CurTiPot. If you accept the terms and conditions given above, you are entitled to use CurTiPot free of charge for unlimited time and number of uses. The Author will enjoy your comments, error reports and suggestions by e-mail.

Q15

Gutz: Before using the Regression module, check if Solver figures under Data / Analysis / ? (Solver) in Excel 2007 or under the Tools list in former versions of Excel. If not, close CurTiPot, open a blank page and install the Solver. For Excel 2003, under Tools/Supplements/check the Solver box, find it and install. If the supplement is not pre-loaded on the HD, insert the Office® installation disk and upload the file. This installation is required only once on a PC. Open CurTiPot again and start using the regression module.

The software CurTiPot, version 1.0 for DOS (Disk Operating System, Microsoft), was created in 1991 in Turbo Basic and launched in 1992.

Instituto de Química - Universidade de São Paulo, São Paulo, SP, Brazil Version 2 appeared in 1992. Besides volumetry, it accepts data from titrations with coulometric generation of reactants.

Head of the Chemistry Department of IQ-USP (2004-2006; 2006-2008)

Member of the Editorial Boards of Talanta (2005-2007) and Electrochemistry Communications (2005 -->)

Honored with the National Order of Scientific Merit, Brazil, 2007

Version 3.3, from January 2008, has a frindlier interface with the Database; logarithmic distribution diagram generation overlayed on the titration curve was added.

Version 3.0 for Excel is an evolution of the DOS version. A new Regression module is the most significant improvement. It was released in 2006 (in Portuguese).

Version 3.1 was the first translated to English. It was launched at May 1st, 2006, at the site www2.iq.usp.br/docente/gutz/Curtipot_.html.

Version 3.2, released in December 2006, includes a separate pH_calc module with activity coefficient estimation.

Some 30 thousand copies of CurTiPot 3.1 and 3.2. were downloaded to over 100 countries from the author's site during the first 20 months; 200 other software sites distribute the program.

CurTiPot was written almost during weekends and holidays, in São Paulo and, sometimes, at the beach: http://maps.google.com/maps?hl=en&ie=UTF8&om=1&z=15&ll=-23.822097,-45.464902&spn=0.020101,0.028753&t=h

HistoryThis freeware is a courtesy of

» generation of curves with equally spaced data in pH or volume

» simulation of experimental random errors in pH and volume

» overlay of multiple simulated curves for comparison






Please report errors and incompatibilities of Curtipot (developed for Excel 9 and 10) to the author;



Some features and uses of CurTiPot (hover on red mark at Q2 to read about the name and origins of the program)

pH calculation of aqueous solutions (>30 species in equilibrium)

Simulation of simple and complex acid-base titration curves - Virtual Titrator

Data analysis of real and simulated curves

Evaluation of curves by interpolation, smoothing and automatic endpoint detection

» determination of concentrations and refinement pKas by non-linear regression

Distribution of species and protonation of bases vs. pH and vs. volume

Configure Microsoft Excel to medium security (Tools/Macro/Security/Security level/Medium), open the curtipot_.xls file and activate the macros

Ionic strength and activity coefficient corrections available only in the pH calc module

Click on the pH_calc tab, at the botton of the page; If you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H21;

Calculate pH; clear all concentrations and check the pH of water; test various solutions with one ore more species of the preloaded acid-base systems;

Switch to the preloaded Simulation of the titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

Find endpoints of your real or simulated curves with Evaluation. There are buttons to load the last titration curve from Simulation;

Play and learn with the Distribution module; enjoy the Graphs before you advance to the less simple but more powerful Regression to fit concentrations and pKas;


Version 2 appeared in 1992. Besides volumetry, it accepts data from titrations with coulometric generation of reactants.


Version 3.0 for Excel is an evolution of the DOS version. A new Regression module is the most significant improvement. It was released in 2006 (in Portuguese).

Version 3.1 was the first translated to English. It was launched at May 1st, 2006, at the site www2.iq.usp.br/docente/gutz/Curtipot_.html.

Version 3.2, released in December 2006, includes a separate pH_calc module with activity coefficient estimation.

Some 30 thousand copies of CurTiPot 3.1 and 3.2. were downloaded to over 100 countries from the author's site during the first 20 months; 200 other software sites distribute the program.







Use the e-mail: [email protected]



(hover on red mark at Q2 to read about the name and origins of the program)

to medium security (Tools/Macro/Security/Security level/Medium), open the curtipot_.xls file and activate the macros

If you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H21;

; clear all concentrations and check the pH of water; test various solutions with one ore more species of the preloaded acid-base systems;

of the titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

. There are buttons to load the last titration curve from Simulation;

before you advance to the less simple but more powerful Regression to fit concentrations and pKas;


Version 2 appeared in 1992. Besides volumetry, it accepts data from titrations with coulometric generation of reactants.


module is the most significant improvement. It was released in 2006 (in Portuguese).

www2.iq.usp.br/docente/gutz/Curtipot_.html.

module with activity coefficient estimation.

3.1 and 3.2. were downloaded to over 100 countries from the author's site during the first 20 months; 200 other software sites distribute the program.


maps?hl=en&ie=UTF8&om=1&z=15&ll=-23.822097,-45.464902&spn=0.020101,0.028753&t=h

pH Calculator

Fill out concentrations; Enter; Click button B18.

Acetic acid Ammonia Citric acid EDTA Alanine

[B]

[HB] 0.061

0.039

0 0 0.1 0 0 0

0 0 0.139 0 0 0

0 0 -0.161 0 0 0

Electrolyte Na+ K+ Ca++ Cl- NO3- ClO4-

0.161

0.161 0 0 0 0 0

Charge Balance OK

Results at chemical equilibrium Correction of ionic strength effects

Ionic strength 0.2220 0.743 9.865E-08 pH


[B] 1.221E-06

[HB] 6.100E-02

3.900E-02

4.018E-07

0.000E+00 0.000E+00 1.000E-01 0.000E+00 0.000E+00 0.000E+00

at pH = 7.006 and p[H] =


% B 99.58 0.43 0.00 94.73 0.53 0.19

% HB 0.42 99.57 61.00 5.26 96.69 99.81

39.00 0.01 2.78 0.00

0.00 0.00 0.00

0.00

0.00

0.00

Solution composition - reagents added, in mol/L

Acid / BaseProtonation

Phosphoric acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

S[H]

SziCi

Ci (mol/L)

ziCi

g H+ a H+

Equilibrium concentration of species, in mol/LAcid / Base protonation

Phosphoric acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

Species distribution (fractional composition, in %)Acid / Base protonation

Phosphoric acid

% H2B

% H3B

% H4B

% H5B

% H6B

G1

pH Calculator - Fast start: This module calculates the pH of simple or complex aqueous solutions, with correction for ionic strength effect based on the Davies equation. Here are some exercises to become familiar with the main resources: - Click on the button "Calculate pH ..." (cell B18) and check cell H21 for the solution of the default acid-base chemical equilibrium problem: a buffer mixture of NaH2PO4 and Na2HPO4. - Change the default concentrations in cells D5 and D6; press Enter; click Calculate pH. - Write the value of D5 in D4 and clear D5; write D6 in D7 and clear D6; click Calculate pH. - Change pKa2 (M6), e.g. 7.2 to 9.2, Enter, Calculate pH. If you haven't learned what acid-base dissociation constants are, or whatfor acids are titrated, perhaps you should go through a simple tutorial first, e.g., a flash animated one: http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch16.htm - Check the pH of water at 25 ºC: Delete D4 and D7, Enter, Calculate pH. - Compare the values of pH, p[H] and "pH" in line 21; have a look at other results in lines 21 to 57 (you don't need to understand all these figures now - some are for advanced users). - formulate multicomponent mixtures and solve them instantly. - load other acid/base systems clicking on K2, selecting another acid and clicking on J2. This acid-base pH calculator first appeared as a separated module in the 3.2 Excel version of CurTiPot, an evolution of the 1.0 Turbo Basic version launched in 1992. Prof. Dr. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

A3

Gutz: Name of the acid or base (of the conjugated acid). To change it, write in cell K3 or load a different system from the Database

B3

Gutz: See comment in cell M1 on how to change acids ans bases.

A4

Gutz: Leave blank/fill out with the concentration (mol/L) of fully deprotonated base (of a conjugated acid) added to the solution, e.g.: [Na2CO3], [Na3PO4], [NH4OH], [pyridine] or [Na4EDTA]

A5

Gutz: Leave blank/fill out with the concentration (mol/L) of monoprotonated base (or acid, HB) added to the solution, e.g.: [Acetic acid], [NH4+], [pyridonium], [NaHCO3] or [Na2HPO4]

A6

Gutz: Leave blank/fill out with the concentration (mol/L) of biprotonated base (H2B) added to the solution, e.g.: [H2CO3], [H2Na2EDTA] or [NaH2PO4]

A7

Gutz:d Leave blank/fill out with the concentration (mol/L) of triprotonated base (H3B) added to the solution, e.g.: [H3PO4]

A11

Gutz: Sum of concentrations of all forms of the base B introduced in the solution: [HB] + [H2B] + [H3B] + ...

B11

Gutz: Do NOT write in this cell or any other one of the same color, not to corrupt the equations.

A12

Gutz: Maximum H+ concentration available from the full deprotonation of all forms of HiB used in the formulation of the solution: [HB] + 2[H2B] + 3[H3B] + ...

A13

Gutz: Cizi = ion concentration times charge of the ion (e.g., 2[Ca2+]).

A14

Gutz: Fill out with the concentration of counter-ions of the salts of acids and bases, as well as other electrolytes added to the solution (e.g., to adjust ionic strength). This data is not essential but it will reduce the uncertainty of the estimation of activity coefficients and pH. Note: sulfate, a common divalent anion, is only fully dissociated a pH>4 because of its first protonation constant of 100 (= pKa2 2 of sulfuric acid). To deal more accurately with this acid/base system, load sulfuric acid from the Database (instead of defining it as electrolyte).

B14

Gutz: Name of the ion (strong electrolyte). To change it, write in cell K11.

A15

Gutz: Para adicionar NH4Cl 0,1 mol/L à solução, lançar 0,1 nesta linha, coluna do Cl- e 0,1 na linha 5, coluna do hidróxido de amônio. NaCl 0,1 mol/L, lançar 0,1 em Na+ e 0,1 em Cl-.

A16

Gutz: Cizi = ion concentration times charge of the ion (e.g., 2[Ca2+]).

A17

Gutz: Electroneutrality is not a must to calculate the pH (by clicking B18). However, there will be some extra uncertainty in the results due to incorrect ionic strength calculation.

G19

Gutz: Definition of pH, see: http://www.iupac.org/goldbook/P04524.pdf Activity coefficient dependence from I, see: http://www.beloit.edu/~chem/Chem220/activity/index.html

A21

Gutz: The amount of electrostatic interaction between ions in solution is related to the ionic strength, I, a parameter used in the Debye Hückel equation for estimation of activity coefficients and extended versions of this equation, suitable for work at I>0.01 mol/L, where the effective hydrated ion size of the species also becomes relevant. As a general trend, the activity coefficient decreases with the increase of I (due to ion-ion interactions like the formation of ion pairs) down to a minimum in the region of I = 0.3 to 0.7 mol/L. At such high values of I, the association constants of each with all other major ions need to be feed to the equations or empirically fitted, to reduce uncertainty in estimates. The Davies equation, based on the average behavior of the ions and used here to deal with in complex mixtures for witch such constants are not readily available, renders estimates with greater uncertainty.

C21

Gutz: This and other activity coefficientes are (uncertain) estimates made with the Davies equation. Read more in cells A21 and K15.

E21

Gutz: This and other activity coefficientes are (uncertain) estimates made with the Davies equation. Read more in cells A21 and K15.

G21

Gutz: This is an estimate of the pH (see definition in http://www.iupac.org/goldbook/P04524.pdf ) that would be measured by a pH meter for a solution with the given composition, at 25ºC (or another temperature specified for the pKa values). The potential of potentiometric sensors (like the glass electrode) changes linearly with the inverse of the logarithm of the activity of hydrated H+ ions, not the concentration (expressed as p[H] in cell L21). The uncertainty of estimated pH values is never lower than the uncertainty of the pKa values in use, and it grows with the ionic strength, I, due to deficiencies of the Davies equation (more about in cells A21 and K15). It can exceed 0.1 pH unit for I>0.05, specially in solutions with highly charged ions (like PO43-).

100.00 100.00 100.00 100.00 100.00 100.00

at pH = 7.006 and I =


0.743 1.000 0.069 0.069 0.009 0.743

1.000 0.743 0.304 0.304 0.069 1.000

0.743 0.743 0.304 0.743

1.000 1.000 0.743

1.000

0.743

0.304

Eletrolyte Na+ K+ Ca++ Cl- NO3- ClO4-

0.743 0.743 0.304 0.743 0.743 0.743

at pH = 7.006

Acid / Base Acetic acid Ammonia Citric acid EDTA Alanine

h 0.004 0.996 1.390 0.053 1.022 0.998

% S[HiB]

Activity coefficient (g) of speciesAcid / Base protonation

Phosphoric acid

g B

g HB

g H2B

g H3B

g H4B

g H5B

g H6B

gi

Average protonation (h) of (conjugated) bases

Phosphoric acid

C42

Gutz: These activity coefficients were estimated with the Davies equation and their uncertainty increases with the ionic strength. More information in cells A21 e K15.

read comment

Fill out concentrations; Enter; Click button B18. 1 2 8

Acid / Base Acetic acid Ammonia Phosphoric acid

Charge of B -1 0 -3

4.757 9.244 2.148

7.199

12.350

SS

0 1.000E-01 Electrolyte

0 1.390E-01 Ion charge 1 1 2

0 -0.161 pKw 13.997

- Davies equation parameters

for activity coefficient estimation D o n o t c h a n g e

0 0.161 A 0.509 C h a n g e c r i t e r i o u s l y

0 b 0.300 Fill out, change or leave blank

7.006 pOH 6.991 p[H] 6.877 p[OH]

Stepwise apparent constants recalculated for I =

Acid / Base Acetic acid Ammonia Phosphoric acid

1.79E-07 Charge of B -1 0 -3

4.499 9.244 11.575

6.683

1.37E-07 1.8898

SS

0.000E+00 1.000E-01 pK'w 13.74

6.877

0.10

85.77

14.14

pKas of the acids and bases in the solution

Carbonic acid

pKa1

pKa2

pKa3

pKa4

pKa5

pKa6

Na+ K+ Ca++

'-log of ion activities '-log of ion concentrations

Carbonic acid

[H+]

pK'an = logK'p1

[OH-] pK'an-1 = logK'p2

pK'an-2 = logK'p3

pK'an-3 = logK'p4

pK'an-4 = logK'p5

pK'an-5 = logK'p6

Carbonic acid

M1

Gutz: Selecting/editing names, charges ans pKas. Options: a) Write directly in the cells K3 to Q10 and R3 to T6; b) Click on names in line 2, slide along the list, click on another name; finally, click on J2 to load the constants from the Database. Frequently used acids missing in the Database should be added to it.

J4

Gutz: Charge of the most deprotonated species of an acid or base in accordance with the highest pKa for the system, e.g., 0 for NH3 or pyridine -1 for acetate/acetic acid -2 for carbonate//carbonic acid -3 for phosphate///phosphoric acid -4 for EDTA

J5

Gutz: Options: a) pKa1 , -logarithm of the dissociation constant of a monoprotic acid or first constant for a polyprotic system. b) logKpi, logarithm of the protonation constant of a (conjugated) base, with i=1 for a monoprotonable base and i= n (most deprotonated species) for polyprotic systems (more about at U5); c) pKw - pKbi, for -log of the dissociation constant of a base, with i=1 for a monoprotonable base and i= n (most deprotonated species) for polyprotonable base. Numerically, values of a, b e c are taken as similar.

J6

Gutz: Options: a) pKa2 , -log of the 2nd dissociation constant of a biprotic or polyprotic acid; b) logKpi, log of the first protonation constant of a biprotonable (conjugated) base or i=n-1 for a system with n protonations; c) pKw - pKbi, with i=1 for a biprotonable base or i=n-1 por a base with n protonations; for a monoprotonable base, leave blank.

I11

Gutz: Total concentration of each base (regardless of the protonation level of the added component) in columns B to H; grand total in column I.

J11

Gutz: Write the name (or formula) of ions of strong electrolytes (not involved in protonation equilibria), like counter-ions of salts of weak acids. This is required for ionic strength calculation and activity coefficient estimation.

I12

Gutz: Maximum concentration of H+ that could possibly be dissociated from all the components added to the solution.

J12

Gutz: Fill out with the charge of the ion.

I13

Gutz: Summation of Cizi of all acidic and basic ingredients; if not zero, it shoud be neutralized by counterions in the electrolyte.

J13

Gutz: The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25ºC, the accepted value is 13.997 (or 14.00). The program corrects for I variation using the Davies eq. and displays the resulting value in K31.

K15

Gutz: CurTiPot recalculates apparent equilibrium constants at the ionic strength, I, of the solution from thermodynamic constants (I=0) by estimating activity coefficients with help of the Davies equation. The accuracy is good for I<0.05, acceptable for I<0.2 and poor for higher values of I. There is no rigorous means to calculate activity coefficients of individual ions, although there are many equations pursuing the reduction of the uncertainty of the estimates by taking in accountt individual effective ion size parameters and specific ion-ion interactions and/or introducing empirical coefficients fitted to real data. Such parameters are readily available only for the most common inorganic and organic ions, limiting their application range in comparision with the simple and general Davies eq. A compilation of over twenty equations with references to original work is available in the file Ionic St_effects.pdf contained in the package http://www.iupac.org/projects/2000/Aq_Solutions.zip For calculations involving seawater (e.g. ionic strength at different salinities), see: http://ioc.unesco.org/oceanteacher/oceanteacher2/02_InfTchSciCmm/01_CmpTch/05_ocsoft/01_toolbox/OcCalc/OcCalc.htm

I16

Gutz: Summation of Cizi of all electrolytes

J16

Gutz: A and b are parameters of the Davies equation, used for activity coefficient estimation. They depend on temperature, dielectric constant, electrolyte, etc. The recommended values for water at 25ºC are: A=0.509; b=0.300. The Davies eq. does not require the size of different hydrated ions but, to some degree, the A and b parameters may be empirically adjusted to more closely describe a given electrolyte. For example: For NaCl + HCl solutions, A=0.43 and b=0.49 conducts to gH+ values in excellent agreement with those provided (up to 0.5 mol/kg) in http://www.iupac.org/projects/2000/Aq_Solutions.zip on base of more complete equations fitted to experimental data. For phosphate solutions, A=0.51 and b=0.20 seems appropriate at pHs above neutrality.

I17

Gutz: Charge Balance of all Cizi of ingredients added (before equilibrium); if not zero, it shoud be neutralized by adding counterions.

J17

Gutz: Read comment in cell J6 (above) and K15.

K21

Gutz: p[H] = -log[H+], calculated with the apparent pKas (cells K25 to Q30), while "pH" (cell O21) is obtained with the thermodinamic pKas, valid only for I=0 (see comment in cell K15), and pH (cell H21) uses estimated activities to como closer to the measurable pH. Although potentiometric sensors respond to activity of species (see comment in G21), it is possible – but not usual – to calibrate a pH meter (a high impedance voltmeter) with H+ concentration standards at a given value of I (to keep the activity coefficients constant) and measure free hydrated proton concentrations directly a this I. Some other techniques like spectrophotometry respond to concentration and may be used to indirectly measure p[H] (e.g., optodes).

I31

Gutz: Summation of the concentrations of all H+ potentially dissociable from reagents available in the solution, coined CHtotal. to be equaled with CHcalc obtained by iteractively changing fitting the pH value.

100.00

0.2220

0.304

0.743

1.000

-

1.140

Carbonic acid

Carbonic acid

Click on K2 to Q2; select acids/bases; click on J2; read M1

4 5 17 3 pKa(n) = -log Kd(HB-->B) = log Kp(1)

Citric acid EDTA Alanine Carbonic acid Acid / Base

-3 -4 -1 -2 Charge of B

3.128 0.000 2.348 6.352

4.761 1.500 9.867 10.329

6.396 2.000

2.680

6.110

10.170

Cl- - Kw

-1 -1 -1

Color coding

D o n o t c h a n g e

C h a n g e c r i t e r i o u s l y

Fill out, change or leave blank

No ion-ion interaction corrections (unity activity coefficients)

6.862 "p[H]" 7.393 "p[OH]" 6.604

Stepwise apparent constants recalculated for I = 0.22200

Citric acid EDTA Alanine Carbonic acid Acid / Base

-3 -4 -1 -2 Charge of B

5.621 9.137 9.609 9.813

4.245 5.335 2.348 6.094

2.8698 2.1635

1.7418

1.5000000605802

0.2582347081289

K'w

Overall protonation constants = bp = SKp (calculated by the program)

bp1

bp2

bp3

bp4

bp5

bp6

NO3- ClO4

-

b'p1

b'p2

b'p3

b'p4

b'p5

b'p6

R5

Gutz: The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up to n, the maximum number of protons accepted by a (conjugated) base (same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 (complete references in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.

O21

Gutz: "pH" is the value found in calculations where concentrations are used in the law of mass action expressions supplied with thermodynamic equilibrium constants – as usual in high school or introductory general chemistry classes and textbooks. Comparison with pH (cell H21) and p[H] (cell K21) reveals that errors are small only for diluted solutions, where ion-ion interactions occur less significant and activities depart less from concentrations (see comments in cells A21 and K15).

pKa(n) = -log Kd(HB-->B) = log Kp(1)


-1 0 -3 -3 -4 -1

5.715E+04 1.754E+09 2.239E+12 2.489E+06 1.479E+10 7.362E+09

3.540E+19 1.435E+11 1.905E+16 1.641E+12

4.977E+21 1.928E+14 9.120E+18

9.120E+20

2.884E+22

2.884E+22

1.01E-14

Overall apparent protonation constants recalculated for I = 0.22200


-1 0 -3 -3 -4 -1

3.15E+04 1.75E+09 3.76E+11 4.18E+05 1.37E+09 4.06E+09

1.81E+18 7.34E+09 2.97E+14 9.05E+11

1.40E+20 5.44E+12 4.32E+16

2.39E+18

7.54E+19

1.37E+20

1.82E-14


Phosphoric acid

Phosphoric acid

Click on J2 to use these pKas in the pH calculation

Carbonic acid Acid / Base Acetic acid Ammonia Citric acid

-2 Charge of B -1 0 -3 -3

2.133E+10 4.757 9.244 2.148 3.128

4.797E+16 7.199 4.761

12.350 6.396

Carbonic acid

-2

6.49E+09

8.06E+15

pKas loaded from the Database

Phosphoric acid

pKa1 = logKpn

pKa2 = logKpn-1

pKa3 = logKpn-2

pKa4 = logKpn-3

pKa5 = logKpn-4

pKa6 = logKpn-5

Z2

Gutz: The pKas shown here are copied automatically from the Database by changing K2 to Q2. See U5 to understand why pKa1 = -logKpn

Z5

Gutz: See R5 to understand the conversion of pKa in logKp

Click on J2 to use these pKas in the pH calculation

EDTA Alanine Carbonic acid

-4 -1 -2

0.000 2.348 6.352

1.500 9.867 10.329

2.000

2.680

6.110

10.170

Virtual Titrator – Simulation of curves

EDTA Acetic acid Ammonia HCl

[B]

[HB]

0.05

0 0.05 0 0 0 0

0 0.15 0 0 0 0

Titrant Strong ACID Strong BASE Carbonic ac.

[B] 0.1 Titrand Water

[HB] Dispensed addedSS 20 0

0 0.1 0 1.00E-01 Titrant max.

0 0 0 0.00E+00 50.00 50

initial "pH" 1.806

Data ID on curves

Copying curves

Resizing axis

Other graphics

Data analysis

Vadd "pH" Vadd "pH" [H] CHtot = Dill. factor

Titrand (sample) and titrant (standard) composition (concentrations in mol/L)

TitrandSpecies

Phosphoric acid

L-Glutamic acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

S[H]

Volumes of titrand and titrant (in mL)

[H2B]

S[HiB] Nº of titrant additions

S[H]

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0 Titrations of hydrochloric, phosphoric and glutamic acids (20 mL, 0.05 mol/L, with 0.1 mol/L NaOH)

Volume of titrant (mL)

pH

G1

"Hands on" the "VIRTUAL TITRATOR": - Click on the button "Clear ret(ained) curves" (cell A32) - all but the last simulated curve will disappear; - click on the button "Titrate with constant volume additions" (A28) - the default tiration of 20 mL of 0.07 mol/L H3PO4 with 0.1 mol/L NaOH will be generated with 50 additions of 1 ml of titrant; - click on "Titrate with constant pH increments" (A24) - notice the difference in data distribution; - click on "Retain curve" (A30); - change the H3PO4 concentration in (C7), press Enter; - titrate again and retain the curve; - change pKa2 (cell M6) from 7.2 to 9.2 (Enter) and titrate; If you haven't learned what acid-base dissociation constants are, or whatfor acids are titrated, perhaps you should go through a simple tutorial first, e.g., a flash animated one: http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch16.htm - click on K2 or L2, select another acid; click on J2; ... - observe the effect of CO2 absorption by NaOH solution by writing 0.001 in D16; - add other components to the mixture and titrate; - add random experimental error to the curve fillng values in cells J17 and J18 (e.g., 0.03 and 0.1); - titrate a phosphate buffer of Na2HPO4 + NaH2PO4 with strong base, retain the curve and titrate it with strong acid; - user your creativity... Remark: This version of the CurTiPot's Virtual Titrator calculates "pH" or p[H] (=-log of the concentration of H+) instead of pH (=-log activity of H+), because it does not (yet) correct for the effect of ionic strength, I, on activity coefficients, taken as unity (see cell A20 or the pH_calc module for more information). This does not however change the volume of titrant spent to reach the inflections, nor does it modify the general shape of the curves. Refer to the pH_calc module to calculate the pH of any solution with estimated activity coefficents. Use the apparent pKas for a given I, computed in pH_calc pasted in cells K3 to Q10 of Simulation to obtain titration curves with pH values closer to reality. Copyright: This acid-base titration curve simulator is an expanded Excel version of the original Turbo Basic for DOS program CURTIPOT launched by the Author in 1992. Prof. Dr. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

A3

Gutz: The titrand is the sample to be evaluated by titration with a strong acid or strong base. Tipically, 5 to 25 mL of titrand (cell F16) are carefully measured and placed in a beaker, a combined glass electrode (connected to a pH meter) and a magnetic stirrer bar are introduced and water is added till the electrode is covered (cell G16). Titration is carried out by adding small aliquots of titrant (usually with a buret or motor driven syringe) and registering the pH afterstabilization of the reading.

B3


A4

Gutz: Leave blank/fill out with the concentration (mol/L) of fully deprotonated base (of a conjugated acid) to be considered in the simulation, e.g.: [Na2CO3], [Na3PO4], [NH4OH], [pyridine] or [Na4EDTA]

A5

Gutz: Leave blank/fill out with the concentration (mol/L) of monoprotonated base (or acid, HB) to be considered in the simulation, e.g.: [Acetic acid], [NH4+], [pyridonium], [NaHCO3] or [Na2HPO4]

A6

Gutz: Leave blank/fill out with the concentration (mol/L) of biprotonated base (H2B) to be considered in the simulation, e.g.: [H2CO3], [H2Na2EDTA] or [NaH2PO4]

A7

Gutz:d Leave blank/fill out with the concentration (mol/L) of triprotonated base (H3B) to be considered in the simulation, e.g.: [H3PO4]

A11

Gutz: Sum of concentrations of all forms of base B introduced in the titrand (e.g., [HB] + [H2B] + [H3B])

B11


A12

Gutz: Maximum H+ concentration available from full deprotonation of all forms of HiB used in the formulation of the titrand (e.g., [HB] + 2[H2B] + 3[H3B])

D13

Gutz: CO2 é absorvido por qualquer titulante ou titulado exposto ao ar; em soluções alcalinas, ocorre acumulação na forma de carbonato; daí ser importante simular o efeito da sua interferência, seja no titulante, seja no titulado, ou em ambos.

B14

Gutz: Leave blank - this cell corresponds to the conjugated base of the acid, e.g., Cl- or NO3-.

C14

Gutz: Leave blank/fill with de concentration of strong monoprotonable base used as titrant e.g., NaOH, KOH (or twice the concentration of Ca(OH)2)

D14

Gutz: Leave blank/fill out with de concentration of carbonate used as titrant To simulate the absorption of CO2 in an alkaline titrant, leave blank and fill cell D16

B15

Gutz: Leave blank/fill with de concentration of strong monoprotic acid used as titrant e.g., HCl. For weak or diprotic acids like H2SO4 change charge and pKas first, at cells R4 to R6.

C15

Gutz: Leave blank - as a rule, this cell corresponds to the protonated of OH- , H2O2, handled as solvent. However, if a different acid/base is system is specified in column S, [HB] may be required.

D15

Gutz: Leave blank/fill out with de concentration of bicarbonate, if used as titrant. To simulate the absorption of CO2 from the air by an alkaline titrant, leave blank and fill H2CO3 (cell D16)

B16

Gutz: Leave blank Fill out just in case you have replaced the base, its charge and pKas in cells S4 to S6.

C16

Gutz: Leave blank Fill out just in case you have replaced the base, its charge and pKas in cells S4 to S6.

D16

Gutz: Leave blank/fill out to simulate the absorption of CO2 by an alkaline titrant (effect visible on the curve for 1% or more of [H2CO3] relative to the titrant concentration)

F16

Gutz: Volume of the aliquot of titrand (with the composition given above) to be titrated

G16

Gutz: Water is frequently added to the sample until the glass electrode bulb and reference electrode junction are covered by the solution. The (undesirable) effect of dillution on the simulated curve may be best appreciated by exagerating this volume, retaining the curve and repeating the titration without added water.

A17

Gutz: Sum of concentrations of all forms of base B introduced in the titrand (e.g., [HB] + [H2B] + [H3B])

A18

Gutz: Maximum H+ concentration available from full deprotonation of all forms of HiB used in the formulation of the titrand (e.g., [HB] + 2[H2B] + 3[H3B])

F18

Gutz: Maximum volume of titrant to be added up to the end of the titration (may be less or equal to the capacity of the buret ).

G18

Gutz: Total number of additions of the titrant from the buret (max.: 120; typical: 30 or 50). You can choose constant volume additions (A24) or constant pH increment (A27).

A20

Gutz: Click on button at A22 to calculate the "pH" of the starting solution, before addition of any titrant (but after dillution, if G16 not zero). Refer to the spreadsheet pH_calc to calculate the pH (instead of "pH") of the same solution and for distiction between pH, p[H] and "pH". These values depart increasingly as the electrolyte concentration (more precisely, the ionic strenght) of a solution increases, due to ion-ion interactions. pH = -log aH+ where aH+ is the proton activity (concentration x activity coefficient) This Simulation module calculates p[H], when pK'as (apparent constants at the I of the solution) are provided, or "pH" when thermodynamic constants (from the Database) are used instead. p[H] = -log [H+] , where [H+] is the hydrated proton concentration, in mol/L.

B34

Gutz: Hover the mouse on a curve and point any data point to readout its ID and coordinates. To add labels to your graphics, activate the drawing tools of Excel and insert text boxes.

B35

Gutz: To copy graphics with simulated curves and paste them into other documents (e.g.: Word or Excel without links to the original: - Fill out the header of the figure (optional) - Click in the box of the figure near the margins, to select it - Repeat the last simulation of a curve - Press Ctrl+C and wait for processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

B36

Gutz: Click twice on the volume or pH scale to redifine it. Use Ctrl+Z (as many times as needed) to undo scale expansion

B37

Gutz: - Use the Graphics spreadsheet to plot derivatives by the DpH/DV aproximation and to overlay curves. - Use Evaluation to generate first and second derivative curves with interpolation and smoothig and to accurately locate inflection points of real and simulated titration curves. - Use Distribution to obtain de fractional composition and the mean protonation level of the bases during the titration as well as in function of pH.

B38

Gutz: - Use Evaluation to accurately evaluate well defined inflection points on real and simulated titration curves, assisted by cubic splines smoothing and interpolation - Use Regression to refine the concentrations of analytes and/or pK values of real or simulated titration curves by nonlinear multiparametric regression and to analyse complex curves, with hidden inflections (some learning required) Data transfer from Simulation to Evaluation or Regression: - Copy data of columns A and B from line 41 on - When evaluating the effect of dispersion (simulation of experimental errors), copy columns A and D instead (select column A, press Ctrl and select column D)

A39

Gutz: Data transfer from Simulation to Evaluation or Regression: - Copy data of columns A and B from line 41 on - When evaluating the effect of dispersion (simulation of experimental errors), copy columns A and D instead (select column A, press Ctrl and select column D) - Paste data in columns A and B of the destination spreadsheet

B39

Gutz: This version of the CurTiPot's Virtual Titrator calculates p[H] (=-log of the concentration of H+) instead of pH (=-log activity of H+), because it does not yet correct for the effect of ionic strength, I, on activity coefficients, taken as unity. This does not change the volume of the inflections, nor the general shape of the curves. Refer to the pH_Calc module to calculate the pH and activity coefficents of any solution. The apparent pKas for a given I can be computed in pH_Calc and pasted in cells K3 to Q10 of this spreadsheet to obtain titration curves closer to pH.

C39

Gutz: Do NOT use this column for Evaluation or Regression. Values displayed to ilustrate the simulated dispersion in the volume dispensing by the "buret". This column will remain blank when null dispersion is choosen in J17 and J18.

D39

Gutz: These pH values with dispersion will be overlayed in the graphic This column will remain blank when null dispersion is choosen in J17 and J18

E39

Gutz: Free hydrated proton concentration (or activity)

F39

Gutz: Total concentration of H+ required to satisfy all protonation equilibria, using the general equation, the concentration s of line 11 and the pKas given or under refinement.

G39

Gutz: Dillution factor of the titrant when added to the sample (+water). For example, when the added titrant equals the volume of sample (+water), the factor is 0.5

(mL) simulated CHcalc

0.000 1.806 1.563E-02 1.500E-01 1.000E+002.157 2.020 9.540E-03 1.354E-01 9.026E-014.096 2.235 5.822E-03 1.245E-01 8.300E-015.754 2.449 3.553E-03 1.165E-01 7.766E-017.077 2.664 2.168E-03 1.108E-01 7.386E-018.061 2.878 1.323E-03 1.069E-01 7.127E-018.749 3.093 8.073E-04 1.044E-01 6.957E-019.210 3.307 4.927E-04 1.027E-01 6.847E-019.508 3.522 3.006E-04 1.017E-01 6.778E-019.697 3.736 1.835E-04 1.010E-01 6.735E-019.817 3.951 1.120E-04 1.006E-01 6.708E-019.894 4.165 6.832E-05 1.004E-01 6.690E-019.944 4.380 4.169E-05 1.002E-01 6.679E-019.982 4.594 2.544E-05 1.001E-01 6.671E-01

10.014 4.809 1.552E-05 9.995E-02 6.664E-0110.050 5.023 9.474E-06 9.983E-02 6.656E-0110.098 5.238 5.781E-06 9.967E-02 6.645E-0110.170 5.452 3.528E-06 9.944E-02 6.629E-0110.282 5.667 2.153E-06 9.907E-02 6.605E-0110.457 5.881 1.314E-06 9.850E-02 6.567E-0110.730 6.096 8.017E-07 9.763E-02 6.508E-0111.144 6.310 4.892E-07 9.633E-02 6.422E-0111.748 6.525 2.985E-07 9.450E-02 6.300E-0112.577 6.739 1.822E-07 9.209E-02 6.139E-0113.626 6.954 1.112E-07 8.922E-02 5.948E-0114.824 7.168 6.784E-08 8.615E-02 5.743E-0116.044 7.383 4.140E-08 8.323E-02 5.549E-0117.146 7.598 2.526E-08 8.076E-02 5.384E-0118.041 7.812 1.542E-08 7.886E-02 5.258E-0118.706 8.027 9.408E-09 7.751E-02 5.167E-0119.169 8.241 5.741E-09 7.659E-02 5.106E-0119.478 8.456 3.503E-09 7.599E-02 5.066E-0119.677 8.670 2.138E-09 7.561E-02 5.041E-0119.804 8.885 1.305E-09 7.537E-02 5.025E-0119.886 9.099 7.961E-10 7.521E-02 5.014E-0119.941 9.314 4.858E-10 7.511E-02 5.007E-0119.982 9.528 2.965E-10 7.503E-02 5.002E-0120.018 9.743 1.809E-10 7.497E-02 4.998E-0120.059 9.957 1.104E-10 7.489E-02 4.993E-0120.115 10.172 6.737E-11 7.478E-02 4.986E-0120.200 10.386 4.111E-11 7.463E-02 4.975E-0120.333 10.601 2.509E-11 7.438E-02 4.959E-0120.548 10.815 1.531E-11 7.399E-02 4.932E-0120.896 11.030 9.342E-12 7.336E-02 4.890E-0121.459 11.244 5.701E-12 7.236E-02 4.824E-0122.365 11.459 3.479E-12 7.081E-02 4.721E-0123.818 11.673 2.123E-12 6.846E-02 4.564E-0126.155 11.888 1.296E-12 6.500E-02 4.333E-0129.983 12.102 7.906E-13 6.002E-02 4.001E-0136.644 12.317 4.824E-13 5.296E-02 3.531E-0150.000 12.531 2.944E-13 4.286E-02 2.857E-01

with "error" (do not use)

simulated with "error"

Titrand (sample)

read instructions

5 8 98

Acid / Base EDTA Phosphoric acid L-Glutamic acid

Charge of B -4 -3 -1

0.000 2.148 2.230

1.500 7.199 4.420

2.000 12.350 9.950

2.680

6.110SS 10.170

0 5.000E-02 pKw 13.997

0 1.500E-01

Sum

(initial vol.)

20.00 Titration speed

S pH= 0.000 Slower 0S Vol= 0.000 Faster delay (s)

Dill. Factor h1 h2 h3 h4 h5


Carbonic acid

pKa1

pKa2

pKa3

pKa4

pKa5

pKa6

of titrand and titrant (in mL)

Dispersion simulation

Nº of titrant additions

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0 Titrations of hydrochloric, phosphoric and glutamic acids (20 mL, 0.05 mol/L, with 0.1 mol/L NaOH)

Volume of titrant (mL)

pH

M1

Gutz: Selecting/editing names, charges ans pKas. Options: a) Write directly in the cells K3 to Q10 and R3 to T6; b) Click on names in line 2, slide along the list, click on another name; finally, click on J2 to load the constants from the Database. Frequently used acids missing in the Database should be added to it.

J4


J5


J6


I11

Gutz: Total concentration of each base (regardless of the protonation level of the added component) in columns B to H; grand total in column I.

J11

Gutz: The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25ºC, the accepted value is 13.997 (or 14.00). Values corrected for I can be calculated with module pH_calc.

I12

Gutz: Maximum concentration of H+ that could possibly be dissociated from all the components added to the solution.

H16

Gutz: Total volume before titration (F16+G16)

J17

Gutz: Simulação opcional de erros aleatórios nas medidas de pH (instabilidade da leitura) especificados como desvio padrão aproximado dos resíduos para a curva completa. Por exemplo, 0,03

L17

Gutz: Keep delay = 0 for titration at maximum speed (dictated by the computer performance) Choose delay > 0 to pause between additions of titrant, resembling the time required to wait for pH measurements to sabilize in a real titrations. Press Escape during a titration to ignore the delay, proceeding at max. speed.

J18

Gutz: Simulação opcional de erros aleatórios nas medidas de volume (p.ex., erro na leitura do menisco da bureta), expressos como desvio padrão dos erros para a curva completa Por exemplo, 0,05

H39

Gutz: Dillution factor of the sample by optional addition of water (at the beginning) and addition of titrant during the experiment

I39

Gutz: Número médio de prótons associados à base 1 no pH dado. Para HiB, h médio seria o valor fracionário de i que reflete a média das concentrações de H+ não dissociado em dado pH.

EDTA Phosphoric acid L-Glutamic acid Acetic acid Ammonia

0.000E+00 2.68739.735E-02 2.57291.700E-01 2.45012.234E-01 2.33312.614E-01 2.23362.873E-01 2.15683.043E-01 2.10193.153E-01 2.06473.222E-01 2.04033.265E-01 2.02483.292E-01 2.01493.310E-01 2.00863.321E-01 2.00433.329E-01 2.00113.336E-01 1.99813.344E-01 1.99473.355E-01 1.99003.371E-01 1.98293.395E-01 1.97183.433E-01 1.95433.492E-01 1.92703.578E-01 1.88563.700E-01 1.82523.861E-01 1.74234.052E-01 1.63744.257E-01 1.51764.451E-01 1.39564.616E-01 1.28544.742E-01 1.19604.833E-01 1.12954.894E-01 1.08314.934E-01 1.05244.959E-01 1.03254.975E-01 1.01994.986E-01 1.01194.993E-01 1.00674.998E-01 1.00325.002E-01 1.00045.007E-01 0.99775.014E-01 0.99455.025E-01 0.98995.041E-01 0.98295.068E-01 0.97195.110E-01 0.95455.176E-01 0.92745.279E-01 0.88635.436E-01 0.82625.667E-01 0.74365.999E-01 0.63906.469E-01 0.51927.143E-01 0.3973

Titrant (buret)

Click on K2 to Q2; select acids/bases; click on J2; read M1

1 2 6 3

Acetic acid Ammonia HCl Carbonic acid Strong ACID

-1 0 -1 -2 -1

4.757 9.244 -7.000 6.352 -6

10.329

Color coding




h6 h7 h1 titrant h2 titrant h3 titrant

R3

Gutz: Strong acids like HCl ou HClO4 have negative pKas, possibly -6 or lower. For a diprotic titrant like H2SO4, use pKa1 = -6 e pKa2 = 1,8. Do not specify systems with more than 2 pKas here.

HCl Carbonic acidStrong ACID Strong BASE Carbonic ac.

1.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99990.99980.99960.9994

Titrant Titrand

Strong BASE Carbonic ac. Acid / Base EDTA

-1 -2 Charge of B -4 -3 -1

15.745 6.352 1.479E+10 2.239E+12 8.913E+09

10.329 1.905E+16 3.540E+19 2.344E+14

9.120E+18 4.977E+21 3.981E+16

9.120E+20

2.884E+22

2.884E+22

Kw 1.007E-14


Phosphoric acid

L-Glutamic acid

bp1

bp2

bp3

bp4

bp5

bp6

S2

Gutz: The titrant may contain up to three diprotic reagents (other than the default ones). Names and constants must be changed manually.

S3

Gutz: The accepted value of the pKa (=log Kp) of the strong base OH- is 15,745 at 25ºC and infinite dilution. As I increases, the activity coefficient of OH- decreases (as can be checked with module pH_calc), and more specific interaction can occur with cations, so that lower values are sometimes mentioned in the literature (see references in the Database for details). Any other mono or biprotonable acid or base can be used instead of OH-

T3

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. But any othe mono- or biprotic system can be specified here. The pKa1 from the Database for for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa1 of 3.58 is found.

U5

Gutz: The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up to n, the maximum number of protons accepted by a (conjugated) base (same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 (complete references in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.

pKa(n) = -log Kd(HB-->B) = log Kp(1)

Titrant

Acetic acid Ammonia HCl Carbonic acid Strong ACID Strong BASE

-1 0 -1 -2 -1 -1

5.715E+04 1.754E+09 1.000E-07 2.133E+10 1.000E-06 5.559E+15

4.797E+16

SKp (calculated by the program)

Click on J2 to use these pKas in the Simulation

Carbonic ac. Acid / Base EDTA Acetic acid

-2 Charge of B -4 -3 -1 -1

2.133E+10 0.000 2.148 2.230 4.757

4.797E+16 1.500 7.199 4.420

2.000 12.350 9.950

2.680

6.110

10.170


Titrand

Phosphoric acid

L-Glutamic acid

pKa1 = logKpn

pKa2 = logKpn-1

pKa3 = logKpn-2

pKa4 = logKpn-3

pKa5 = logKpn-4

pKa6 = logKpn-5

AF2


AF5

Gutz: See U5 to understand why pKa1 = logKpn

Click on J2 to use these pKas in the Simulation

Ammonia HCl Carbonic acid

0 -1 -2

9.244 -7.000 6.352

10.329

Curvas anteriores retidas

Vol

1

03.1648025.5508217.2044498.2847328.9634679.379517

9.63079.7809579.8703479.9233519.9547199.9732629.9842159.9906839.9945019.9967559.998085

9.998879.9993349.9996099.999772

9.999879.99993

9.99997110

10.0000410.0000810.0001510.0002610.0004510.0007610.0012910.0021910.0037110.0062810.0106510.01805

10.030610.0518810.0880210.1494610.25414

10.433210.7415111.2784812.23258

13.989617.44934

25.257550

Curvas anteriores retidas

pH Vol pH Vol pH Vol pH Vol pH

1 2 2 3 3 4 4 5 5

1.30103 0 1.838538 0 1.301031.530077 2.049407 2.050888 3.165531 1.5301371.759125 3.938869 2.263239 5.551868 1.7592451.988172 5.618284 2.475589 7.205499 1.988352

2.21722 7.032329 2.687939 8.285625 2.217462.446267 8.170884 2.900289 8.964158 2.4465672.675315 9.08299 3.112639 9.380021 2.6756752.904362 9.858687 3.32499 9.631052 2.904782

3.13341 10.60375 3.53734 9.781198 3.133893.362457 11.41871 3.74969 9.870507 3.3629973.591505 12.37769 3.96204 9.923457 3.5921053.820552 13.50223 4.174391 9.954788 3.821212

4.0496 14.74101 4.386741 9.973306 4.050324.278647 15.98032 4.599091 9.984243 4.2794274.507695 17.09362 4.811441 9.990701 4.5085354.736742 17.99712 5.023791 9.994512 4.737642

4.96579 18.67074 5.236142 9.996762 4.966755.194837 19.14162 5.448492 9.99809 5.1958575.423885 19.45613 5.660842 9.998873 5.4249655.652932 19.65993 5.873192 9.999336 5.654072

5.88198 19.78955 6.085542 9.99961 5.883186.111027 19.87128 6.297893 9.999772 6.1122876.340075 19.92293 6.510243 9.99987 6.3413956.569122 19.95629 6.722593 9.999931 6.570502

6.79817 19.97918 6.934943 9.999971 6.799617.027217 19.99705 7.147293 10 7.0287177.256265 20.01421 7.359644 10.00004 7.2578257.485312 20.0348 7.571994 10.00008 7.486932

7.71436 20.06374 7.784344 10.00015 7.716047.943407 20.10787 7.996694 10.00026 7.9451478.172455 20.17736 8.209045 10.00045 8.1742558.401502 20.28762 8.421395 10.00076 8.403362

8.63055 20.46167 8.633745 10.00129 8.632478.859597 20.73226 8.846095 10.00218 8.8615779.088645 21.1421 9.058445 10.0037 9.0906859.317692 21.7385 9.270796 10.00627 9.319792

9.54674 22.55746 9.483146 10.01063 9.54899.775787 23.59709 9.695496 10.01802 9.77800710.00483 24.79377 9.907846 10.03054 10.0071110.23388 26.02813 10.1202 10.0518 10.2362210.46293 27.17152 10.33255 10.0879 10.4653310.69198 28.14247 10.5449 10.14927 10.6944410.92102 28.93161 10.75725 10.25386 10.9235411.15007 29.59039 10.9696 10.43277 11.1526511.37912 30.21046 11.18195 10.74088 11.3817611.60817 30.91664 11.3943 11.27756 11.6108711.83721 31.88401 11.60665 12.23125 11.8399712.06626 33.38986 11.819 13.98773 12.0690812.29531 35.93712 12.03135 17.44677 12.2981912.52436 40.57981 12.2437 25.25432 12.5273

12.7534 50 12.45605 50 12.7564

Vol pH Vol pH Vol pH Vol pH Vol

6 6 7 7 8 8 9 9 10

pH Vol pH Vol pH Vol pH

10 11 11 12 12 13 13

Distribution Diagrams and Protonation Curves

Acid/base system Overall protonation constants

8 for the pKas

2.148

of the acid/base system 7.199

Phosphoric acid 12.350

a) as a function of pH e b) overlayed on

1

Charge of B -3 Protonations

pKa1 = logKpn b1

pKa2 = logKpn-1 b2

pKa3 = logKpn-2 b3

pKa4 = logKpn-3 b4

pKa5 = logKpn-4 b5

pKa6 = logKpn-5 b6

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.00

0.20

0.40

0.60

0.80

1.00Distribution of HiB species

pH

ai

<— aHiB aB—>

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00


pH

log

ai

<— aHiB aB—>

E2

Gutz: Options for selecting pKas: a) Click on control D3, slide along the list, click on a name; the pKas will be loaded from the Database; finally, click on B3 to plot the curves; b) Write the pKas of any real or hypothetical system in line 10 of the Database (or at the end of the list); return to Distribution and proceed as before (option a). Frequently used systems can be added definitively to the Database by saving the updated curtipot_.xls file.

E4

Gutz: Do not write here! Click on D3 to select an acid or base. To try other real or hypothetical systems, write their pKas in line 10 of the Database (or at the end of the list); return to Distribution and proceed as before.

F4

Gutz: The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up from 1 to n (the maximum number of protons accepted by a (conjugated) base, same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa.

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5Average protonation (h) of the base B

pH

av

era

ge

pro

ton

ati

on

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00


pH

log

ai

<— aHiB aB—>

read comment

Overall protonation constants Color coding of species

2.239E+12

3.540E+19 Data ID on curves

4.977E+21 How to copy/paste a curve

How to change the axis of a curve

3

bp a B

a HB

a H2B

a H3B

a H4B

a H5B

a H6B

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.00

0.20

0.40

0.60

0.80


pH

ai

<— aHiB aB—>

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.20

0.40

0.60

0.80

1.00

Distribution of HiB species along a titration

Volume (mL)

ai

<— aHiB aB—>

pH

7

0

1414

0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00


pH

log

ai

<— aHiB aB—>0.0 10.0 20.0 30.0 40.0 50.0 60.0

-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00Distribution of HiB species along a titration

Volume (mL)

lo

g a

i

<— aHiB aB—> 14

pH

7

0

G1

Gutz: The distribution diagrams (or alpha plots) of acids and bases reveal the molar fraction of each species in equilibrium at any pH of the solution. For example, phosphoric acid / phosphate system at pH 7.0: a0 = 0.00 or 0% and log a0 = -5.76 a1 = 0.387 or 38.7% and log a1 = -0,412 a2 = 0.613 or 61.3% and log a2 = -0,213 a3 = 0.00 or 0% and log a3 = -5.07 Since the index i of ai is the numbe or protons bound to the base, we have H2PO4– as dominant species, with 61.3%, followed by HPO4= with 38.7%, while only 0.0002% of phosphate and 0.0009% of H3PO4 coexist at this pH; the average number of protons bond to each phosphate is 1.61, as shown in column P (the data used to plot the figures appears at columns O to BE).

G4


I5

Gutz: Hover the mouse on a curve and point any data point to readout its ID and coordinates.

I6

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word o Excel) without links to the original: - Fill out the header of the graphic - Click in the box of the graphic near the margins, to select it - Repeat generation of at least one curve - Press Ctrl+C and wait processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

I7


0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5Average protonation (h) of the base B

pH

av

era

ge

pro

ton

ati

on

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.5

1.0

1.5

2.0

2.5

3.0Average protonation (h) of the base along a titration

Volume (mL)

av

era

ge

pro

ton

ati

on

14

pH

7

0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00


pH

log

ai

<— aHiB aB—>0.0 10.0 20.0 30.0 40.0 50.0 60.0

-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00


Volume (mL)

lo

g a

i

<— aHiB aB—> 14

pH

7

0

Color coding




Molar fraction of each species as a funciton of pH

alpha 0

pH h B0.000 2.993 0.0000.200 2.989 0.0000.400 2.982 0.0000.600 2.972 0.0000.800 2.957 0.0001.000 2.934 0.0001.200 2.899 0.0001.400 2.848 0.0001.600 2.779 0.0001.800 2.690 0.0002.000 2.584 0.0002.200 2.470 0.0002.400 2.359 0.0002.600 2.261 0.0002.800 2.182 0.0003.000 2.123 0.0003.200 2.081 0.0003.400 2.053 0.0003.600 2.034 0.0003.800 2.021 0.0004.000 2.013 0.0004.200 2.008 0.0004.400 2.004 0.0004.600 2.001 0.0004.800 1.998 0.0005.000 1.995 0.0005.200 1.991 0.0005.400 1.985 0.0005.600 1.976 0.0005.800 1.962 0.0006.000 1.941 0.0006.200 1.909 0.0006.400 1.863 0.0006.600 1.799 0.0006.800 1.715 0.0007.000 1.613 0.0007.200 1.499 0.0007.400 1.386 0.0007.600 1.284 0.0007.800 1.200 0.000

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.20

0.40

0.60

0.80

1.00

Distribution of HiB species along a titration

Volume (mL)

ai

<— aHiB aB—>

pH

7

0

1414

0

0.0 10.0 20.0 30.0 40.0 50.0 60.0-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00


Volume (mL)

lo

g a

i

<— aHiB aB—> 14

pH

7

0

8.000 1.136 0.0008.200 1.091 0.0008.400 1.059 0.0008.600 1.038 0.0008.800 1.024 0.0009.000 1.015 0.0009.200 1.009 0.0019.400 1.005 0.0019.600 1.002 0.0029.800 1.000 0.003

10.000 0.997 0.00410.200 0.994 0.00710.400 0.990 0.01110.600 0.983 0.01710.800 0.973 0.02711.000 0.957 0.04311.200 0.934 0.06611.400 0.899 0.10111.600 0.849 0.15111.800 0.780 0.22012.000 0.691 0.30912.200 0.586 0.41412.400 0.471 0.52912.600 0.360 0.64012.800 0.262 0.73813.000 0.183 0.81713.200 0.124 0.87613.400 0.082 0.91813.600 0.053 0.94713.800 0.034 0.96614.000 0.022 0.978

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.5

1.0

1.5

2.0

2.5

3.0Average protonation (h) of the base along a titration

Volume (mL)

av

era

ge

pro

ton

ati

on

14

pH

7

0

0.0 10.0 20.0 30.0 40.0 50.0 60.0-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00


Volume (mL)

lo

g a

i

<— aHiB aB—> 14

pH

7

0

Simulated titration curve

Titration curve under Evaluation

Titration curve under Regression

No titration curve

Molar fraction of each species as a funciton of pH Molar fraction of each species during titration

alpha 1 alpha 2 alpha 3 alpha 4 alpha 5 alpha 6

HB Vol pH0.000 0.007 0.993 0.000 1.8060.000 0.011 0.989 2.157 2.0200.000 0.018 0.982 4.096 2.2350.000 0.028 0.972 5.754 2.4490.000 0.043 0.957 7.077 2.6640.000 0.066 0.934 8.061 2.8780.000 0.101 0.899 8.749 3.0930.000 0.152 0.848 9.210 3.3070.000 0.221 0.779 9.508 3.5220.000 0.310 0.690 9.697 3.7360.000 0.416 0.584 9.817 3.9510.000 0.530 0.470 9.894 4.1650.000 0.641 0.359 9.944 4.3800.000 0.739 0.261 9.982 4.5940.000 0.818 0.182 10.014 4.8090.000 0.877 0.123 10.050 5.0230.000 0.918 0.081 10.098 5.2380.000 0.947 0.053 10.170 5.4520.000 0.966 0.034 10.282 5.6670.000 0.978 0.022 10.457 5.8810.001 0.986 0.014 10.730 6.0960.001 0.990 0.009 11.144 6.3100.002 0.993 0.006 11.748 6.5250.003 0.994 0.004 12.577 6.7390.004 0.994 0.002 13.626 6.9540.006 0.992 0.001 14.824 7.1680.010 0.989 0.001 16.044 7.3830.016 0.984 0.001 17.146 7.5980.025 0.975 0.000 18.041 7.8120.038 0.961 0.000 18.706 8.0270.059 0.940 0.000 19.169 8.2410.091 0.909 0.000 19.478 8.4560.137 0.863 0.000 19.677 8.6700.201 0.799 0.000 19.804 8.8850.285 0.715 0.000 19.886 9.0990.387 0.613 0.000 19.941 9.3140.501 0.499 0.000 19.982 9.5280.614 0.386 0.000 20.018 9.7430.716 0.284 0.000 20.059 9.9570.800 0.200 0.000 20.115 10.172

Options of the A8 slider

H2B H3B H4B H5B H6B

0.863 0.137 0.000 20.200 10.3860.909 0.091 0.000 20.333 10.6010.941 0.059 0.000 20.548 10.8150.962 0.038 0.000 20.896 11.0300.975 0.024 0.000 21.459 11.2440.984 0.016 0.000 22.365 11.4590.989 0.010 0.000 23.818 11.6730.993 0.006 0.000 26.155 11.8880.994 0.004 0.000 29.983 12.1020.995 0.002 0.000 36.644 12.3170.994 0.002 0.000 50.000 12.5310.992 0.001 0.0000.988 0.001 0.0000.982 0.000 0.0000.972 0.000 0.0000.957 0.000 0.0000.934 0.000 0.0000.899 0.000 0.0000.849 0.000 0.0000.780 0.000 0.0000.691 0.000 0.0000.585 0.000 0.0000.471 0.000 0.0000.360 0.000 0.0000.262 0.000 0.0000.183 0.000 0.0000.124 0.000 0.0000.082 0.000 0.0000.053 0.000 0.0000.034 0.000 0.0000.022 0.000 0.000

Simulated titration curve

Titration curve under Evaluation

Titration curve under Regression

No titration curve

Molar fraction of each species during titration

alpha 0 alpha 1 alpha 2 alpha 3 alpha 4 alpha 5 alpha 6

h B HB2.687 0.000 0.000 0.313 0.6872.573 0.000 0.000 0.427 0.5732.450 0.000 0.000 0.550 0.4502.333 0.000 0.000 0.667 0.3332.234 0.000 0.000 0.766 0.2342.157 0.000 0.000 0.843 0.1572.102 0.000 0.000 0.898 0.1022.065 0.000 0.000 0.935 0.0652.040 0.000 0.000 0.959 0.0412.025 0.000 0.000 0.975 0.0252.015 0.000 0.001 0.984 0.0152.009 0.000 0.001 0.990 0.0102.004 0.000 0.002 0.993 0.0062.001 0.000 0.002 0.994 0.0041.998 0.000 0.004 0.994 0.0021.995 0.000 0.007 0.992 0.0011.990 0.000 0.011 0.988 0.0011.983 0.000 0.018 0.982 0.0001.972 0.000 0.029 0.971 0.0001.954 0.000 0.046 0.954 0.0001.927 0.000 0.073 0.927 0.0001.886 0.000 0.114 0.885 0.0001.825 0.000 0.175 0.825 0.0001.742 0.000 0.258 0.742 0.0001.637 0.000 0.363 0.637 0.0001.518 0.000 0.482 0.518 0.0001.396 0.000 0.604 0.396 0.0001.285 0.000 0.715 0.285 0.0001.196 0.000 0.804 0.196 0.0001.129 0.000 0.870 0.129 0.0001.083 0.000 0.917 0.083 0.0001.052 0.000 0.947 0.052 0.0001.032 0.000 0.967 0.033 0.0001.020 0.000 0.979 0.020 0.0001.012 0.001 0.987 0.012 0.0001.007 0.001 0.991 0.008 0.0001.003 0.001 0.994 0.005 0.0001.000 0.002 0.995 0.003 0.0000.998 0.004 0.994 0.002 0.0000.994 0.007 0.992 0.001 0.000

Options of the A8 slider

H2B H3B H4B H5B H6B

0.990 0.011 0.989 0.001 0.0000.983 0.017 0.982 0.000 0.0000.972 0.028 0.971 0.000 0.0000.955 0.046 0.954 0.000 0.0000.927 0.073 0.927 0.000 0.0000.886 0.114 0.886 0.000 0.0000.826 0.174 0.826 0.000 0.0000.744 0.256 0.744 0.000 0.0000.639 0.361 0.639 0.000 0.0000.519 0.481 0.519 0.000 0.0000.397 0.603 0.397 0.000 0.000

logarithm of molar fraction of each species as a funciton of pH

scaling scaling log alpha 0 log alpha 1 log alpha 2 log alpha 3

pH/14 n*pH/14 [H] [OH] B HB0.129 0.387 0.000 14.000 -21.700 -9.350 -2.151 -0.0030.144 0.433 0.200 13.800 -21.102 -8.952 -1.953 -0.0050.160 0.479 0.400 13.600 -20.505 -8.555 -1.756 -0.0080.175 0.525 0.600 13.400 -19.909 -8.159 -1.560 -0.0120.190 0.571 0.800 13.200 -19.316 -7.766 -1.367 -0.0190.206 0.617 1.000 13.000 -18.727 -7.377 -1.178 -0.0300.221 0.663 1.200 12.800 -18.143 -6.993 -0.994 -0.0460.236 0.709 1.400 12.600 -17.568 -6.618 -0.819 -0.0710.252 0.755 1.600 12.400 -17.005 -6.255 -0.656 -0.1080.267 0.801 1.800 12.200 -16.458 -5.908 -0.509 -0.1610.282 0.847 2.000 12.000 -15.930 -5.580 -0.381 -0.2330.298 0.893 2.200 11.800 -15.425 -5.275 -0.276 -0.3280.313 0.939 2.400 11.600 -14.942 -4.992 -0.193 -0.4450.328 0.985 2.600 11.400 -14.480 -4.730 -0.131 -0.5830.343 1.030 2.800 11.200 -14.036 -4.486 -0.087 -0.7390.359 1.076 3.000 11.000 -13.606 -4.256 -0.057 -0.9090.374 1.122 3.200 10.800 -13.186 -4.036 -0.037 -1.0890.389 1.168 3.400 10.600 -12.773 -3.823 -0.024 -1.2760.405 1.214 3.600 10.400 -12.364 -3.614 -0.015 -1.4670.420 1.260 3.800 10.200 -11.959 -3.409 -0.010 -1.6620.435 1.306 4.000 10.000 -11.555 -3.205 -0.006 -1.8580.451 1.352 4.200 9.800 -11.153 -3.003 -0.004 -2.0560.466 1.398 4.400 9.600 -10.752 -2.802 -0.003 -2.2550.481 1.444 4.600 9.400 -10.352 -2.602 -0.003 -2.4550.497 1.490 4.800 9.200 -9.952 -2.402 -0.003 -2.6550.512 1.536 5.000 9.000 -9.552 -2.202 -0.003 -2.8550.527 1.582 5.200 8.800 -9.154 -2.004 -0.005 -3.0570.543 1.628 5.400 8.600 -8.756 -1.806 -0.007 -3.2590.558 1.674 5.600 8.400 -8.360 -1.610 -0.011 -3.4630.573 1.720 5.800 8.200 -7.966 -1.416 -0.017 -3.6690.589 1.766 6.000 8.000 -7.576 -1.226 -0.027 -3.8790.604 1.812 6.200 7.800 -7.190 -1.041 -0.042 -4.0930.619 1.858 6.400 7.600 -6.813 -0.863 -0.064 -4.3160.635 1.904 6.600 7.400 -6.446 -0.697 -0.098 -4.5500.650 1.950 6.800 7.200 -6.095 -0.545 -0.146 -4.7980.665 1.996 7.000 7.000 -5.762 -0.412 -0.213 -5.0650.681 2.042 7.200 6.800 -5.450 -0.301 -0.302 -5.3530.696 2.088 7.400 6.600 -5.162 -0.212 -0.413 -5.6650.711 2.134 7.600 6.400 -4.895 -0.145 -0.546 -5.9980.727 2.180 7.800 6.200 -4.647 -0.097 -0.698 -6.350

H2B H3B

0.742 2.226 8.000 6.000 -4.414 -0.064 -0.865 -6.7170.757 2.272 8.200 5.800 -4.191 -0.041 -1.042 -7.0940.773 2.318 8.400 5.600 -3.977 -0.027 -1.228 -7.4800.788 2.363 8.600 5.400 -3.767 -0.017 -1.418 -7.8700.803 2.409 8.800 5.200 -3.561 -0.011 -1.612 -8.2640.818 2.455 9.000 5.000 -3.357 -0.007 -1.808 -8.6600.834 2.501 9.200 4.800 -3.155 -0.005 -2.006 -9.0580.849 2.547 9.400 4.600 -2.953 -0.003 -2.204 -9.4560.864 2.593 9.600 4.400 -2.752 -0.002 -2.403 -9.8550.880 2.639 9.800 4.200 -2.552 -0.002 -2.603 -10.2550.895 2.685 10.000 4.000 -2.353 -0.003 -2.804 -10.656

10.200 3.800 -2.153 -0.003 -3.004 -11.05610.400 3.600 -1.955 -0.005 -3.206 -11.45810.600 3.400 -1.758 -0.008 -3.409 -11.86110.800 3.200 -1.562 -0.012 -3.613 -12.26511.000 3.000 -1.369 -0.019 -3.820 -12.67211.200 2.800 -1.180 -0.030 -4.031 -13.08311.400 2.600 -0.996 -0.046 -4.247 -13.49911.600 2.400 -0.821 -0.071 -4.472 -13.92411.800 2.200 -0.658 -0.108 -4.709 -14.36112.000 2.000 -0.510 -0.160 -4.961 -14.81312.200 1.800 -0.382 -0.232 -5.233 -15.28512.400 1.600 -0.277 -0.327 -5.528 -15.78012.600 1.400 -0.194 -0.444 -5.845 -16.29712.800 1.200 -0.132 -0.582 -6.183 -16.83513.000 1.000 -0.088 -0.738 -6.539 -17.39113.200 0.800 -0.057 -0.907 -6.908 -17.96013.400 0.600 -0.037 -1.087 -7.288 -18.54013.600 0.400 -0.024 -1.274 -7.675 -19.12713.800 0.200 -0.015 -1.465 -8.066 -19.71814.000 0.000 -0.010 -1.660 -8.461 -20.312

logarithm of molar fraction of each species as a funciton of pH logarithm of molar fraction of each species during titration

log alpha 4 log alpha 5 log alpha 6 same same log alpha 0 log alpha 1 log alpha 2

Vol pH B HB-16.442 -5.898 -0.505-15.878 -5.548 -0.369-15.339 -5.224 -0.260-14.826 -4.925 -0.176-14.337 -4.651 -0.116-13.866 -4.395 -0.074-13.410 -4.153 -0.047-12.963 -3.921 -0.029-12.523 -3.695 -0.018-12.087 -3.474 -0.011-11.654 -3.255 -0.007-11.223 -3.038 -0.005-10.792 -2.822 -0.003-10.363 -2.607 -0.003

-9.934 -2.393 -0.003-9.505 -2.179 -0.003-9.078 -1.966 -0.005-8.652 -1.754 -0.008-8.228 -1.545 -0.013-7.806 -1.338 -0.020-7.390 -1.136 -0.033-6.981 -0.941 -0.053-6.582 -0.757 -0.083-6.199 -0.589 -0.129-5.837 -0.441 -0.196-5.498 -0.317 -0.286-5.186 -0.219 -0.403-4.898 -0.146 -0.544-4.633 -0.095 -0.708-4.384 -0.060 -0.888-4.147 -0.038 -1.080-3.918 -0.023 -1.280-3.694 -0.015 -1.486-3.474 -0.009 -1.695-3.257 -0.006 -1.906-3.040 -0.004 -2.118-2.825 -0.003 -2.332-2.610 -0.002 -2.546-2.395 -0.003 -2.761-2.182 -0.003 -2.976

H4B H5B H6B H2B

-1.969 -0.005 -3.192-1.757 -0.008 -3.409-1.548 -0.013 -3.629-1.341 -0.020 -3.851-1.139 -0.033 -4.078-0.944 -0.052 -4.312-0.760 -0.083 -4.557-0.591 -0.129 -4.817-0.442 -0.195 -5.098-0.318 -0.285 -5.402-0.220 -0.401 -5.733

logarithm of molar fraction of each species during titration

log alpha 3 log alpha 4 log alpha 5 log alpha 6 scaling

pH (-8 a 0)-0.163 -6.968-0.242 -6.845-0.347 -6.723-0.477 -6.600-0.632 -6.478-0.805 -6.355-0.992 -6.233-1.189 -6.110-1.392 -5.987-1.600 -5.865-1.810 -5.742-2.022 -5.620-2.235 -5.497-2.449 -5.375-2.664 -5.252-2.879 -5.129-3.095 -5.007-3.312 -4.884-3.532 -4.762-3.754 -4.639-3.981 -4.517-4.215 -4.394-4.460 -4.271-4.721 -4.149-5.002 -4.026-5.307 -3.904-5.638 -3.781-5.994 -3.659-6.372 -3.536-6.766 -3.413-7.173 -3.291-7.587 -3.168-8.008 -3.046-8.431 -2.923-8.857 -2.801-9.284 -2.678-9.712 -2.555

-10.140 -2.433-10.570 -2.310-10.999 -2.188

H3B H4B H5B H6B

-11.430 -2.065-11.862 -1.943-12.296 -1.820-12.732 -1.697-13.174 -1.575-13.622 -1.452-14.082 -1.330-14.557 -1.207-15.052 -1.085-15.571 -0.962-16.116 -0.839

Degree of smoothing

(0 to 100%) 90

Interpolated points 100

Volume pH Interp. Vol. Fitted pH dpH/dV

0.000 2.265 0.0000 2.2628 0.0293 0.00002.499 2.386 0.5051 2.2781 0.0321 0.00574.618 2.664 1.0101 2.2963 0.0408 0.01146.278 2.784 1.5152 2.3202 0.0552 0.01717.499 3.059 2.0202 2.3529 0.0753 0.02288.355 3.302 2.5253 2.3973 0.1011 0.02758.934 3.437 3.0303 2.4542 0.1220 0.01399.318 3.552 3.5354 2.5182 0.1292 0.00049.569 3.823 4.0404 2.5824 0.1227 -0.01329.734 3.891 4.5455 2.6399 0.1026 -0.02689.844 4.301 5.0505 2.6858 0.0830 -0.00739.922 4.118 5.5556 2.7280 0.0883 0.01779.984 4.422 6.0606 2.7792 0.1188 0.0427

10.042 4.841 6.5657 2.8514 0.1660 0.037910.108 5.186 7.0707 2.9426 0.1904 0.010410.198 5.192 7.5758 3.0391 0.1879 -0.005410.328 5.380 8.0808 3.1369 0.2075 0.044110.525 5.567 8.5859 3.2590 0.3024 0.202710.825 5.768 9.0909 3.4881 0.6572 0.519411.278 6.083 9.5960 3.9810 1.3338 0.741611.953 6.222 10.1010 4.8038 1.7494 -0.308612.926 6.444 10.6061 5.5487 1.1537 -0.630614.267 6.617 11.1111 5.9890 0.6246 -0.419516.007 6.828 11.6162 6.2152 0.3059 -0.211118.090 6.995 12.1212 6.3331 0.1884 -0.061120.362 7.224 12.6263 6.4154 0.1428 -0.029122.596 7.537 13.1313 6.4827 0.1273 -0.008224.584 7.631 13.6364 6.5453 0.1216 -0.003226.199 7.783 14.1414 6.6063 0.1208 0.001727.418 7.983 14.6465 6.6678 0.1221 -0.001028.288 8.285 15.1515 6.7287 0.1183 -0.006328.885 8.406 15.6566 6.7864 0.1093 -0.011529.284 8.629 16.1616 6.8383 0.0955 -0.013629.547 8.798 16.6667 6.8835 0.0844 -0.008429.720 9.096 17.1717 6.9244 0.0785 -0.003329.836 9.085 17.6768 6.9636 0.0778 0.001929.918 9.400 18.1818 7.0038 0.0822 0.006529.983 9.451 18.6869 7.0472 0.0900 0.009030.045 9.812 19.1919 7.0952 0.1003 0.011430.116 10.285 19.6970 7.1489 0.1130 0.013830.212 10.295 20.2020 7.2097 0.1282 0.016230.354 10.522 20.7071 7.2784 0.1424 0.008830.570 10.628 21.2121 7.3516 0.1452 -0.003230.905 10.915 21.7172 7.4231 0.1360 -0.015131.427 11.085 22.2222 7.4869 0.1146 -0.0271

Evaluation of Real and Simulated Titration Data by Derivatives with Interpolation

Interpolation and smoothing by cubic splines

d2pH/dV2

Assisted calculation of concentrationsVol. of titrand (sample)

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00smoothed data derivatives 2nd derivative

Volume (mL)

dp

H/d

V

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000

0.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000

14.0000

raw data smoothed data

Volume (mL)

pH

F2

Gutz: Interpolation with smoothing is a valuable tool to rapidly and precisely locate well defined inflections on titration curves. Up to 1000 points can be interpolated (select in cell I4) Successive inflections may correspond to the stepwise deprotonation of a multiprotic acid like phosphoric (or protonation of a multiprotonable base like ethylenediamine) or be originated by various acids or bases contained in a sample. Auxiliary calculations can be made in the table at I49. Warning: care should be exercised with unknown samples because there may be hidden/unresolved inflections (e.g., citric acid, see example in Regression). It is wise to compare the experimental curve with the simulated one based on the supposed interpretation of the results (this can be done with Simulation and Graphs or better, for skilled users, with the Regression module). Although Regression is far superior for hidden or overlapped inflections, no chemometric tool can extract accurate results from poor data (insufficient measurements, data with high scatter, etc.).

F3

Gutz: Click Clear and paste or fill out with up to 300 data points from a real titration, or Copy previously simulated data using one of the buttons.

H3

Gutz: The smoothig factor is selected empirically. Start with 80% and try other factors until you find the best compromise between dispersion reduction and curve flattening/distortion. 0% - minimum filtering, cubic pline curve passes though all points. 100%- maximum filtering; the fitted curve approaches linearity.

H4

Gutz: Defines the number of points to be interpolated from the initial to the final volume. Minimum: 4 Typical: 100 Maximum 1000

A5

Gutz: Delete existing data (or click the Clear button) before you write or paste experimental data, or copy data from Simulation by clicking on the buttons above. Volume values in mL are expected, but mass of titrant or number o coulombs (coulometric titration) can be used instead.

B5

Gutz: Copy or paste pH values, experimental or simulated, with our without dispersion (simulated random errors). Uncalibrated pH electrodes do not impair the determination of concentrations at sharp inflections, but will offset pKa values estimated graphically. Electrode potentials can replace pH values when evaluating data from other ion selective electrodes.

C5

Ivano Gebhardt Rolf Gutz: The number of interpolated points can be chosen from 4 to 1000 in cell I4.

32.239 11.226 22.7273 7.5369 0.0821 -0.0324 Sample Water33.495 11.385 23.2323 7.5713 0.0564 -0.0184 20 035.422 11.677 23.7374 7.5963 0.0449 -0.0044 Vol. Inflection38.365 11.805 24.2424 7.6191 0.0475 0.0095 1ª 10.0242.878 12.007 24.7475 7.6466 0.0635 0.0195 2ª 30.0250.000 12.224 25.2525 7.6838 0.0839 0.0210 3ª

25.7576 7.7317 0.1060 0.0226 4ª26.2626 7.7911 0.1296 0.0242 5ª26.7677 7.8629 0.1552 0.0264 6ª27.2727 7.9482 0.1829 0.0285 7ª27.7778 8.0485 0.2170 0.0422 8ª28.2828 8.1704 0.2689 0.0606 9ª28.7879 8.3443 0.4662 0.3326 10ª29.2929 8.6892 0.9508 0.629429.7980 9.3414 1.6279 0.5750 Results of the Example: 30.3030 10.2021 1.5367 -0.6649 0,0501 mol/L H3PO4 and 0,0499 mol/L NaH2PO430.8081 10.8020 0.8563 -0.5952 Remember: half of the determined H2PO4- comes from the H3PO431.3131 11.1038 0.3852 -0.325231.8182 11.2345 0.1605 -0.143132.3232 11.2920 0.0909 -0.013232.8283 11.3363 0.0880 0.007333.3333 11.3843 0.1056 0.027733.8384 11.4454 0.1349 0.021734.3434 11.5175 0.1475 0.003434.8485 11.5913 0.1416 -0.015035.3535 11.6575 0.1172 -0.033435.8586 11.7080 0.0838 -0.029536.3636 11.7434 0.0577 -0.022236.8687 11.7675 0.0390 -0.014837.3737 11.7841 0.0278 -0.007537.8788 11.7969 0.0240 -0.000138.3838 11.8096 0.0276 0.007038.8889 11.8252 0.0341 0.005839.3939 11.8438 0.0394 0.004739.8990 11.8648 0.0436 0.003640.4040 11.8877 0.0466 0.002440.9091 11.9118 0.0485 0.001341.4141 11.9365 0.0493 0.000241.9192 11.9614 0.0489 -0.000942.4242 11.9858 0.0474 -0.002142.9293 12.0091 0.0448 -0.003143.4343 12.0309 0.0418 -0.002843.9394 12.0513 0.0390 -0.002644.4444 12.0704 0.0365 -0.002444.9495 12.0882 0.0342 -0.002245.4545 12.1049 0.0321 -0.002045.9596 12.1206 0.0302 -0.001746.4646 12.1355 0.0285 -0.001546.9697 12.1495 0.0271 -0.001347.4747 12.1629 0.0259 -0.001147.9798 12.1757 0.0249 -0.000948.4848 12.1881 0.0241 -0.000748.9899 12.2001 0.0236 -0.000449.4949 12.2119 0.0232 -0.0002

I53

Gutz: Fill out with the volumes of the inflections (in mL)

50.0000 12.2236 0.0231 0.0000

Color coding

Volume dpH/dV D o n o t c h a n g e

Initial volume 0.000 Maximum 10.02093 1.775186 C h a n g e c r i t e r i o u s l y

Final volume 50.000 Minimum Fill out, change or leave blank

How to change the axis of a curveConcentration of How to copy/paste a curve

Evaluation of Real and Simulated Titration Data by Derivatives with Interpolation

Fitting range (zoom)Inflection

auto-finder

Assisted calculation of concentrations (optional)Vol. of titrand (sample)

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00smoothed data derivatives 2nd derivative

Volume (mL)

dp

H/d

V

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000

0.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000

14.0000

raw data smoothed data

Volume (mL)

pH

Titration with 0.100 mol/L NaOH of 20 mLof sample containing 0.05 mol/L H3PO4 and 0.05 mol/L NaH2PO4 with simulated dispersion (sVol=0.05 mL and spH=0.05)

L2

Gutz: The program calculates the maximum and the minimum of the first derivative in the region bracketed by the initial and final volumes. Thus, inflections are to be evaluated one at a time. For the titration of acids with bases, inflections correspond to the maxima. For bases titrated with acids, the inflections are given by the minima. Precision of the inflection point by interpolation with smoothing is better than for the conventional dpH/dV calculation suggested in textbooks (and quite independent of the selected number of interpolated points). Of course, good data near the inflections is decisive. The Regression module may provide superior results, due to fitting to a general equation describing the entire curve instead of empirical splines fitted with an arbitrary smoothing factor (that influences the result for poor data or undefined inflections).

N2

Gutz: Maximum value of the first derivative of the curve at the inflection, as calculated from the fitted cubic spline. Precision is higher than for the conventional dpH/dV calculation suggested in textbooks. The Regression module may provide superior results, due to fitting to a general equation describing the curve instead of empirical splines. Of course, good data near the inflections is decisive for all approaches.

J3

Gutz: Starting volume for the smoothing/interpolation process. Zero is OK unless there are various inflections; in such case the initial and final volumes should bracket one inflection at a time, in order to auto-detect the interpolated volume of the inflection point.

L3

Gutz: The maximum reveals the volume of an inflection of a titration performed with a base as titrant. (ignore the excess of digits of the results)

M3

Gutz: The spreadshhet starting at cell I49 can be used or adapted to assist trivial stoichiometric calculations. Copy and paste the volumes of all inflections to R6, R7, etc. and inform the required other parameters

J4

Gutz: Maximum volume of titrant to be considered for the smoothing/interpolation process. For curves with various inflections, the initial and final volumes should bracket one inflection at a time.

L4

Gutz: The minimum reveals the volume of an inflection of a titration performed with an acid as titrant

P49

Gutz: Click twice on the dpH/dV or pH scale to redifine it. Use Ctrl+Z (as many times as needed) to undo scale expansion

P50

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word o Excel) without links to the original: - Fill out the header of the graphic (optional) - Click in the box of the graphic near the margins, to select it - Repeat generation of at least one curve - Press Ctrl+C and wait processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

Total Data ID on curves

20 0.1n (mols) delta n [species]

0.001002 0.001002 0.05010.003002 0.002 0.1

Results of the Example: 0,0501 mol/L H3PO4 and 0,0499 mol/L NaH2PO4Remember: half of the determined H2PO4- comes from the H3PO4

titrant (mol/L)

P51


J53

Gutz: Calculated number of mols of titrant added up to the inflection

K53

Gutz: Number of mols of titrant added between inflections

L53

Gutz: Concentration of a titrated species (em mol/L) in the sample as calculated from the titrant consumed to reach an inflection. Sucessive inflections may correspond to the stepwise deprotonation of a multiprotic acid like fosforic (or protonation of a multiprotonable base like ethylenediamine) or to various acids or bases mixed in the same sample. Warning: care should be exercised with unknown samples because there may be hidden/unresolved inflections (e.g., citric acid, see example in Regression) It nontrivial samples, is wise to compare the experimental curve with the simulated one based on the suposed interpretation of the results (this can be done with Simulation and Graphs orbetter (for skilled users) with Regression.

Titration Data Analysis - Multiple Regression

Citric acid Phosphoric acid Ascorbic acid Acetic acid Ammonia

[B] 1.25748925E-09 0 1.41193601E-13 0 0

[HB] 1.63936634E-05 0 0.000456023002 0 0

0.004952765302 0 0.030071734876 0 0

0.034835294201 0 2.02922506E-29 0 0

9.46653875E-28 0 1.06292336E-31 0 0

4.95864425E-30 0 5.56767257E-34 0 0

2.59737518E-32 0 2.91638879E-36 0 0

0.03980445442 0 0.03052775788 0 00.114427806871 0 0.060599492755 0 0

max. free H 0.004985556401 0 0.000456023003 0 0

Titrant Strong ACID Strong BASE Carbonic ac. Vol. Tittrand (mL)

[B] 0.1 Sample Water

[HB] 20 0SS

S[HiB] 0 0.1 0 0.1 SS[HiB]

0 0 0 0

Fitted total concentrations of all forms of each base (in blue) and equilibrium conc. at the initial pH (in mol/L)

Titrand Species

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

S[H] bound

[H2B]

S[H] SS [H]

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00 Titration with 0.100 mol/L NaOH of 20.0 mLof a mixture of 0.040 mol/L citric acid

+ 0.030 mol/L ascorbic acid(sVol=0.02; spH=0.02)

Titrant volume (mL)

pH

F1

Gutz: This module employs multiparametric nonlinear regression (MPNLR) to assist you in the determination of the concentration of acidic and basic components by volumetric acid-base titration; optionally, pK’a values can be determined or refined. MPNLR is a powerful alternative to the graphical evaluation of titration data, being faster and, in general, more accurate. It is the method of choice for complex mixtures and/or very diluted samples; valuable also to detect (and, possibly, quantify) the presence of minor components, perhaps overlooked in the graphical evaluation. Some learning is required to understand and use this module properly (the red dot comments cover essential aspects). The supplement Solver of the software Excel MUST be previously installed. See instructions in comment I19. Differently from the pH_calc module, Regression does not (yet) correct for ion-ion interactions. Consequently, thermodynamic constants from the Database (valid strictly at I=0) may not generate the best possible fit to experimental curves. More coincident curves will be obtained by refining the pKas after a first fit of the concentrations (viable when their values fall within the pH region explored during the titration). The returned “constants” may be described as pK’as (=conditional or apparent pKas), valid at the average ionic strength (I) along the titration (and temperature). Alternatively, pk'as at a given I can be calculated in the pH_calc module and used here. The parameter denoted as pH in this module is closer to “pH” when using pKas for I=0 and to p[H], after fitting pK’as. The more diluted the solutions, the closer "pH" and p[H] come to pH (see definitions in pH_calc). Inaccurate calibration of the sensor (unreliable buffer solutions, temperature different from specified) and deviation from Nersntian reponse and/or alkalyne error of the glass electrode are also sources of deviation that can, sometimes, be compensated by inclusion of N12 and N13 as variable cells in the Solver, at a refinement stage of the fitting. Warning: no chemometric tool can extract accurate results from poor data (insufficient measurements, data with high scatter, systematic errors, etc.). Before you analyze difficult titration data with Regression, collect the best data you can in the laboratory, after careful planning (assisted by Simulation) and well executed experiments with calibrated instrumentation and high purity well standardized reagents. The program fits the user-selected parameters by minimizing the squares of the difference of calculated and fitted total dissociable H+ concentrations (or the the non-squared residue, user's choice, I19 or I20). The macro may be modified to minimize the pH differences instead (slower calculation), or to consider data weighting.

B3


A4

Gutz: Fitted equilibrium concentration of the deprotonated (conjugated) base at the initial pH (J15); The fitted global concentration of all forms of the acid-base system, [B]+[HB]+[H2B]+... appears in line 11

B4


A5

Gutz: Fitted equilibrium concentration of the monoprotonated (conjugated) base at the initial pH (J15); The global concentration [B]+[HB]+[H2B]+... appears in line 11

A11

Gutz: Total concentration of the acid or base identified in line 3, obtained by summing up the contributions of all forms in equilibrium: [B]+[HB]+[H2B]+... This concentration is a parameter fitted by regression with help of the Solver. The more the pKas of a system depart from the pH region explored in the titration, the more inaccurate the fitted concentration. Strong acids pose the worst condition; their concentration cannot be fitted directly, but is obtained from the excess of H+ (cell I14). Convergence is accelarated with good initial guesses but, in general, zero is an acceptable starting value for the concentrations to fit.

B11

Gutz: You may write 0 (zero) as starting value in all cells of line 11 (B11 to H11). During regression, the values of the cells specified by you in the Solver setup will be adjusted accordingly. For complicated systemsm an initial guess, based on graphical evaluatian, will help and speed up Solver's convergence.

A12

Gutz: Dissociable H+ concentration still bound to each (conjugated) base at the initial pH.

A13

Gutz: Free H+ originated from each acid or (conjugated) base at the initial pH, supposing that it was added to the sample protonated to neutrality, and not as a salt (e.g., H3PO4 but not H2NaPO4). As this is frequently not the case, the value can be zero or negative. E.g., dissolved NH3 (same as NH4OH) dissociates no protons; it will remove protons from acids with lower pKa (weaker bases) if available, or from water, in small extent). The undissociated H+ at the initial pH is not include here; it appears in line 12.

D14

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. But any other mono- or biprotic system can be specified in T3.

C15

Gutz: Leave blank/fill with de concentration of strong monoprotonable base used as titrant e.g., NaOH, KOH (or twice the concentration of Ca(OH)2). For diprotic systems see cell S3.

B16

Gutz: Leave blank/fill with the concentration of strong monoprotic acid used as titrant e.g., HC. For a diprotic acid like H2SO4 see comment at cell R3.

E16

Gutz: Volume of the aliquot of titrand (sample)

F16

Gutz: Water (or electrolyte solution) is frequently added to the sample until the glass electrode bulb and reference electrode junction are covered by the solution.

D17

Gutz: Leave blank/fill out with the concentration of CO2 that may have been absorbed by the the titrant. CO2 absorption is most relevant for dilluted alkaline titrants. It is advisable to titrate the dilluted base against a strong standardized acid to determine this concentration of bicarbonate/carbonate with help of Regression before using the base as a titrant for the titration of unknown samples.

Vad "pH" [H] delta^2

(mL) fitted mol/L

0.000 2.2808 2.2699 5.24E-03 6.440E-08 2.538E-040.897 2.4714 2.4715 3.38E-03 8.885E-12 2.981E-061.864 2.6625 2.6733 2.18E-03 6.589E-08 2.567E-042.961 2.8606 2.8750 1.38E-03 1.352E-07 3.677E-044.198 3.0950 3.0766 8.04E-04 2.472E-07 4.972E-045.548 3.2735 3.2779 5.33E-04 1.431E-08 1.196E-046.970 3.4831 3.4790 3.29E-04 1.222E-08 1.105E-048.440 3.6744 3.6798 2.12E-04 1.968E-08 1.403E-049.958 3.8778 3.8803 1.32E-04 3.935E-09 6.273E-05

11.528 4.0878 4.0807 8.17E-05 3.272E-08 1.809E-0413.142 4.2595 4.2811 5.50E-05 2.799E-07 5.291E-0414.769 4.4838 4.4816 3.28E-05 2.585E-09 5.084E-0516.357 4.6824 4.6823 2.08E-05 1.102E-11 3.319E-0617.845 4.8894 4.8829 1.29E-05 1.456E-08 1.207E-0419.182 5.0960 5.0835 8.02E-06 3.942E-08 1.985E-0420.352 5.2953 5.2841 5.07E-06 2.260E-08 1.503E-0421.384 5.5012 5.4851 3.15E-06 3.569E-08 1.889E-0422.343 5.6876 5.6867 2.05E-06 9.438E-11 9.715E-0623.297 5.8781 5.8889 1.32E-06 1.420E-08 1.191E-0424.292 6.0934 6.0913 8.06E-07 5.686E-10 2.385E-0525.326 6.3069 6.2936 4.93E-07 2.263E-08 1.504E-0426.348 6.4902 6.4957 3.23E-07 3.408E-09 5.838E-0527.280 6.6985 6.6975 2.00E-07 7.277E-11 8.530E-0628.063 6.8921 6.8993 1.28E-07 2.662E-09 5.160E-0528.670 7.0866 7.1010 8.19E-08 5.963E-09 7.722E-0529.112 7.3027 7.3027 4.98E-08 5.642E-15 7.511E-0829.419 7.5183 7.5045 3.03E-08 1.175E-09 3.428E-0529.625 7.7039 7.7066 1.98E-08 2.058E-11 4.537E-0629.761 7.9083 7.9090 1.24E-08 6.090E-13 7.804E-0729.849 8.1150 8.1121 7.67E-09 3.970E-12 1.992E-0629.906 8.2506 8.3161 5.62E-09 9.866E-10 3.141E-0529.944 8.5723 8.5212 2.68E-09 2.069E-10 1.438E-0529.969 8.6735 8.7271 2.12E-09 1.335E-10 1.155E-0529.988 8.9492 8.9322 1.12E-09 7.869E-12 2.805E-0630.004 9.1846 9.1337 6.54E-10 6.829E-11 8.263E-0630.021 9.2019 9.3312 6.28E-10 5.219E-10 2.285E-0530.043 9.5546 9.5273 2.79E-10 5.161E-11 7.184E-0630.073 9.7397 9.7241 1.82E-10 3.582E-11 5.985E-0630.120 9.9213 9.9221 1.20E-10 2.200E-13 4.691E-0730.192 10.1181 10.1213 7.62E-11 7.931E-12 2.816E-0630.304 10.3403 10.3212 4.57E-11 7.237E-10 2.690E-0530.479 10.5265 10.5216 2.97E-11 1.117E-10 1.057E-0530.749 10.7167 10.7223 1.92E-11 3.220E-10 1.794E-0531.161 10.9218 10.9232 1.20E-11 4.864E-11 6.975E-0631.777 11.1236 11.1243 7.52E-12 1.929E-11 4.392E-0632.681 11.3351 11.3254 4.62E-12 9.528E-09 9.761E-0533.983 11.5157 11.5268 3.05E-12 2.291E-08 1.514E-0435.846 11.7421 11.7283 1.81E-12 6.786E-08 2.605E-04

simul. "pH" or |CHRNL-Chcalc|

measured pH

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

2.00

4.00

6.00

8.00

10.00

12.00



Titrant volume (mL)p

H

A39

Gutz: Click on the Clear data button and then: a) Type or paste experimental pH vs. Volume data from real titrations or b) Click on one of the Simulation buttons in line 38 to copy previously simulated curves (with or without random errors).

B39

Gutz: Copy "pH" data from the simulation (click B38 for "clean" data or D38 for data with dispersion ) or type or paste real pH data.

C39

Gutz: Click on button B20 to calculate the fitted curve and overlay it on the raw data graphically.

D39

Gutz: Free hydrated proton concentration (or activity, for real pH measurements)

E39

Gutz: Squared value of the residues given in column G, minimized by the Solver by fitting the selected parameters.

F39

Gutz: Absolute value of the residues calculated in column G.

D41

Gutz: Do NOT write in this colored region! You will corrupt the equations.

38.567 11.9191 11.9302 1.20E-12 7.917E-08 2.814E-0442.781 12.1346 12.1324 7.34E-13 6.367E-09 7.979E-0550.000 12.3300 12.3347 4.68E-13 6.234E-08 2.497E-04

1.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+001.00E+00

read important remarks and instructions

62

HCl Carbonic acid Acid / Base Citric acid

0 0 Charge of B -3

0 0 3.128

0 0 4.761

0 0 6.396

0 0

0 0

0 0 SS

0 0 7.033E-02

0 0 1.750E-01

0 0 5.442E-03

Vol. Tittrand (mL) 5.027E-05

Total [H]=10^-p[H] 5.238E-03 2.281 initial "pH"

20.00 [OH]=Kw/[H] 1.922E-12 11.716 initial "pOH"

initial CHcalc 1.803E-01

1.805E-01

1.293E-06 <--- Minimize with Solver

5.069E-03 Alternatively, minimize with Solver (instead of I19)


and equilibrium conc. at the initial pH (in mol/L)

pKa1

pKa2

pKa3

pKa4

pKa5

pKa6

SS[bases]

SS[H] bound

SS[H] max.free H+ (negative results are possible)

"Extra" H+ from non-fitted HiB (e.g., a strong acid), if any.

CHRNL <---Fit with Solver: CHRNL + concentrations (line 11, in blue)

S(CHRNL-CHcalc)2

S|CHRNL-CHcalc|

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

2.00

4.00

6.00

8.00

10.00

12.00



Titrant volume (mL)

pH

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-6.0E-04

-4.0E-04

-2.0E-04

0.0E+00

2.0E-04

4.0E-04

6.0E-04 Residues (CH,RNL - CH,calc)

Titrant volume (mL)

CH

RN

L-C

Hc

alc

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02

1.0E-01 Residues (pH - pHRNL) To update click Overlay curve (B20)

Titrant volume (mL)

pH

RN

L-p

H

J4


J5


J6


G11

Gutz: Do not include the concentration of HCl or any other strong acid as a variable to be fitted by the Solver. The pH data of a titration is to far from the pKa of these acids (below zero, impossible to reach in aqueous medium) thus the fitted value will be meaningless. The concentration of HCl or other strong acids is obtained indirectly, at cell I14. As a check, you may write the regression result for I14 in cell G11; the result shoul be compatible.

I12

Gutz: Summation of the undissociated H+ at the initial pH for all bases

I13

Gutz: Summation of the free H+ of each base, supposing that it was added to the sample protonated to neutrality, and not as a salt (e.g., H3PO4 but not H2NaPO4). As this is frequently not the case, the value can be zero or negative (e.g., NH3 or NH4OH will not only provide no protons but will borrow them from acids with lower pKa if present, or even from water) The H+ undissociated at the initial pH does not appear here but in I12.

I14

Gutz: A positive value indicates that, after satisfying the protonation needs of the bases included in the regression, there is still H+ available originated by the dissociation of a (relatively) strong acid (possibly not included in the regression due to low pKa). Writing this concentration in line 11 (G11 for HCl) should result in a null value for I14 by repeating the regression (still not fitting G11). A negative value will be observed for NaH2PO4 (or NH3), if there is no simultaneous excess of HCl. A sligthly negative or positive value (compared to I13) may well be caused by experimental data scatter. Necessary to say that by acid-base titration it is not possible do differentiate samples like: 0.1 mol/L H3PO4; 0.1 HCl + 0.1 NaH2PO4 or 0.2 HCl e 0.1 Na2HPO4. All will the same curve and a null I14. It would be necessary to measure the conc. of Cl- or Na+ to conclude about.

G16

Gutz: Total volume before titration

I17

Gutz: CH calculated for the titrand based on the initial pH (before addition of tittrant), based on concentrations (and pKas) fitted by the Solver.

I18

Gutz: Read comment in cell I19 on how to open the Solver and define the destination cell. In the field for variable cells of the Solver, write: I18 for a sample containing solely strong acid(s), what means, with pKa values lower than the region of pH covered by the titration. and the index of cells of the concentrations of acids/bases in the sample to be fitted (B11-H11, in blue). I18;B11; ... cell(s) of line 11 corresponding to the acids/bases with pKas in the explored pH region (or near it) and supposed to be present (at any protonation level). Refinement of some pKa values that are within the explored pH region can be considered in a second fitting, to adjust them to the real conditions (temperature and ionic strength) of the titration. In special cases, the concentration of components of the titrant may be also refined, e.g., the contamination with carbon dioxide. Do to data scatter, the Solver may return a message that no solution was found (to the stringent convergence criteria), but the fitted values are OK anywhere (fitting can be repeated for possible improvement). In case of convergence problems, use Escape to interrupt the regression. Start again including the smallest possible number of most relevant components, providing reasonable initial estimates of the concentrations and pKas. Convergence criteria can be changed in the Solver setup. 200 iteractions and 50 seconds is a good default.

I19

Gutz: This blue cell I19 is the Destination cell of the Solver (Office 2007) Data / Analysis / ? (Solver) (older Office) Tools/Solver Configure the second line of the setup box: Equal to: Value: 0 (zero). Destination cell (to be minimized): I19 Variable cells: I18 and cells of line 11 corresponding to acids/bases supposedly present in the sample, separated by a semicolon. pKas cab also be fitted, but see I18 and F1. (you can also hold down Ctrl and click on all cells to be fitted). At the first regression, enter the Solver Options and check the box ordering the program to fit only positive values. Adjust other options, if required or to see if there is any improvement in the regression. If the Solver is not listed in Tools of Excel (2003) or Data / Analysis (Excel 2007), proceed as follows: (Excel 97-2003) - Close CURTIPOT - Open a blank form - Click Tools/Supplements - Mark the Solver box and install it - If the file is not on the hard disk, locate it on the Office installation CD - Once Solver appears on the Tools list, load Curtipot again This procedure is required only once on a computer. (Excel 2007) - Click on the Windows button (upper left corner) - Click on the Excel options at the last line - Look for suplements and load the Solver like described above.

I20

Gutz: For scattered data, minimisation of the modulus of the residues (instead of the squares of the residues) should be considered sometimes because if there are outliers, their weigth will be lower in the regression and a better general fit may be obained (compare the residues graphs).

Ready for 100 real or simulated data points; to expand range to 160, copy all columns from line 141 down to 200

CHcalc Dill. Titrant Dil Titrand

mol/L mol/l mol/L

2.538E-04 1.81E-01 1.80E-01 0.0000 1.0000-2.981E-06 1.73E-01 1.73E-01 0.0429 0.9571-2.567E-04 1.65E-01 1.65E-01 0.0853 0.9147-3.677E-04 1.57E-01 1.58E-01 0.1289 0.87114.972E-04 1.49E-01 1.49E-01 0.1735 0.8265-1.196E-04 1.41E-01 1.41E-01 0.2172 0.78281.105E-04 1.34E-01 1.34E-01 0.2584 0.7416-1.403E-04 1.27E-01 1.27E-01 0.2968 0.7032-6.273E-05 1.21E-01 1.21E-01 0.3324 0.66761.809E-04 1.15E-01 1.14E-01 0.3656 0.6344-5.291E-04 1.09E-01 1.09E-01 0.3965 0.60355.084E-05 1.04E-01 1.04E-01 0.4248 0.57523.319E-06 9.93E-02 9.93E-02 0.4499 0.55011.207E-04 9.54E-02 9.53E-02 0.4715 0.52851.985E-04 9.21E-02 9.19E-02 0.4896 0.51041.503E-04 8.95E-02 8.93E-02 0.5044 0.49561.889E-04 8.72E-02 8.71E-02 0.5167 0.48339.715E-06 8.53E-02 8.53E-02 0.5277 0.4723-1.191E-04 8.34E-02 8.35E-02 0.5381 0.46192.385E-05 8.15E-02 8.15E-02 0.5485 0.45151.504E-04 7.97E-02 7.95E-02 0.5588 0.4412-5.838E-05 7.79E-02 7.80E-02 0.5685 0.43158.530E-06 7.64E-02 7.64E-02 0.5770 0.4230-5.160E-05 7.51E-02 7.52E-02 0.5839 0.4161-7.722E-05 7.42E-02 7.43E-02 0.5891 0.41097.511E-08 7.35E-02 7.35E-02 0.5928 0.40723.428E-05 7.31E-02 7.30E-02 0.5953 0.4047-4.537E-06 7.28E-02 7.28E-02 0.5970 0.4030-7.804E-07 7.26E-02 7.26E-02 0.5981 0.40191.992E-06 7.24E-02 7.24E-02 0.5988 0.4012-3.141E-05 7.23E-02 7.24E-02 0.5992 0.40081.438E-05 7.23E-02 7.23E-02 0.5995 0.4005-1.155E-05 7.23E-02 7.23E-02 0.5998 0.40022.805E-06 7.22E-02 7.22E-02 0.5999 0.40018.263E-06 7.22E-02 7.22E-02 0.6000 0.4000-2.285E-05 7.22E-02 7.22E-02 0.6002 0.39987.184E-06 7.21E-02 7.21E-02 0.6003 0.39975.985E-06 7.21E-02 7.21E-02 0.6006 0.3994-4.691E-07 7.20E-02 7.20E-02 0.6010 0.3990-2.816E-06 7.19E-02 7.19E-02 0.6015 0.39852.690E-05 7.18E-02 7.17E-02 0.6024 0.39761.057E-05 7.15E-02 7.15E-02 0.6038 0.3962-1.794E-05 7.11E-02 7.12E-02 0.6059 0.3941-6.975E-06 7.06E-02 7.06E-02 0.6091 0.3909-4.392E-06 6.97E-02 6.97E-02 0.6137 0.38639.761E-05 6.85E-02 6.84E-02 0.6204 0.3796-1.514E-04 6.69E-02 6.70E-02 0.6295 0.37052.605E-04 6.46E-02 6.44E-02 0.6419 0.3581

CHRNL-CHcalc CHRNL

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2.00

4.00

6.00

8.00

10.00

12.00



Titrant volume (mL)

pH

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02


Titrant volume (mL)

pH

RN

L-p

H

G39

Gutz: Residue (difference) of the total H+ concentration fitted with the Solver (column H) and the calculated one by the general equation (column I).

H39

Gutz: Value of the H+ concentration fitted by the Solver by minimization of the squares of the residues (column E) (or of the residues modulus (column F)), taking dilution in consideration.

I39

Gutz: Total concentration of H+ required to satisfy all protonation equilibria, using the general equation, the concentrations of line 11 and the pKas given or under refinement.

J39

Gutz: Dilution factor of the titrant when added to the sample (+water). For example, when the added titrant equals the volume ofthe sample (+water), the factor is 0.5

K39

Gutz: Dilution factor of the sample by optional addition of water (at the beginning) and addition of titrant during the experiment

-2.814E-04 6.16E-02 6.19E-02 0.6585 0.34157.979E-05 5.75E-02 5.74E-02 0.6814 0.3186-2.497E-04 5.16E-02 5.18E-02 0.7143 0.2857

1.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.00001.81E-01 1.18E+00 0.0000 1.0000

Click on K2 to Q2; select acids/bases; click on J2; other options, read M1

8 31 1 2 6

Phosphoric acid Ascorbic acid Acetic acid Ammonia HCl

-3 -2 -1 0 -1

2.148 4.100 4.757 9.244 -7.000

7.199 11.790

12.350

Correction of the pH sensor calibration

7.0000 intersection (may be fitted)

1.0000 slope (fittable, read comment)

Alternatively, minimize with Solver (instead of I19)

of the acids and bases in the solution

negative results are possible)

from non-fitted HiB (e.g., a strong acid), if any.

RNL + concentrations (line 11, in blue)

+ optionally, pKas

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-6.0E-04

-4.0E-04

-2.0E-04

0.0E+00

2.0E-04

4.0E-04

6.0E-04 Residues (CH,RNL - CH,calc)

Titrant volume (mL)

CH

RN

L-C

Hc

alc

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02


Titrant volume (mL)

pH

RN

L-p

H

M1

Gutz: Options for selecting/editing names, charges and pKas: a) Write directly in the cells K3 to Q10 and R3 to T6 (ignoring line 2 settings); b) Click on names in line 2, slide along the list, click on another name (or a blank line); finally, click on J2 to load the constants from the Database; c) When applicable (see comments F1 and I18) , refine the pKas loaded by options a or b, by including them in the regression. Frequently used acids missing in the Database should be added to it.

N11

Gutz: Systematic departure of fitted curves from the experimental ones may have various (combined) causes, such as: i) Inaccurate calibration of the sensor (unreliable buffer solutions, temperature different from specified); ii) Deviation from Nersntian reponse and/or alkalyne error of the glass electrode; Possible compensation of errors i) and ii) - inclusion of N12 and N13 as variable cells in the Solver, at a refinement stage of the fitting. iii) Standardization errors of the titrant or decomposition/contamination (CO2 absorption, etc.); Some improvement may be reached by the fitting CO2 contamination in the titrant. iv) Missing correction of ionic strength and temperature on activity coefficients and pKas in this Module; Most pKa values in the Database are for I=0; they can be converted to conditional pKw and pKa values for a given I in the pH_calc module, or fitted by MPNLR, if all other parameters are accurately known.

Ready for 100 real or simulated data points; to expand range to 160, copy all columns from line 141 down to 200

h1 h2 h3 h4 h5

Citric acid Phosphoric acid Ascorbic acid Acetic acid Ammonia

2.8747 2.4241 1.9851 0.9967 1.00002.8176 2.3220 1.9770 0.9948 1.00002.7414 2.2342 1.9648 0.9920 1.00002.6420 2.1623 1.9455 0.9875 1.00002.5034 2.1014 1.9100 0.9787 1.00002.3906 2.0696 1.8702 0.9682 1.00002.2600 2.0440 1.8054 0.9495 1.00002.1478 2.0286 1.7271 0.9236 1.00002.0353 2.0178 1.6252 0.8833 1.00001.9209 2.0106 1.5070 0.8236 1.00001.8233 2.0065 1.4092 0.7587 1.00001.6851 2.0027 1.2924 0.6523 1.00001.5535 1.9999 1.2073 0.5428 1.00001.4131 1.9969 1.1397 0.4244 1.00001.2782 1.9933 1.0917 0.3142 0.99991.1579 1.9884 1.0600 0.2245 0.99991.0428 1.9808 1.0382 0.1527 0.99980.9417 1.9704 1.0252 0.1050 0.99970.8356 1.9546 1.0164 0.0703 0.99960.7077 1.9274 1.0100 0.0441 0.99930.5735 1.8864 1.0062 0.0274 0.99880.4588 1.8365 1.0041 0.0182 0.99820.3390 1.7600 1.0025 0.0113 0.99720.2450 1.6697 1.0016 0.0073 0.99560.1708 1.5644 1.0010 0.0047 0.99310.1109 1.4406 1.0006 0.0028 0.98870.0704 1.3240 1.0003 0.0017 0.98150.0470 1.2382 1.0002 0.0011 0.97200.0299 1.1633 1.0000 0.0007 0.95590.0188 1.1082 0.9999 0.0004 0.93080.0138 1.0815 0.9998 0.0003 0.90780.0066 1.0404 0.9994 0.0002 0.82440.0053 1.0322 0.9993 0.0001 0.78810.0028 1.0171 0.9986 0.0001 0.66350.0016 1.0095 0.9975 0.0000 0.53410.0016 1.0091 0.9974 0.0000 0.52420.0007 1.0028 0.9942 0.0000 0.32850.0005 1.0004 0.9912 0.0000 0.24210.0003 0.9982 0.9867 0.0000 0.17370.0002 0.9954 0.9792 0.0000 0.11790.0001 0.9910 0.9657 0.0000 0.07420.0001 0.9857 0.9483 0.0000 0.04960.0000 0.9776 0.9221 0.0000 0.03260.0000 0.9642 0.8807 0.0000 0.02060.0000 0.9441 0.8226 0.0000 0.01300.0000 0.9120 0.7403 0.0000 0.00800.0000 0.8723 0.6529 0.0000 0.00530.0000 0.8022 0.5275 0.0000 0.0032

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02


Titrant volume (mL)

pH

RN

L-p

H

L39

Gutz: Average number of protons associated with the base B1 at the given pH

0.0000 0.7295 0.4262 0.0000 0.00210.0000 0.6215 0.3114 0.0000 0.00130.0000 0.5115 0.2239 0.0000 0.00082.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.00002.9993 2.9929 1.9999 1.0000 1.0000

Click on K2 to Q2; select acids/bases; click on J2; other options, read M1

3 Titrant Titrand

Carbonic acid Strong ACID Strong BASE Carbonic ac. Acid / Base Citric acid

-2 -1 -1 -2 Charge of B -3

6.352 -6 15.745 6.352 2.489E+06

10.329 10.329 1.435E+11

1.928E+14

pKw 10E-10

13.9970 10E-10

10E-10

Color coding




Overall protonation constants = bp = PKp (calculated by the program)

bp1

bp2

bp3

bp4

bp5

bp6

S2

Gutz: The titrant may contain up to three diprotic reagents (other than the default ones). Names and constants must be changed manually.

R3

Gutz: Strong acids like HCl ou HClO4 have negative pKas, possibly -6 or lower. For a diprotic titrant like H2SO4, use pKa1 = -6 e pKa2 = 1,8. Do not specify systems with more than 2 pKas here.

S3

Gutz: The accepted value of the pKa (=log Kp) of the strong base OH- is 15,745 at 25ºC and infinite dilution. As I increases, the activity coefficient of OH- decreases (as can be checked with module pH_calc), and more specific interaction can occur with cations, so that lower values are sometimes mentioned in the literature (see references in the Database for details). Any other mono or biprotonable acid or base can be used instead of OH-

T3

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. But any othe mono- or biprotic system can be specified here. The pKa1 from the Database for for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa1 of 3.58 is found.

U5

Gutz: Blank cells were filled with an insignificant dummy constant 10-10 for calculation convenience. The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up to n, the maximum number of protons accepted by a (conjugated) base (same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 (complete references in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.

R8

Gutz: The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25ºC, the accepted value is 13.997 (or 14.00). Values corrected for I can be calculated in module pH_calc.

h6 h7 h1 titrant h2 titrant h3 titrant

HCl Carbonic acid Strong ACID Strong BASE Carbonic ac. -5.26E-02

0.0000 1.9999 0.0000 1.0000 1.9999 0.01090.0000 1.9999 0.0000 1.0000 1.9999 -0.00010.0000 1.9998 0.0000 1.0000 1.9998 -0.01080.0000 1.9997 0.0000 1.0000 1.9997 -0.01440.0000 1.9994 0.0000 1.0000 1.9994 0.01840.0000 1.9992 0.0000 1.0000 1.9992 -0.00440.0000 1.9986 0.0000 1.0000 1.9986 0.00410.0000 1.9979 0.0000 1.0000 1.9979 -0.00540.0000 1.9967 0.0000 1.0000 1.9967 -0.00240.0000 1.9946 0.0000 1.0000 1.9946 0.00720.0000 1.9920 0.0000 1.0000 1.9920 -0.02160.0000 1.9866 0.0000 1.0000 1.9866 0.00220.0000 1.9790 0.0000 1.0000 1.9790 0.00020.0000 1.9667 0.0000 1.0000 1.9667 0.00650.0000 1.9475 0.0000 1.0000 1.9475 0.01250.0000 1.9193 0.0000 1.0000 1.9193 0.01120.0000 1.8764 0.0000 1.0000 1.8764 0.01600.0000 1.8220 0.0000 1.0000 1.8220 0.00090.0000 1.7486 0.0000 1.0000 1.7486 -0.01080.0000 1.6446 0.0000 1.0000 1.6446 0.00210.0000 1.5259 0.0000 1.0000 1.5259 0.01330.0000 1.4210 0.0000 1.0000 1.4210 -0.00550.0000 1.3103 0.0000 1.0000 1.3103 0.00090.0000 1.2234 0.0000 1.0000 1.2234 -0.00720.0000 1.1550 0.0000 1.0000 1.1550 -0.01440.0000 1.0998 0.0000 1.0000 1.0998 0.00000.0000 1.0623 0.0000 1.0000 1.0623 0.01380.0000 1.0402 0.0000 1.0000 1.0402 -0.00270.0000 1.0232 0.0000 1.0000 1.0232 -0.00070.0000 1.0109 0.0000 1.0000 1.0109 0.00290.0000 1.0042 0.0000 1.0000 1.0042 -0.06540.0000 0.9888 0.0000 1.0000 0.9888 0.05110.0000 0.9831 0.0000 1.0000 0.9831 -0.05360.0000 0.9625 0.0000 1.0000 0.9625 0.01710.0000 0.9345 0.0000 1.0000 0.9345 0.05090.0000 0.9320 0.0000 1.0000 0.9320 -0.12930.0000 0.8567 0.0000 1.0000 0.8567 0.02730.0000 0.7956 0.0000 1.0000 0.7956 0.01560.0000 0.7191 0.0000 1.0000 0.7191 -0.00080.0000 0.6192 0.0000 1.0000 0.6192 -0.00320.0000 0.4936 0.0000 1.0000 0.4936 0.01910.0000 0.3883 0.0000 1.0000 0.3883 0.00490.0000 0.2906 0.0000 1.0000 0.2906 -0.00560.0000 0.2035 0.0000 1.0000 0.2035 -0.00140.0000 0.1383 0.0000 1.0000 0.1383 -0.00060.0000 0.0898 0.0000 1.0000 0.0898 0.00970.0000 0.0611 0.0000 0.9999 0.0611 -0.01110.0000 0.0372 0.0000 0.9999 0.0372 0.0138

pH - pHRNL

0.0000 0.0251 0.0000 0.9999 0.0251 -0.01110.0000 0.0154 0.0000 0.9998 0.0154 0.00220.0000 0.0099 0.0000 0.9996 0.0099 -0.00470.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.00000.0000 2.0000 0.0000 1.0000 2.0000

Ascorbic acid Acetic acid Ammonia HCl Carbonic acid

-3 -2 -1 0 -1 -2

2.239E+12 6.166E+11 5.715E+04 1.754E+09 1.000E-07 2.133E+10

3.540E+19 7.762E+15 10E-10 10E-10 10E-10 4.797E+16

4.977E+21 10E-10 10E-10 10E-10 10E-10 10E-10

10E-10 10E-10 10E-10 10E-10 10E-10 10E-10

10E-10 10E-10 10E-10 10E-10 10E-10 10E-10

10E-10 10E-10 10E-10 10E-10 10E-10 10E-10

Overall protonation constants = bp = PKp (calculated by the program)

Phosphoric acid

Titrant Click on J2 to use these pKas in the Regression

Strong ACID Strong BASE Carbonic ac. Acid / Base Citric acid

-1 -1 -2 Charge of B -3 -3

1.000E-06 5.559E+15 2.133E+10 3.128 2.148

10E-10 10E-10 4.797E+16 4.761 7.199

6.396 12.350

Kw

1.01E-14


Titrand

Phosphoric acid

pKa1 = logKpn

pKa2 = logKpn-1

pKa3 = logKpn-2

pKa4 = logKpn-3

pKa5 = logKpn-4

pKa6 = logKpn-5

AF2


AF5

Gutz: See U5 to understand why pKa1 = logKpn

Click on J2 to use these pKas in the Regression

Ascorbic acid Acetic acid Ammonia HCl Carbonic acid

-2 -1 0 -1 -2

4.100 4.757 9.244 -7.000 6.352

11.790 10.329

Titration curves and first derivatives overlay

Source of data to plot/overlay

1 0 0 0

0 0 1 1

1 0 0 1

0.0 10.0 20.0 30.0 40.0 50.0 60.00

2

4

6

8

10

12

14 Titration curve(s) and/or derivative(s)

Titrant Volume (mL)

pH

DpH

/DV

Simulador dpH/dV Simulador c/ dispersão dpH/dV

Analise I

Analise II

dpH/dV Analise I c/alisamento dpH/dV

dpH/dV Analise II c/ajuste dpH/dV

How to change the axis of a curve Data ID on curves

How to copy/paste a curve

Update curve(s) on any change in Simulation, Evaluation or Regression

0.0 10.0 20.0 30.0 40.0 50.0 60.00

2

4

6

8

10

12

14 Titration curve(s) and/or derivative(s)

Titrant Volume (mL)

pH

DpH

/DV

O3

Gutz: Uncheck and check a curve again to update it.

L4


O4


L5

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word o Excel) without links to the original: - Fill out the header of the graphic - Click in the box of the graphic near the margins, to select it - Replot at least one curve (uncheck / check again) - Press Ctrl+C and wait processing - Switch to the other Office document - Select Insert/Paste Special/Picture (enhanced metafile)

Simulation Simulation with dispersion (random errors)Vol pH Vol dpH/dVol Vol pH Vol dpH/dVol Vol

0 1.80593272.1570917 2.02043534.0960384 2.23493795.7539624 2.4494405

7.077085 2.66394328.0608041 2.87844588.7492476 3.09294849.2095434 3.3074519.5078177 3.52195369.6974923 3.73645629.8172889 3.95095889.8936795 4.1654614

9.944385 4.37996419.9815251 4.594466710.014129 4.808969310.050161 5.023471910.098345 5.237974510.170081 5.452477110.281694 5.666979710.457025 5.881482310.729794 6.09598511.143875 6.3104876

11.74754 6.524990212.576545 6.739492813.625773 6.953995414.824492 7.16849816.043755 7.383000617.145787 7.597503218.040535 7.812005918.705899 8.0265085

19.16921 8.241011119.477513 8.4555137

19.676958 8.6700163

19.804374 8.884518919.886334 9.099021519.941236 9.313524119.981976 9.528026820.018398 9.742529420.059441 9.95703220.115237 10.17153520.199536 10.386037

20.332999 10.6005420.548016 10.81504220.896024 11.02954521.458622 11.24404822.364653 11.4585523.818284 11.67305326.154666 11.88755529.983217 12.10205836.643807 12.316561

50 12.531063

Evaluation Evaluation with smoothing/interpolation Regression raw datapH Vol dpH/dVol Vol pH Vol dpH/dVol Vol pH

0 2.262843 0 2.2808280.505051 2.278105 0.252525 0.030219 0.896889 2.4714171.010101 2.296272 0.757576 0.035971 1.864139 2.6624661.515152 2.320249 1.262626 0.047475 2.96058 2.8605852.020202 2.352942 1.767677 0.064731 4.198095 3.0949882.525253 2.397254 2.272727 0.087738 5.548356 3.2735313.030303 2.454185 2.777778 0.112724 6.970387 3.4831263.535354 2.518213 3.282828 0.126775 8.440223 3.6744164.040404 2.582421 3.787879 0.127133 9.957523 3.8778454.545455 2.639895 4.292929 0.113798 11.52783 4.0878325.050505 2.685782 4.79798 0.090857 13.14204 4.2595045.555556 2.727971 5.30303 0.083534 14.76872 4.4838216.060606 2.779204 5.808081 0.101442 16.35673 4.6824086.565657 2.851413 6.313131 0.142973 17.84478 4.8893597.070707 2.942587 6.818182 0.180525 19.18178 5.0960087.575758 3.039096 7.323232 0.191089 20.35167 5.2953258.080808 3.136852 7.828283 0.193556 21.38416 5.5011588.585859 3.259046 8.333333 0.241944 22.34269 5.6875899.090909 3.488134 8.838384 0.453595 23.297 5.878136

9.59596 3.981049 9.343434 0.975971 24.29235 6.09340610.10101 4.803839 9.848485 1.629124 25.32645 6.30686810.60606 5.54874 10.35354 1.474904 26.34764 6.49015311.11111 5.988962 10.85859 0.871639 27.28033 6.69847911.61616 6.215154 11.36364 0.447861 28.06266 6.89212212.12121 6.333082 11.86869 0.233497 28.66975 7.08658112.62626 6.415374 12.37374 0.162937 29.11192 7.30271613.13131 6.482656 12.87879 0.133219 29.41908 7.51833513.63636 6.545299 13.38384 0.124033 29.62548 7.70387214.14141 6.606289 13.88889 0.12076 29.76118 7.90832314.64646 6.667766 14.39394 0.121724 29.84931 8.11499115.15152 6.728696 14.89899 0.12064 29.90639 8.25063615.65657 6.786415 15.40404 0.114284 29.94375 8.572292

16.16162 6.838272 15.90909 0.102678 29.96912 8.673532

16.66667 6.88349 16.41414 0.089531 29.98786 8.94923417.17172 6.924402 16.91919 0.081007 30.00398 9.18458517.67677 6.963639 17.42424 0.077688 30.02098 9.20191918.18182 7.003827 17.92929 0.079572 30.04253 9.55459418.68687 7.047217 18.43434 0.085913 30.07328 9.73971519.19192 7.095174 18.93939 0.094955 30.11979 9.92132819.69697 7.148936 19.44444 0.106448 30.19183 10.1180920.20202 7.209739 19.94949 0.12039 30.30418 10.34027

20.70707 7.278429 20.45455 0.136007 30.47903 10.5265121.21212 7.351573 20.9596 0.144825 30.74903 10.7167121.71717 7.423101 21.46465 0.141626 31.16063 10.9217722.22222 7.486905 21.9697 0.126331 31.77711 11.1236422.72727 7.536913 22.47475 0.099018 32.68142 11.3351323.23232 7.571308 22.9798 0.068101 33.98339 11.5156623.73737 7.596314 23.48485 0.049511 35.84641 11.7421224.24242 7.619052 23.9899 0.045023 38.56744 11.9191324.74747 7.64661 24.49495 0.054564 42.78071 12.1345825.25253 7.68377 25 0.073577 50 12.3299825.75758 7.73166 25.50505 0.09482126.26263 7.791081 26.0101 0.11765326.76768 7.862903 26.51515 0.14220827.27273 7.948185 27.0202 0.16885927.77778 8.048515 27.52525 0.19865528.28283 8.170411 28.0303 0.24135328.78788 8.344293 28.53535 0.34428729.29293 8.689172 29.0404 0.6828629.79798 9.341411 29.54545 1.29143430.30303 10.20212 30.05051 1.70419430.80808 10.802 30.55556 1.18777431.31313 11.10381 31.06061 0.59758931.81818 11.23449 31.56566 0.25874332.32323 11.29197 32.07071 0.11379832.82828 11.33626 32.57576 0.08770933.33333 11.38428 33.08081 0.09506933.83838 11.44539 33.58586 0.12101234.34343 11.51749 34.09091 0.14275834.84848 11.59131 34.59596 0.14614835.35354 11.65745 35.10101 0.13096935.85859 11.70797 35.60606 0.10001636.36364 11.74341 36.11111 0.0701836.86869 11.76754 36.61616 0.04777237.37374 11.78411 37.12121 0.03280437.87879 11.79687 37.62626 0.02527638.38384 11.80959 38.13131 0.02518738.88889 11.82522 38.63636 0.03094639.39394 11.84383 39.14141 0.03684339.89899 11.86484 39.64646 0.04159940.40404 11.88767 40.15152 0.04521440.90909 11.91176 40.65657 0.04768941.41414 11.93652 41.16162 0.04902341.91919 11.96137 41.66667 0.04921642.42424 11.98575 42.17172 0.04826942.92929 12.00908 42.67677 0.0461843.43434 12.03092 43.18182 0.04325543.93939 12.05132 43.68687 0.04038644.44444 12.07038 44.19192 0.03773844.94949 12.08821 44.69697 0.0353145.45455 12.10493 45.20202 0.033103

45.9596 12.12065 45.70707 0.03111746.46465 12.13547 46.21212 0.029352

46.9697 12.14951 46.71717 0.02780747.47475 12.16289 47.22222 0.026483

47.9798 12.17571 47.72727 0.02537948.48485 12.18808 48.23232 0.024497

48.9899 12.20012 48.73737 0.02383549.49495 12.21193 49.24242 0.023393

50 12.22364 49.74747 0.023173

Regression raw data Regression fitted curveVol dpH/dVol Vol pH Vol dpH/dVol

0.448444 0.2240981.380514 0.207715

2.41236 0.1834463.579338 0.1627044.873226 0.1491966.259372 0.1418657.705305 0.1374469.198873 0.13316510.74268 0.12876912.33493 0.12510913.95538 0.12418715.56273 0.12705417.10076 0.13556118.51328 0.15072119.76673 0.17220120.86791 0.19449421.86342 0.20919322.81984 0.20982223.79468 0.20112

24.8094 0.19408325.83705 0.19677126.81399 0.215593

27.6715 0.25755128.3662 0.332484

28.89084 0.45765229.2655 0.659608

29.52228 0.98556829.69333 1.50677529.80525 2.36370229.87785 3.66708429.92507 5.64038

29.95644 8.73928

29.97849 11.621629.99592 12.4803230.01248 11.2149930.03176 8.45459230.05791 6.0298630.09654 4.12794630.15581 2.73042330.24801 1.748924

30.3916 1.13489330.61403 0.74059830.95483 0.48735531.46887 0.32548432.22927 0.22272933.33241 0.154696

34.9149 0.10826237.20693 0.07410240.67408 0.0478246.39035 0.027878

Database of dissociation constants of acids / protonation constants of bases

Most constants given in this compilation of ~250 systems – but not all – were obtained at 25º C and are thermodynamic ones (I=0), as required by the pH_calc module.

More systems, e.g., from the sources given next, can be added: a) at the end of the list; b) in alphabetic order by inserting line(s) and redoing the sequential numbering (column B).

Larger compilations of equilibrium constants and examples of on-line literature on acid-base equilibrium

Martell, A. E., Smith, R. M., Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976.

Perrin, D. D., Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965; Supplement, 1972.

Serjeant, E. P., and Dempsey, B., Ionization Constants of Organic Acids in Aqueous Solution, Pergamon, Oxford, 1979.

Albert, A., "Ionization Constants of Heterocyclic Substances", in Physical Methods in Heterocyclic Chemistry, Katritzky, A. R., Ed., Academic Press, New York, 1963.

Perrin, D. D., Dempsey, B., and Serjeant, E. P., pKa Prediction for Organic Acids and Bases, Chapman & Hall, London, 1981.

Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M., Data for Biochemical Research, Oxford Science Publications, Oxford, 1986.

Dissociation constants of inorganic and organic compounds (compliation with 33 pages)

Dissociation constants of organic compounds (~600 compounds)

Visual Indicators for acid-base titrations

Activity coefficient estimation:an appreciation of 20 equations: Ionic St_effects.pdf in the package: http://www.iupac.org/projects/2000/Aq_Solutions.zip

Ácid or Base Charge, fully

deprotonated

F R E Q U E N T L Y U S E D 1 Acetic acid -1 4.7572 Ammonia 0 9.2443 Carbonic acid -2 6.352 10.3294 Citric acid -3 3.128 4.761 6.3965 EDTA -4 0 1.5 26 HCl -1 -77 Hydroxide ion -1 15.7458 Phosphoric acid -3 2.148 7.199 12.359

1011 A L P H A B E T I C O R D E R Insert new lines anywere to add more systems; renumber column B12 Acetamide 0 0.6313 Acetic acid -1 4.75714 Acetoacetic acid -1 3.5815 Acrylic acid -1 4.2516 Adipic acid -2 4.43 5.4117 Alanine -1 2.348 9.86718 Aminobenzene = aniline 0 4.619 2-Aminobenzoic acid -1 2.108 4.94620 4-Animobenzoic acid -1 2.501 4.87421 2-Aminobutanoic acid -1 2.29 9.8322 6-Aminohexanoic acid -1 4.373 10.80423 5-Aminopentanoic acid -1 4.27 10.76624 2-Aminophenol -1 4.78 9.9725 -1 3.55 10.2426 Ammonia 0 9.24427 Aniline 0 4.63

No guarantee is given that the compiled pKas or the calculations made with CurTiPot are correct or accurate. CurTiPot takes in account only protonation equilibria and other chemical reactions can occur for many combinations of two or more of the listed systems.

The module pH_calc estimates gi using the Davies equation:

pKa1 pKa2 pKa3

b-Alanine

A3

Gutz: Gray or red numbers denote knowingly uncertain pKas; the number os decimal places is indicative of precision, but values may be wrong or innacurate; for many systems, the "constants" vary from author to author or depend of the experimental technique used to study the equilibria. For other systems, no reliable determination is available.

A5

Gutz: Attention: some extensive compilations of equilibrium constants present protonation constants (or their logarithms) instead of dissociation constants. The conversion is straightforward as shown in cells M12-M18.

D19

Gutz: Charge of the most deprotonated (dissociated) form of the (conjugated) base considered in the equilibria of an acid-base system for the constants given.

E20

Gutz: Uncertain pKa values are displayed in gray; very uncertain values, in red.

C24

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. The pKa1 for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa of 3.58 is found.

E24

Gutz: This is the aparent pKa. By considering that only a part of the dissolved CO2 is converted in H2CO3 and part remains as CO2(aq), the "true" pKa would be 3.58

B28

Gutz: Soluções aquosas expostas ao ar ou armazenadas em frascos plásticos (permeáveis a gases) apresentam grau variável de contaminação com CO2 (que pode se acumular na forma de bicarbonato ou carbonato em soluções alcalinas, com consumo de hidróxido). Recomenda-se, pois, incluir sempre este sistema na análise de titulações por regressão, bem como na simulação de curvas, principalmente para titulados e titulantes diluídos (<0,01 mol/L). O pKa1 aparente do H2CO3 apresentado ao lado engloba o equilíbrio entre o gás carbônico hidratado, dissolvido como tal, CO2(aq), e a pequena fração convertida em H2CO3; o pKa "verdadeiro" é 3,58.

28 Arginine -1 1.823 8.991 12.4829 Arsenic acid -3 2.24 6.96 11.530 Arsenous acid -1 9.2231 Ascorbic acid -2 4.1 11.7932 Asparagine -1 2.14 8.7233 Aspartic acid -2 1.99 3.9 10.00234 Barbital 0 7.4335 Barbituric acid -1 4.0136 Benzenesulfonic acid -1 0.737 Benzoic acid -1 4.1938 Benzylamine 0 9.3339 2-Benzylpyridine 0 5.1340 Betaine -1 1.8341 Boric acid -3 9.236 12.74 13.842 Butanoic acid -1 4.8343 3-Butenoic acid -1 4.3444 Butylamine 0 10.7745 sec-Butylamine 0 10.5646 tert-Butylamine 0 10.6847 Cadaverine 0 10.05 10.9348 Carbonic acid -2 6.352 10.32949 Catechol -2 9.4 12.850 Chloroacetic acid -1 2.86551 2-Chloroaniline 0 2.6552 3-Chloroaniline 0 3.4653 4-Chloroaniline 0 4.1554 2-Chlorobenzoic acid -1 2.9255 3-Chlorobenzoic acid -1 3.8256 4-Chlorobenzoic acid -1 3.9857 3-Chlorophenol -1 8.8558 4-Chlorophenol -1 9.1859 2-Chlorophenol -1 8.4960 Choline 0 13.961 Chromic acid -2 –0,2 6.5162 Citric acid -3 3.128 4.761 6.39663 Codeine 0 8.2164 Creatinine 0 4.83 9.265 m-Cresol -1 10.0166 O-Cresol -1 10.267 p-Cresol -1 10.1768 Cupferron -1 4.1669 Cyanic acid -1 3.4670 Cysteine -2 1.71 8.36 10.7771 Decylamine 0 10.6472 2,4-Diaminobutanoic acid -1 1.85 8.24 10.4473 Dichloroacetic acid -1 1.374 2,3-Dichlorophenol -1 7.4675 Diethylamine 0 10.93376 Diisopropylamine 0 11.0577 Dimethylamine 0 10.77478 Dimethylglyoxime -2 10.66 12.079 2,3-Dimethylpyridine 0 6.5880 2,4-Dimethylpyridine 0 6.9981 2,5-Dmethylpyridine 0 6.4

E69

Gutz: Este é o pKa aparente que engloba o equilíbrio entre o gás carbônico hidratado, dissolvido como tal, CO2(aq), e a pequena fração convertida em H2CO3; o pKa "verdadeiro" é 3,58.

82 2,6-Dimethylpyridine 0 6.6583 3,4-Dimethylpyridine 0 6.4684 3.5-Dimethylpyridine 0 6.1585 Dinicotinic acid -1 2.886 Diphenylamine 0 0.7987 Dipicolinic acid -2 2.16 4.7688 Dopamine -1 8.9 10.689 d-Ephedrine 0 10.13990 Ethanolamine 0 9.591 Ethylamine 0 10.63692 Ethylenediamine 0 6.848 9.92893 Ethylenediaminetetraacet -4 0 1.5 294 Ethyleneimine 0 8.0195 2-Ethylpyridine 0 5.8996 Formic acid -1 3.74597 Fumaric acid -2 3.053 4.49498 L-Glutamic acid -1 2.23 4.42 9.9599 L-Glutamine -1 2.17 9.13

100 L-Glutathione -2 2.12 3.59 8.75101 Glyceric acid -1 3.52102 Glycerol -1 14.15103 Glycine -2 2.35 9.778104 Glycolic acid -1 3.831105 Glyoxylic acid -1 3.18106 Heptanedioic acid -1 4.71107 Heptanoic acid -1 4.89108 Heptylamine 0 10.67109 Hexamethylenediamine 0 11.857 10.762110 Hexanoic acid -1 4.85111 Hexylamine 0 10.56112 Histamine 0 6.04 9.75113 Histidine -1 1.7 6.02 9.08114 Hydrazine 0 8.07115 Hydroazoic -1 4.72116 Hydrogen bromide -1 -9117 Hydrogen chloride -1 -7

118 Hydrogen chromate ion -1 6.52119 Hydrogen cyanide -1 9.21120 Hydrogen fluoride -1 3.17121 Hydrogen peroxide -1 11.65

122 Hydrogen selenate ion -1 1.66123 Hydrogen sulfide -2 7.02 13.9124 Hydrogen thiocyanate -1 0.9125 Hydroquinone 0 10.35126 Hydroxylamine 0 5.96127 m-Hydroxybenzoic acid -2 4.06 9.92128 p-Hydroxybenzoic acid -2 4.48 9.32129 3-Hydroxypropanoic acid -1 4.51130 8-Hydroxyquinoline -1 4.91 9.81131 Hypobromous -1 8.63132 Hypochlorous -1 7.53133 Hypoiodous -1 10.64134 Imidazole 0 6.953135 Iodic acid -1 0.77

136 Isocitric acid -3 3.29 4.71 6.4137 Isoleucine -1 2.319 9.754138 Lactic acid -1 3.86139 l-Ephedrine 0 9.958140 l-Leucine -1 2.328 9.744141 Lysine -1 2.04 9.08 10.69142 Maleic acid -2 1.91 6.332143 Malic acid -2 3.459 5.097144 Malonic acid -2 2.847 5.696145 Melamine = 1,3,5-triazine- 0 5146 Methionine = (S)-2-amino- -1 2.13 9.27147 Methylamine 0 10.63148 2-Methylaniline = o-toui 0 4.447149 4-Methylaniline = p-tolui 0 5.084150 2-Methylbenzimidazole 0 6.19151 2-Methylbutanoic acid -1 4.8152 3-Methylbutanoic acid -1 4.77153 Methylmalonic acid -2 3.07 5.76154 Methyl-1-naphthylamine 0 3.67155 4-Methylpentanoic acid -1 4.84156 1-Methylpiperidine 0 10.08157 2-Methylphenol = o-creso -1 10.28158 4-Methylphenol = p-creso -1 10.26159 2-Methylpyridine 0 5.97160 3-Methylpyridine 0 5.68161 4-Methylpyridine 0 6.02162 Morphine 0 8.21163 Morpholine 0 8.33164 1-Naphthol -1 9.34165 2-Naphthol -1 9.51166 Nicotine 0 8.02 3.12167 Nitrilotriacetic acid -3 1.1 1.65 2.94168 2-Nitroaniline 0 -0.26169 3-Nitroaniline 0 2.466170 4-Nitroaniline 0 1171 2-Nitrobenzoic acid -1 2.179172 2-Nitrophenol -1 7.21173 3-Nitrophenol -1 8.39174 4-Nitrophenol -1 7.15175 3-Nitrobenzoic acid -1 3.449176 4-Nitrobenzoic acid -1 3.442177 Nitrous acid -1 3.15178 Noradrenaline -1 8.64 9.7179 Octadecylamine 0 10.6180 Octanedioic acid -1 4.52181 Octanoic acid -1 4.89182 Oxalic acid -2 1.252 4.266183 Oxaloacetic acid -2 2.22 3.89 13.03184 Papaverine 0 6.4185 Pentanoic acid -1 4.84186 Perchloric acid -1 -10187 p-Periodic acid -2 1.55 8.28188 1,10-Phenanthroline 0 4.84189 m-Phenetidine 0 4.18

190 o-Phenetidine 0 4.43191 Phenol -1 9.98192 Phenylacetic acid -1 4.28193 Phenylalanine -1 2.2 9.31194 Phenylethylamine 0 9.84195 Phenylglycine -1 1.83 4.39196 Phosphoric acid -3 2.148 7.199 12.35197 m-Phthalic acid -2 3.54 4.6198 o-Phthalic acid -2 2.95 5.408199 p-Phthalic acid -2 3.51 4.82200 Picolinic acid -2 1.07 5.25201 Picric acid -1 0.38202 Pilocarpine 0 6.87203 Piperazine 0 9.83 5.56204 Piperidine 0 11.123 7.53205 p-Phenetidine 0 5.2206 Proline -1 1.952 10.64207 Propanoic acid -1 4.874208 Propylamine 0 10.566209 Purine 0 2.3 8.96210 Pyridine 0 5.229211 3-Pyridinecarboxylic acid -1 4.85212 4-Pyridinecarboxylic acid -1 4.96213 Pyrimidine 0 6.35214 Pyrocatechol -2 9.4 12.8215 Pyrophosphoric -4 1.52 2.36 6.6216 Pyrrolidine 0 11.27217 Pyruvic acid -1 2.39218 Quinine 0 8.52 4.13219 Quinoline 0 4.9220 Resorcinol -2 9.3 11.06221 Saccharin -1 11.68222 Salicylic acid -2 2.97 13.74223 Selenic acid -1 1.92224 Selenous acid -2 2.64 8.28225 Serine -1 2.19 9.05226 o-Silicic acid -2 9.66 11.7227 m-Silicic acid -2 9.7 12228 Strychnine 0 8.26229 Succinic acid -2 4.207 5.636230 Sulfuric acid -2 -3 1.99231 Sulfurous acid -2 1.91 7.18232 d-Tartaric acid -2 3.036 4.366233 meso-Tartaric acid -2 3.22 4.82234 Terephthalic acid -1 3.51235 Thiazole 0 2.44236 Thioacetic acid -1 3.33237 Thiosulfuric acid -2 0.6 1,6 3238 Threonine -1 2.088 9.1239 m-Toluic acid -1 4.27240 o-Toluic acid -1 3.91241 p-Toluic acid -1 4.36242 Trichloroacetic acid -1 0.66243 Triethanolamine 0 7.762

244 Triethylamine 0 10.715245 Trimethylacetic acid -1 5.03246 Trimethylamine 0 9.8247 Tris(hydroxymethyl)- amin 0 8.075248 Tryptophan -1 2.35 9.33249 Tyramine 0 9.74 10.52250 Tyrosine -1 2.17 9.19 10.47251 Urea 0 0.1252 Uric acid -1 3.89253 Valine -1 2.286 9.718254255256257258259260261262263264265266267268269270271272273274275276277278279280

Database of dissociation constants of acids / protonation constants of bases


More systems, e.g., from the sources given next, can be added: a) at the end of the list; b) in alphabetic order by inserting line(s) and redoing the sequential numbering (column B).

Larger compilations of equilibrium constants and examples of on-line literature on acid-base equilibrium

Martell, A. E., Smith, R. M., Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976. Tutorial on acids and bases

Perrin, D. D., Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965; Supplement, 1972. Properties of acids and bases

Serjeant, E. P., and Dempsey, B., Ionization Constants of Organic Acids in Aqueous Solution, Pergamon, Oxford, 1979. Measurement of pH. Definitions, Standards and Procedures (IUPAC - 2002)

Albert, A., "Ionization Constants of Heterocyclic Substances", in Physical Methods in Heterocyclic Chemistry, Katritzky, A. R., Ed., Academic Press, New York, 1963. Temperature dependence of potassium hydrogen phtalate 0.05 mol/kg buffer

Perrin, D. D., Dempsey, B., and Serjeant, E. P., pKa Prediction for Organic Acids and Bases, Chapman & Hall, London, 1981. Primiary standard buffer solutions pH at various temperatures

Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M., Data for Biochemical Research, Oxford Science Publications, Oxford, 1986.

Conversion of dissociation constants of acids in protonation constants of their conjugated bases

Activity coefficient estimation:an appreciation of 20 equations: Ionic St_effects.pdf in the package: http://www.iupac.org/projects/2000/Aq_Solutions.zip

where I, the ionic stregth is:

Temperat. Ionic

ºC strength Formula

25 0 CH3COOH25 0 NH325 0 H2CO325 0 H3C6H5O7

2.68 6.11 10.17 25 0.1 C10H16N2O8

25 0 NaOH25 0 H3PO4

Insert new lines anywere to add more systems; renumber column B Find more values in the references and links25 0 C2H5NO 25 0 CH3COOH18 0 C4H6O3 25 0 C3H4O2 25 0 C6H10O4 25 0 C3H7NO225 0 C6H7N25 0 C7H7NO2 25 0 C7H7NO2 25 0 C4H9NO2 25 0 C6H13NO2 25 0 C5H11NO2 20 0 C6H7NO25 0 C3H7NO2 25 0 NH325 0 C6H7N

is given that the compiled pKas or the calculations made with CurTiPot are correct or accurate. CurTiPot takes in account only protonation equilibria and other chemical reactions can occur for many combinations of two or more of the listed systems.

http://research.chem.psu.edu/brpgroup/pKa_compilation.pdf

http://www.zirchrom.com/organic.htm pKa1 = logKpn

http://www.beloit.edu/~chem/Chem220/indicator/ pKa2 = logKpn-1

pKa3 = logKpn-2

pKa4 = logKpn-3

pKa5 = logKpn-4

pKa6 = logKpn-5

pKa4 pKa5 pKa6

http://research.chem.psu.edu/brpgroup/pKa_compilation.pdf

http://www.zirchrom.com/organic.htm

http://www.beloit.edu/~chem/Chem220/indicator/

L12

Gutz: Protonation constants, Kp, (or global protonation constants, bp) are preferred in the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants. Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. The index n inKpn is the maximum number protons accepted by the most deprotonated form of a (conjugated) base.

M20

Gutz: The structural formula of most of the acids and bases listed here can be found in the Wikipedia, en.wikipedia.org

25 0 C6H14N4O2 25 0 H3AsO4

0 H3AsO3 24 0 C6H8O6 25 0.1 C4H8N2O3 25 0 C4H7NO4 25 0 C8H12N2O3 25 0 C4H4N2O3 25 0 C6H6O3S 25 0 C7H6O2 25 0 C7H9N 25 0 C12H11N 0 0 C5H11NO2

20 0 H3BO325 0 C4H8O2 25 0 C4H6O2 20 0 C4H11N 25 0 C4H11N 25 0 C4H11N 25 0 C5H14N2 25 0 H2CO325 0 C6H4(OH)225 0 ClCH2COOH25 0 C6H6CIN 25 0 C6H6CIN 25 0 C6H6CIN 25 0 C7H5CIO2 25 0 C7H5CIO2 25 0 C7H5CIO2 25 0 C6H5CIO 25 0 C6H5CIO 25 0 C6H5CIO 25 0 C5H14NO 20 0 H2CrO425 0 H3C6H5O7 25 0 C18H21NO3 25 0 C4H7N3O 25 0 C7H8O 25 0 C7H8O 25 0 C7H8O 25 0.1 C6H6N2O

HCNO 25 0 C3H7NO2S 25 0 C10H23N 25 0 C4H10N2O2 25 0 Cl2CHCOOH25 0 C6H4Cl2O 25 0 (CH3CH2)2NH25 0 C6H15N 25 0 (CH3)2NH25 0 C4H12O2N225 0 C7H9N 25 0 C7H9N 25 0 C7H9N

25 0 C7H9N 25 0 C7H9N 25 0 C7H9N 25 0 C7H5NO4 25 0 C12H11N 25 0 C7H5NO4 25 0 C8H11NO2 10 0 C10H15NO 25 0 C2H7NO 25 0 CH3CH2NH225 0 H2NCH2CH2NH2

2.68 6.11 10.17 25 0.1 C10H16N2O825 0 C2H5N 25 0 C7H9N 20 0 HCOOH25 0 C4H4O4 25 0 C5H9NO4 25 0 C5H10N2O3

9.65 25 0 C10H17N3O6S 25 0 C3H6O4 25 0 C3H8O3 25 0 H2NCH2COOH25 0 HOCH2COOH25 0 C2H2O3 25 0 C7H12O4 25 0 C7H14O2 25 0 C7H17N 0 0 C6H16N2

25 0 C6H12O2 25 0 C6H15N 25 0 C5H9N3 25 0.1 C6H9N3O2 30 N2H4

HN3 HIHCl

25 0 HCN25 0 HF25 0 H2O2

25 0 H2S25 0 HSCN20 C6H6O2 25 0 NH2OH19 0 C7H6O3 19 0 C7H6O3 25 0 C3H6O3 25 025 0 HOBr25 0 HOCl25 0 HOI25 0 C3H4N2 25 0 HIO3

HCrO4-

HSeO4-

25 0 C6H8O7 25 0 C6H13NO2

HC3H5O3 10 0 C10H15NO 25 0 C6H13NO2 25 0.1 C6H14N2O2 25 0 C4H4O4 25 0 C4H6O5 25 0 HOOCCH2COOH25 0 C3H6N6 25 0 C5H11NO2S 25 0 CH5N 25 0 C7H9N25 0 C7H9N25 0 C8H8N2 25 0 C5H10O2 25 0 C5H10O2 25 0 C4H6O4 27 0 C11H11N 18 0 C6H12O2 25 0 C6H13N 25 0 C7H8O 25 0 C7H8O 20 0 C6H7N 20 0 C6H7N 20 0 C6H7N 25 0 C17H19NO3 25 0 C4H9NO 25 0 C10H8O 25 0 C10H8O 25 0 C10H14N2

10.334 20 025 0 C6H6N2O2 25 0 C6H6N2O2 25 0 C6H6N2O2 25 0 C7H5NO4 25 0 C6H5NO3 25 0 C6H5NO3 25 0 C6H5NO3 25 0 C7H5NO4 25 0 C7H5NO4 25 0 HNO225 0 C8H11NO3 25 0 C18H39N 25 0 C8H14O4 25 0 C8H16O2 25 0 C2H2O4 25 0 C4H4O5 25 0 C20H21NO4 25 0 C5H10O2

HClO4H5IO6

25 0 C12H8N2 25 0 C8H11NO

28 0 C8H11NO 25 0 HC6H5O 18 0 C8H8O2 25 0 C9H11NO2 25 0 C8H11N 25 0 C8H9NO2 25 0 H3PO425 0 C8H6O4 25 0 C8H6O4 25 0 C8H6O4 25 0 C6H5NO2

C6H3N3O7 30 0 C11H16N2O2 23 0 C4H10N2 25 0 C5H11N28 0 C8H11NO 25 0 C5H9NO225 0 CH3CH2COOH25 0 CH3CH2CH2NH220 0 C5H4N4 25 0 C5H5N25 0 C6H5NO2 25 0 C6H5NO2 20 0 C11H8N2 20 0 C6H6O2

9.25 H4P2O7 25 0 C4H9N 25 0 C3H4O3 25 0 C20H24N2O2 20 0 C9H7N 25 0 C6H6O2 18 0 C7H5NO3S 25 0 C7H6O3 25 0 H2SeO4

0 H2SeO3 25 0 C3H7NO3

H4SiO4H2SiO3

25 0 C21H22N2O2

25 0 H2SO4 25 0 H2SO325 0 C4H6O6 25 0 C4H6O6 25 0 C8H6O4 20 0 C3H3NS 25 0 C2H4OS 25 0 H2S2O325 0 C4H9NO325 0 C8H8O2 25 0 C8H8O2 25 0 C8H8O2 25 0.1 Cl3CCOOH25 0

HOOCCH2CH2COOH

(HOCH2CH2)3N

25 0 (CH3CH2)3NH25 0 C5H10O2 25 0 (CH3)3NH25 0 (HOCH2)3CNH325 0.1 C11H12N2O2 25 0 C8H11NO 25 0 C9H11NO3 21 0 CH4N2O 12 0 C5H4N4O3 25 0 C5H11NO2


Tutorial on acids and bases http://achpc50.chemie.uni-karlsruhe.de/Cours%20de%20Chris%20Anson/OHP8acids.doc

Properties of acids and bases http://ptcl.chem.ox.ac.uk/MSDS/msds-searcher.html

Measurement of pH. Definitions, Standards and Procedures (IUPAC - 2002) http://www.iupac.org/publications/pac/2002/pdf/7411x2169.pdf

Temperature dependence of potassium hydrogen phtalate 0.05 mol/kg buffer http://nvl.nist.gov/pub/nistpubs/jres/081/1/V81.N01.A03.pdf

Primiary standard buffer solutions pH at various temperatures http://nvl.nist.gov/pub/nistpubs/jres/066/2/V66.N02.A06.pdf

Conversion of dissociation constants of acids in protonation constants of their conjugated bases

Molar mass

g/mol

60.05217.026

192.027

292.09

97.976

59.06760.052

102.08972.063

146.14389.094

93.13137.138137.138

17.026

is given that the compiled pKas or the calculations made with CurTiPot are correct or accurate. CurTiPot takes in account only protonation equilibria and other chemical reactions can occur for many combinations of two or more of the listed systems.

Overall protonation constants = bp = SKp

N19

Gutz: Molecular weight calculator Java Applet: http://www.ch.cam.ac.uk/magnus/MolWeight.html

184.19128.09

110.1

153.18165.23

116.07147.13146.15

75.07

68.08

131.18

165.23

31.1107.17107.17

108.14108.14

180.3

166.14166.14

208.259

85.15

115.13

120.1179.1

110.1177.98

88.06324.42129.16

110.1

138.12

105.09

334.41118.09

98.0882.07

150.09150.09

119.12

http://achpc50.chemie.uni-karlsruhe.de/Cours%20de%20Chris%20Anson/OHP8acids.doc

http://ptcl.chem.ox.ac.uk/MSDS/msds-searcher.html

http://www.iupac.org/publications/pac/2002/pdf/7411x2169.pdf

http://nvl.nist.gov/pub/nistpubs/jres/081/1/V81.N01.A03.pdf

http://nvl.nist.gov/pub/nistpubs/jres/066/2/V66.N02.A06.pdf

a pH calculator

a Data Analyzer

» titration curves and derivatives are presented graphically for visual inspection/evaluation or for printing or pasting in other documents;

a Virtual Titrator

» user selectable increments of pH, volume and titration speed;

» overlay of curves (>10) for visualization of the effect of changing parameters;

» unlimited generation of different titration curves for drilling exercises and students' examinations.

a Distribution Diagram Generator

a pKa Database

Installation and Use

What's inside CurTiPot?

» fast pH calculation of any aqueous solution of acids, bases and salts, including buffers, zwitterionic

» pH values are estimated with help of the Davies equation, from p[H] values iteractively computed with an accurate

» fractional distribution, activities and apparent dissociation constants of all species at equilibrium are displayed

» input data: pH vs. volume simulated with the Virtual Titrator, read on the pH-meter during a potentiometric titration with a combined glass electrode as sensor, or imported/pasted from external source (e.g., automatic titrator);

» inflection points (end points or equivalence points) of the curves are displayed automatically, one at a time, with

» determination of multiple concentrations and refinement of pKa values by multiparametric least squares nonlinear

» simulation of pH vs. volume titration curves of any aqueous solution of acids, bases and mixtures;

» simulation of "near real" data tables and plots with random errors (Gaussian distribution) in pH and/or volume, to test data analysis procedures;

» distribution diagrams (alpha plots) of mono or multiprotic acids or bases showing the fractional contribution of each protonated and unprotonated species in equilibrium, plotted against pH (helpful to locate isoelectric points of amino acids);

» distribution curves plotted against volume of titrant, with overlayed titration curve, revealing the principal species at the inflections and the contribution of each species at any stage of the titration;

» protonation curves of acids or bases showing the average number of protons bound to the Bronsted-Lowry (or Lewis) base as a function of pH as well as volume of titrant (with overlayed titration curve).

» equilibrium constants of some 250 acids and bases (see list) are already available in this user-expandable database.

» pH_calc, Simulation and Regression modules with quick loading of pKas of 1 to 7 acids-base systems automatically from the Database.

CurTiPot is released as freeware for personal, educational and non-commercial use; for other applications, contact the author (copyright holder).Download the most recent version of CurTiPot from this page <www2.iq.usp.br/docente/gutz/Curtipot_.html>. Various download sites confirm that CurTiPot is safe and free of virus, spyware and addware. There is

Remarks and Limitations

Ion-ion iteraction corrections are disregarded in the simulation, evaluation and regression modules of the current CurTiPot version. This is not a problem because volumes of well defined end points (stoichiometric or equivalence points) of titration curves are unaffected by the little vertical shifts caused by the use of “pH” instead of pH.

Bug reports and suggestions welcomed by e-mail [email protected].

Examples and Comments

The program is helpful also for other tasks like determining the amount of acid or base required to neutralize a sample (neutralization), to prepare or displace the pH of a buffer, to change color of a visual indicator, to find the isoelectric point of amino acids, etc.

If no action occurs when clicking on CurTiPot's buttons, habilitate macros in Excel 2007 or adjust Excel 97-2003 to medium security (Tools / Options / Security / Macro security / Security Level / Medium) and reload CurTiPot, allowing the activation of macros (required for iterative computing of pH, distribution curves generation, smoothing, etc.). All worksheets have embedded instructions and comments, expandable by the user. The worksheet with the Regression module uses the Solver supplement of Excel - provided by Microsoft with the Office package. In the menu Tools/Supplements/Solver, check the Solver box, search for the file on the HD or load it from the Office installation disk.

CurTiPot uses the Solver as a chemometric tool for the determination of concentrations and pKas of acids and bases from titration data by

The Brönsted and Lowry concept is used to define acids and bases and the protonation-deprotonation equilibrium is considered instantaneous. No other type of chemical reaction or phase transition is taken into account in the calculations made by CurTiPot, although they will occur for many combinations of acids and bases of the Database. The pH Calculator estimates activity coefficients with help of the Davies equation. This is necessary at increased ionic strength, I, because ion-ion interactions reduce the activity coefficients (gamma) of all ions including the hydrated protons, H+, and pH is strictly defined as -log a[H+] (where a[H+] is the activity of hydrated protons, see definition of pH).The Davies equation gives reasonable estimates over a wider range of I then the Debye Hückel equation, but is not as good as the Pitzer equation or other ones that take in account individual hydrated ion-size parameters and ion-ion association constants (not readily available for all acids and bases in the Database) or include fitted parameters for a given electrolyte. Besides pH, the pH Calculator also displays the p[H] and the "pH". Both correspond to -log [H+] with the difference that "pH" is computed (like in high school) with thermodynamic constants (strictly valid only at I=0), while the constants used in the p[H] calculation (and pH as well) are previously corrected for ion-ion interaction by the Davies equation.

The author provides you the freeware on an "as is" basis, with no warranties, express or implied, and reserves the right not to be responsible for the correctness, completeness, accuracy and error-free operation of CurTiPot. The author has introduced no spyware, adware, viruses or any form of malicious code in the program, as checked and assured by many of the distributors of the software (see list).

The all-in-one modular and interactive design of CurTiPot is user-friendly and lets you rapidly calculate the pH of any aqueous solution, from the simplest to the most complex one.The

Introduce your experimental data pairs of volume of titrant and pH directly into the spreadsheet of the

A background in chemometrics, statistics or numerical data analysis is valuable but not essential to profitably explore the power and recognize the limits of the Regression module, in special, for data untreatable by graphical and linearization methods (Gran plot). For example, with

http://www2.iq.usp.br/docente/gutz/Curtipot_Regression.gif

http://en.wikipedia.org/wiki/PH

http://www2.iq.usp.br/docente/gutz/Curtipot-.html#Sites

» titration curves and derivatives are presented graphically for visual inspection/evaluation or for printing or pasting in other documents;

» unlimited generation of different titration curves for drilling exercises and students' examinations.

buffers, zwitterionic amino acids, from single component to complex mixtures (30 or more species in equilibrium);

values iteractively computed with an accurate general equation (instead of the simple Henderson-Hasselbalch equation);

» fractional distribution, activities and apparent dissociation constants of all species at equilibrium are displayed.

simulated with the Virtual Titrator, read on the pH-meter during a potentiometric titration with a combined glass electrode as sensor, or imported/pasted from external source (e.g., automatic titrator);

(end points or equivalence points) of the curves are displayed automatically, one at a time, with interpolation and controlled smoothing (cubic splines);

by multiparametric least squares nonlinear regression - this feature is essential for very diluted and/or complex samples that exhibit titration curves with undefined inflections, eg., acid rain.

of any aqueous solution of acids, bases and mixtures;

(Gaussian distribution) in pH and/or volume, to test data analysis procedures;

(alpha plots) of mono or multiprotic acids or bases showing the fractional contribution of each protonated and unprotonated species in equilibrium, plotted against pH (helpful to locate isoelectric points of amino acids);

plotted against volume of titrant, with overlayed titration curve, revealing the principal species at the inflections and the contribution of each species at any stage of the titration;

of acids or bases showing the average number of protons bound to the Bronsted-Lowry (or Lewis) base as a function of pH as well as volume of titrant (with overlayed titration curve).

» equilibrium constants of some 250 acids and bases (see list) are already available in this user-expandable database.

modules with quick loading of pKas of 1 to 7 acids-base systems automatically from the Database.





for the determination of concentrations and pKas of acids and bases from titration data by multiple nonlinear least squares regression.



The all-in-one modular and interactive design of CurTiPot is user-friendly and lets you rapidly calculate the pH of any aqueous solution, from the simplest to the most complex one.The Virtual Titrator

Introduce your experimental data pairs of volume of titrant and pH directly into the spreadsheet of the Evaluation module. Do it point by point during the titration in the laboratory, or afterwards. Select the

A background in chemometrics, statistics or numerical data analysis is valuable but not essential to profitably explore the power and recognize the limits of the Regression module, in special, for data untreatable by graphical and linearization methods (Gran plot). For example, with




, from single component to complex mixtures (30 or more species in equilibrium);

simulated with the Virtual Titrator, read on the pH-meter during a potentiometric titration with a combined glass electrode as sensor, or imported/pasted from external source (e.g., automatic titrator);

- this feature is essential for very diluted and/or complex samples that exhibit titration curves with undefined inflections, eg., acid rain.

(alpha plots) of mono or multiprotic acids or bases showing the fractional contribution of each protonated and unprotonated species in equilibrium, plotted against pH (helpful to locate isoelectric points of amino acids);

plotted against volume of titrant, with overlayed titration curve, revealing the principal species at the inflections and the contribution of each species at any stage of the titration;

of acids or bases showing the average number of protons bound to the Bronsted-Lowry (or Lewis) base as a function of pH as well as volume of titrant (with overlayed titration curve).







Virtual Titrator makes the simulation of the titration curve of any acid, base or mixture a breeze; flexibility in the selection of sample size, concentration of ingredients, titration range, type, size and speed of titrant addition and dispersion of the "measurements" give great realism to the process. Quick loading of dissociation constants and one-click data transfer from the

module. Do it point by point during the titration in the laboratory, or afterwards. Select the smoothing factor of the spline that shows the most accurate interpolation of the endpoints (stoichiometric points or equivalence points) on the derivative curves.You will be pleasantly surprised with the effectiveness of spline smoothing for volumetric titration curves with clearly defined inflections and with the power of the Regression module to deal with more difficult data analysis. Try the

A background in chemometrics, statistics or numerical data analysis is valuable but not essential to profitably explore the power and recognize the limits of the Regression module, in special, for data untreatable by graphical and linearization methods (Gran plot). For example, with Regression, minute concentrations of some acidic and basic components in




CurTiPot is released as freeware for personal, educational and non-commercial use; for other applications, contact the author (copyright holder).Download the most recent version of CurTiPot from this page <www2.iq.usp.br/docente/gutz/Curtipot_.html>. Various download sites confirm that CurTiPot is safe and free of virus, spyware and addware. There is no need to install (or uninstall) CurTiPot. Simply run the Microsoft Excel





makes the simulation of the titration curve of any acid, base or mixture a breeze; flexibility in the selection of sample size, concentration of ingredients, titration range, type, size and speed of titrant addition and dispersion of the "measurements" give great realism to the process. Quick loading of dissociation constants and one-click data transfer from the

that shows the most accurate interpolation of the endpoints (stoichiometric points or equivalence points) on the derivative curves.You will be pleasantly surprised with the effectiveness of spline smoothing for volumetric titration curves with clearly defined inflections and with the power of the Regression module to deal with more difficult data analysis. Try the

Regression, minute concentrations of some acidic and basic components in acid rain samples titrated with strong base can be determined individually or grouped as follows: strong acids (H




(or uninstall) CurTiPot. Simply run the Microsoft ExcelTM software and open the curtipot_.xls file like any other spreadsheet. All preprogrammed equations and Visual Basic macros are self-contained, and completely removed when closing CurTiPot. No functions are added to Excel.



makes the simulation of the titration curve of any acid, base or mixture a breeze; flexibility in the selection of sample size, concentration of ingredients, titration range, type, size and speed of titrant addition and dispersion of the "measurements" give great realism to the process. Quick loading of dissociation constants and one-click data transfer from the


samples titrated with strong base can be determined individually or grouped as follows: strong acids (H2SO4 + HNO3), weak carboxylic acid (formic + acetic), bicarbonate (H



software and open the curtipot_.xls file like any other spreadsheet. All preprogrammed equations and Visual Basic macros are self-contained, and completely removed when closing CurTiPot. No functions are added to Excel.



makes the simulation of the titration curve of any acid, base or mixture a breeze; flexibility in the selection of sample size, concentration of ingredients, titration range, type, size and speed of titrant addition and dispersion of the "measurements" give great realism to the process. Quick loading of dissociation constants and one-click data transfer from the Virtual Titrator to any of the data analysis modules -


), weak carboxylic acid (formic + acetic), bicarbonate (H2CO3/HCO3-/CO3=) and ammonium ion (NH4+/NH3) (FORNARO, A.; GUTZ, I.G.R., Wet deposition and related atmospheric chemistry in the São Paulo metropolis, Brazil. Part 3: Trends in precipitation chemistry during 1983–2003, Atmospheric Environment, 2006, 40(30), 5893-5901). In principle, CurTiPot can simulate any titration curve in aqueous medium regardless of the number of mixed acid-base systems in equilibrium (within limitations given above). The program is frequently downloaded by users looking for the simulation and evaluation of titration curves of diprotic and triprotic



software and open the curtipot_.xls file like any other spreadsheet. All preprogrammed equations and Visual Basic macros are self-contained, and completely removed when closing CurTiPot. No functions are added to Excel.



to any of the data analysis modules - Evaluation and Regression - make it easy to compare a "graphical" or empirical method with the numerical one in a matter of seconds! This is great for learning and teaching as well as for the optimization of new titrations.

that shows the most accurate interpolation of the endpoints (stoichiometric points or equivalence points) on the derivative curves.You will be pleasantly surprised with the effectiveness of spline smoothing for volumetric titration curves with clearly defined inflections and with the power of the Regression module to deal with more difficult data analysis. Try the Regression module to obtain the best possible estimation of the concentrations (and pKas) of species involved in protonation chemical equilibria. The chemometric approach of

/NH3) (FORNARO, A.; GUTZ, I.G.R., Wet deposition and related atmospheric chemistry in the São Paulo metropolis, Brazil. Part 3: Trends in precipitation chemistry during 1983–2003, Atmospheric Environment, 2006, 40(30), 5893-5901). In principle, CurTiPot can simulate any titration curve in aqueous medium regardless of the number of mixed acid-base systems in equilibrium (within limitations given above). The program is frequently downloaded by users looking for the simulation and evaluation of titration curves of diprotic and triprotic




- make it easy to compare a "graphical" or empirical method with the numerical one in a matter of seconds! This is great for learning and teaching as well as for the optimization of new titrations.

module to obtain the best possible estimation of the concentrations (and pKas) of species involved in protonation chemical equilibria. The chemometric approach of multiparametric least-squares nonlinear regression

) (FORNARO, A.; GUTZ, I.G.R., Wet deposition and related atmospheric chemistry in the São Paulo metropolis, Brazil. Part 3: Trends in precipitation chemistry during 1983–2003, Atmospheric Environment, 2006, 40(30), 5893-5901). In principle, CurTiPot can simulate any titration curve in aqueous medium regardless of the number of mixed acid-base systems in equilibrium (within limitations given above). The program is frequently downloaded by users looking for the simulation and evaluation of titration curves of diprotic and triprotic



- make it easy to compare a "graphical" or empirical method with the numerical one in a matter of seconds! This is great for learning and teaching as well as for the optimization of new titrations.

multiparametric least-squares nonlinear regression is effective when all relevant pKas fall within (or near outside) the pH range covered by your titration data.




is effective when all relevant pKas fall within (or near outside) the pH range covered by your titration data.




) (FORNARO, A.; GUTZ, I.G.R., Wet deposition and related atmospheric chemistry in the São Paulo metropolis, Brazil. Part 3: Trends in precipitation chemistry during 1983–2003, Atmospheric Environment, 2006, 40(30), 5893-5901). In principle, CurTiPot can simulate any titration curve in aqueous medium regardless of the number of mixed acid-base systems in equilibrium (within limitations given above). The program is frequently downloaded by users looking for the simulation and evaluation of titration curves of diprotic and triprotic amino acids. We have used CurTiPot, eg., to simulate and feed pH vs. titrant volume values to a new method of analysis of conductometric titration data (COELHO, L.H.G. and GUTZ, I.G.R., Trace analysis of acids and bases by conductometric titration with multiparametric non-linear regression, Talanta, 2006,



. We have used CurTiPot, eg., to simulate and feed pH vs. titrant volume values to a new method of analysis of conductometric titration data (COELHO, L.H.G. and GUTZ, I.G.R., Trace analysis of acids and bases by conductometric titration with multiparametric non-linear regression, Talanta, 2006,


. We have used CurTiPot, eg., to simulate and feed pH vs. titrant volume values to a new method of analysis of conductometric titration data (COELHO, L.H.G. and GUTZ, I.G.R., Trace analysis of acids and bases by conductometric titration with multiparametric non-linear regression, Talanta, 2006, 69(1), 204-209).

curtipot - pka calculator

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