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METTLER TOLEDO Titrators

Validation of Titration MethodsApplication brochure 16

Det Lim

Res

Conc

Conf Lim

Conf LimCalibration Line

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V

/28 METTLER TOLEDO Validation of Titration Methods

Editorial

Dear Reader

this Application Brochure provided by METTLER TOLEDO shows you how tovalidate a titration method. The recommendations and remarks have been put to-gether by Chris Walter, Application Chemist of the Market Support AnaChem. Healso measured all the results and evaluated them.

A validation of a method brings indeed some work, but thoughtful planning andcareful preparation limit the efforts. And you win a reliable method which you dailyapply with certainty.

We got the preface by courtesy of a user in the pacific region, who is a long timeexpert in “method making”.

We wish you many successful titrations

G. Reutemann H. HuberManager Market Support Regional Market ManagerNorth East Asia

Validation of Titration Methods METTLER TOLEDO /28

Contents

Preface .................................................................................................................. 4

1 Summary .............................................................................................................. 5

2 Principle of Validation......................................................................................... 5

3 Steps of Validation and Recommended Limits ................................................. 63.1 Definition of Accuracy .......................................................................................... 6

3.2 Definition of Precision .......................................................................................... 6

3.3 Systematic Errors and Linearity ............................................................................ 7

3.3.1 Definition of Systematic Errors ............................................................................. 7

3.3.2 Definition of Linearity ........................................................................................... 7

3.4 Definition of Robustness and Ruggedness ............................................................ 8

3.5 Definition of Determination Limit ........................................................................ 9

4 Practical Hints ................................................................................................... 104.1 Preparations and Precautions............................................................................... 10

4.2 Titration Control Parameters ............................................................................... 10

4.3 Titration Evaluation Parameters .......................................................................... 10

4.4 Titration ............................................................................................................... 11

5 Possible Sources of Error .................................................................................. 11

6 Recommendations for Troubleshooting ........................................................... 12

7 Results not Conforming to Specifications ....................................................... 13

8 Examples ............................................................................................................ 148.1 Determination of Sulphuric Acid ........................................................................ 14

8.2 Titer Determination ............................................................................................. 15

8.3 Precision and Accuracy ....................................................................................... 16

8.4 Systematic Errors, Linearity ................................................................................ 17

8.5 Robustness and Ruggedness ................................................................................ 18

8.6 Determination Limit ............................................................................................ 20

8.7 Closing Remarks ................................................................................................. 21

9 Appendix 1 ......................................................................................................... 22

10 Appendix 2 ......................................................................................................... 2410.1 Assessment of Results ......................................................................................... 24

10.2 Precision versus Accuracy ................................................................................... 24

11 Glossary .............................................................................................................. 25

12 Literature ........................................................................................................... 26


Preface

In this increasingly competitive world of business, the challenge of delivering highest-qual-ity products to consumers is a must. Behind any quality product are robust analytical meth-ods that ensure accurate addition of ingredients needed to deliver what is promised.

The method must be simple yet accurate. Serious consideration must be given to the possibil-ity of the method being automated. This strategy eliminates human errors, increases produc-tivity and reduces the time needed to release the product to consumers without compromisingmethod accuracy and reproducibility hence, product quality. Of course along with all themethods simplification comes analysis cost-saving. In addition, the method must be environ-ment-friendly via reduction, if not elimination, of the conventional use of organic solvents,especially non-biodegradable and toxic chemical reagents.

Accepted protocols/SOP's followed during method validation work are generally universal,irrespective of country, industry, company or product category. The only thing that is differ-ent between them is the accuracy required, with the strictest limits applied to those productsprepared for human consumption, e.g., food and medicine.

In this brochure, METTLER TOLEDO summarizes the general method development protocols.These include accuracy, reproducibility, linearity, ruggedness and limit of determination. Eachmethod must pass all these tests, just like the consumer products for which the method will beused.


1 Summary

The goal of all measurements and determinations is to generate correct results. Correct re-sults are accurate compared to the true value and precise in their statistical deviation [1].

A detailed method is applied to obtain correct results. This method describes all the differentsteps from the sampling to the result. Whether correct results can be obtained or not with acertain method has to be validated. Validation of a method comprises tests for accuracy,precision, linearity, systematic errors, robustness/ruggedness and detection limit/determina-tion limit. So the validation of a method proves, whether or not the instruments used for thispurpose fulfill the specific requirements.

In the context of validation a variety of expressions is used. Please refer to the glossary(chapter 11) for a short definition of the expressions used in this brochure.

2 Principle of Validation

Accuracy, Precision, Linearity, Systematic Errors, Robustness/Ruggedness and Determina-tion limit are checked, considering the complete analytical procedure from taking the sampleto result calculation and documentation.

• Use of a standard substance (Primary standard) allows the assessment of accuracy.

• Statistical evaluation of multiple sample series shows precision/reproducibility.

• Varying the analyte concentration indicates the linearity and systematic errors.

• If the results show no deviations due to different analysts, time or day of analysis, instru-ments and electrodes, temperature or matrix effects, the method can be considered asrobust/rugged.

• The smallest amount of substance giving a detectable potential change with a quantifiabletitrant consumption is the detection limit. The smallest amount of sample that can be ti-trated with a good precision is the determination limit. So for the validation only thedetermination limit is needed, since it includes the detection limit.

The following application serves as a guideline, showing how a titration method can be vali-dated. As an example, the method for the determination of sulphuric acid was validated.

Recommended limits for accuracy, reproducibility and linearity are subject to the tested method.Other methods e.g. analysis of foods and drugs may require much stricter limits.


3 Steps of Validation and Recommended Limits

The titrant to be used in this validation has to be standardised first against a primary standard.Primary standards are commercially available substances with the following characteristics[1], [2], [3]:

• Clearly defined composition and high degree of purity.

• Large equivalent mass (minimizing weighing errors).

• Accurately weighable (not hygroscopic, insensitive to oxygen and/or CO2).

• Stable in solutions and easily soluble in adequate solvents.

• Rapid and stoichiometric reaction with the titrant.

See appendix 1 for typical combinations of titrant and primary standard.

3.1 Definition of Accuracy

Multiple series of standard samples or of samples with exactly known concentration are ti-trated. The analyte concentration therein should cover the complete determination range. Thesample size should be varied randomly and result in a consumption of titrant of ca. 30 to 90%of the burette volume. A refilling of the burette should be avoided.

The mean value x of each series represents the result of the titration. The difference betweenthis mean value and the true value (i.e. the known concentration) allows the determination ofaccuracy.

Recommendation:

Results obtained should not deviate from the true value by more than 0.3%.

3.2 Definition of Precision

Multiple series of a sample are titrated. Thereby the analyte concentration in the titrationbeaker should cover the complete determination range. This is done by varying the samplesize randomly so that a titrant consumption of ca. 30 to 90% of the burette volume results. Arefilling of the burette should be avoided.An outlier test according to Grubbs [1] is performed on the results of these sample series inorder to eliminate distinct outliers. Then a statistical evaluation is performed on each sampleseries to get the mean value and the relative standard deviation RSD. The RSD expresses theprecision of the method.

Recommendation:

The relative standard deviation obtained from individual samples series should not be greaterthan 0.3%.


3.3 Systematic Errors and Linearity

To discover systematic errors and the linearity of the method, the titrant consumption ob-tained in Chapter 3.2 is plotted against the respective sample size which determines the analyteconcentration per single analysis.A linear regression is performed on these data. The regression line is described by the for-mula y = a + bx , where a represents the intercept on the y-axis and b is the slope of theregression line.

3.3.1 Definition of Systematic Errors

Systematic errors of a titration are for example disturbing influences due to the method itselfor to solvent blank values.In the linear regression according to chapter 3.3 systematic errors show up as a significantdeviation of the y-axis intercept a of the regression line from the zero point coordinates (seegraph 1), i.e. asys is clearly different from zero.

Recommendation:

The systematic error asys should be smaller than 15 µL. If it can not be eliminated by optimizingthe method or the reagents, it has to be corrected for in the results calculation of the titrationmethod.

3.3.2 Definition of Linearity

Linearity expresses whether a certain method produces correct results over the interestingconcentration range [4]. In titration the analyte concentration depends on the sample concen-tration, on the sample size and on the solvent volume added for the analysis. By varying thesample size and thereby the analyte concentration, the linearity of a titration method may bedetected in the range of interest.

graph 1:

sample size

v

olum

e

asy

s


There are two practical ways to check a titration method for linearity:

A) The regression coefficient (R2) of the linear regression described in graph 1 must bebetter than a given limit, depending on the demanded accuracy for the specific determi-nation:

i.e. R2 > 0.995

B) A significant positive or negative slope b (resp ∆R/∆V) of the regression line in graph2 (results of the titration versus sample size) indicates a non-linearity of the titrationmethod, meaning that the result depends on the sample size.

Recommendation:

If ∆R/∆V is greater than 0.1%, a systematic non-linearity has to be assumed.

3.4 Definition of Robustness and Ruggedness

The ROBUSTNESS describes whether a titration method is sensitive to "hardware effects",such as different instruments (electrodes, titrators etc.), time and day of analysis, differentoperators or varying ambiental conditions in different laboratories. To check the robustness,the validation steps should be repeated with the same sample by different persons on differ-ent days and on different titrators.

This kind of check also is recommended, if unsatisfactory results are subsequently obtained:

(a) during certain steps of the validation procedure and/or

(b) during the routine application of the method.

The RUGGEDNESS describes the correctness of the results obtained under disturbed experi-mental (analytical) conditions such as different matrices (e.g. solutions, reagents etc.), othertemperatures of the analyte solution or elsewise deviating conditions. To determine rugged-ness, the same sample is titrated with and without exposure to relevant disturbances. If theresults are the same, the method is considered to be rugged against this specific influence.

graph 2:

resu

lt

non linear

sample size sample size

resu

lt

linear


The method is checked against influences likely to occur e.g. temperature deviations in aspecific laboratory or CO

2 uptake of a titrant etc.

Multiple series of samples are titrated under the condition to be evaluated. The sample sizeshould be varied in random order and result in a consumption of titrant of ca. 30 to 90% of theburette volume. Refilling of the burette should be avoided.An outlier test according to Grubbs is performed on the results of the sample series in order toeliminate distinct outliers. Then a statistical evaluation is performed on these experimentaldata. The results obtained are compared with the results obtained in the precision evaluation.If the method is rugged, there should not be any difference.

Recommendation:

In normal routine titration the deviation should not be greater than 0.3%.

3.5 Definition of Determination Limit

Since the detection limit for a specific titration method is of rather academic interest only, itis not determined in a regular validation. Though in very special cases this could change.

The determination limit is determined by titrating sample series, each with a continuouslyreduced amount of sample. The determination limit is the smallest amount of substance (mmol)or sample, which can be titrated with a good precision (RSD) of ≤ 0.3%. It can be evaluatedby intrapolation of the graph “amount of substance versus relative standard deviation”.

In normal routine titration the determination limit is not a problem, since one can simplyenlarge the sample size to get a better response from the electrode. However, this can bedifferent, if the analyte has a very low concentration in the sample.

amount of substance [mmol]

rel.

stan

d. d

ev.

[RS

D]

0.3%

determination limit

graph 3:


4 Practical Hints

4.1 Preparations and Precautions

In order to obtain good results it is essential to observe the following points:

• The primary standard must be dried in a drying oven (e.g. 2 h at 105 °C, depending on thetype of primary standard) and cooled to ambient temperature in a desiccator for at least 1hour. It should always be stored in a desiccator.

• For acid/base endpoint titrations, it is necessary to calibrate the pH electrode. Certifiedbuffers from METTLER TOLEDO may be used for this purpose.

• The experimental setup must be protected from direct sunlight and should be in thermalequilibrium with the environment.

• The analytical balance must have a vibration free standing and should be calibrated regu-larly. METTLER TOLEDO balances of the MT, AT and PR series offer FACT (FullyAutomatic Calibration Technology), which automatically executes a calibration wheneverneeded. All steps to ensure proper weighing must be observed [5].

4.2 Titration Control Parameters

The control parameters are subject to the titration performed. Titrations with primary stand-ards should be executed with the same or very similar parameters as the titrations of thesample. This is especially important for the basic settings such as [1]:

Titration mode: EndpointEquivalence point

Titrant addition: Dynamic IncrementalContinuous

Measure mode: EquilibriumFixed time interval

4.3 Titration Evaluation Parameters

The evaluation procedure is subject to the type of the titration reaction and the indication. Foracid/base titrations and by default, the standard evaluation procedure is applied.

Evaluation procedure: Standard AsymmetricMaximum MinimumSegmented


4.4 Titration

• Samples should be titrated immediately after weighing and dissolution. Enough solventmust be added to cover the sensor.

• When performing a series of titrations, the interval time between samples should be keptto a minimum.

• In sample series, the electrode as well as stirrer and temperature sensor should be rinsedbetween two measurements.

• Temperature compensation is essential for pH endpoint titrations.

5 Possible Sources of Error

• Primary standard unsuitable, impure, moist, inhomogeneous, no guaranteed primarystandard quality, contaminated (e.g. by CO

2, O

2).

• Sample size/Balance balance not accurate, air humidity too high or too low, contami-nated balance, temperature changes or gradient from titration ves-sel to balance, careless weighing, sample weight, concentration orvolume too low or too high, sample inhomogeneous, impropersampling.

• Titration vessel contaminated, unsuitable.

• Dispensing unit tube connections not tight, contaminated burette cylinder (visiblecorrosion marks), leaky piston (liquid film or crystals below thepiston), leaking burette tip, air in tubing system, three-way stop-cock leaking.

• Sample matrix effects from other species.

• Reaction kinetics too slow.

• Solvent impure (blank value), poor solubilising power, not stable, contami-nated (e.g. by CO

2, O

2), wrong pH value or ionic strength.

• Titrant impure, decomposed, contaminated (e.g. by CO2), light sensitive,

wrong pH value or ionic strength, very high or low concentration.

• Measurement unsuitable sensor type, contaminated electrode, blocked diaphragm,loose contact at connector, faulty cable, poor mixing of samplesolution, unfavourable arrangement of burette tip and electrode,excessive response time of electrode, insufficient rinsing of elec-trode and stirrer before the next titration.

• Titration parameters unsuitable titration mode, wrong measure mode parameters, titra-tion rate too fast or too slow, unsuitable evaluation procedure.


• Temperature temperature fluctuations, especially perceptible with titrants inorganic solvents, highly endothermal or exothermal reaction.

• Environmental changing, fluctuating, adverse conditions (humidity, temperature,lighting).

6 Recommendations for Troubleshooting

a) Relative Standard Deviation too high(poor reproducibility)

• Ensure complete dissolution of the weighed sample in the solvent.

• Optimise the arrangement of burette tip, electrode and stirrer.

• Regenerate or replace the electrode.

• Optimise titration parameters (see METTLER TOLEDO Application Brochures).

• Remove the burette, clean and possibly change tubing as well as piston and/or cylinder.

• Weigh the sample only after establishing a temperature equilibrium between balance, ti-tration vessel and sample.

• Increase the sample concentration if possible.

• Select bigger or smaller burette size.

• Check temperature of sample solution (e.g. use water bath).

• Optimise pH value of sample solution (e.g. add buffer).

b) Relative Systematic Deviation too high(accuracy unsatisfactory)

• Use pure solvent (without blank value), degass the water if necessary.

• Dry the primary standard substance.

• Ensure complete dissolution of the weighed sample in the solvent before titration starts.

• Visual inspection of the burette and its replacement if need be.

• Check electrode. Eventually regenerate or replace.

• Check titration parameters.

• Increase the sample concentration if possible.

• Check the balance.

• Optimise solution temperature using a water bath, and pH value adding a buffer.

• Increase concentration of sample solution if possible.

• Reduce, if not eliminate possible influences, e.g. filtration, centrifugation, extraction etc.


7 Results not Conforming to Specifications

If inaccurate or imprecise results, systematic errors, non-linearity or problems with the ro-bustness/ruggedness are found, an attempt must be made to optimise the titration method inorder to meet the required limits.In some cases it may be necessary to use an unchanged method. However, systematic errorsand non-linearity can then be compensated for in the calculations.

All non-conforming values must be reported and commented on in the validation record andthe subsequent procedure noted and explained.

If relevant deviations are found, the sections “Possible Sources of Error” and “Recommen-dations for Troubleshooting” must be checked carefully and the disturbing influences elimi-nated. It is essential to repeat the validation afterwards.

The titrators of METTLER TOLEDO have undergone various tests during development andmanufacturing. Furthermore, they have been time tested by numerous users in different ap-plications all over the world and considered to be okay. If irregular results are obtained,primary consideration should be given to the working technique of the operator or to wrongor accidentally altered titration parameters.


Sample: Sulphuric acid solution

Substance: H2SO

4 0.05 mol/L

Preparation: 40 mL deion. water

Titrant: Sodium hydroxide

c(NaOH) = 1.0 mol/L

Instruments: METTLER DL77

Option RS232

Option Temperature

Sample changer ST20A

Printer HP Deskjet

Accessories: DT120 T-sensor

Indication: DG111-SC

8 Examples

8.1 Determination of Sulphuric Acid

Method Val1 Determination of H2SO4

Version 22-Dec-1995 20:33

Title Method ID . . . . . . . . . . . . Val1 Title . . . . . . . . . . . . . . Determination of H2SO4

Date/time . . . . . . . . . . . . 22-Dec-1995 20:33Sample Number samples . . . . . . . . . . 6 Titration stand . . . . . . . . . ST20 1 Entry type . . . . . . . . . . . . Fixed volume U Volume [mL] . . . . . . . . . . 30.0 ID1 . . . . . . . . . . . . . . . H2SO4

Molar mass M . . . . . . . . . . . 98.08 Equivalent number z . . . . . . . 2 Temperature sensor . . . . . . . . TEMP APump Auxiliary reagent . . . . . . . . H2O Volume [mL] . . . . . . . . . . . 30.0Stir Speed [%] . . . . . . . . . . . . 50 Time [s] . . . . . . . . . . . . . 10Titration Titrant . . . . . . . . . . . . . NaOH Concentration [mol/L] . . . . . . 1.0 Sensor . . . . . . . . . . . . . . DG111-SC Unit of meas. . . . . . . . . . . As installed Titration mode . . . . . . . . . . EQP Predispensing 1 . . . . . . . . mL Volume [mL] . . . . . . . . 2 Titrant addition . . . . . . . DYN ∆E(set) [mV] . . . . . . . . 8.0 Limits ∆V . . . . . . . . . Absolute ∆V(min) [mL] . . . . . . 0.05 ∆V(max) [mL] . . . . . . 0.3 Measure mode . . . . . . . . . EQU ∆E [mV] . . . . . . . . . . 1.0 ∆t [s] . . . . . . . . . . . 1.0 t(min) [s] . . . . . . . . . 3.0 t(max) [s] . . . . . . . . . 15.0 Threshold . . . . . . . . . . . 3.0 Maximum volume [mL] . . . . . . 10.0 Termination after n EQPs . . . Yes n = . . . . . . . . . . . . 1 Evaluation procedure . . . . . StandardRinse Auxiliary reagent . . . . . . . . H2O Volume [mL] . . . . . . . . . . . 10.0Calculation Result name . . . . . . . . . . . H2SO4 Conc. Formula . . . . . . . . . . . . . R=Q*C/U Constant . . . . . . . . . . . . . C=M/z Result unit . . . . . . . . . . . g/L Decimal places . . . . . . . . . . 5Record Output unit . . . . . . . . . . . Printer Raw results last sample . . . . . Yes Table of values . . . . . . . . . Yes E - V curve . . . . . . . . . . . YesConditioning Interval . . . . . . . . . . . . . 1 Time [s] . . . . . . . . . . . . . 10 Rinse . . . . . . . . . . . . . . Yes Auxiliary reagent . . . . . . . H2O Volume [mL] . . . . . . . . . . 10.0Statistics Ri (i=index) . . . . . . . . . . . R1 Standard deviation s . . . . . . . Yes Rel. standard deviation srel . . . Yes Outlier test . . . . . . . . . . . YesRecord Output unit . . . . . . . . . . . Printer All results . . . . . . . . . . . Yes

METTLER TOLEDO DL70 Titrator V1.0 Mettler Toledo AGJim 4 Market Support Laboratory


8.2 Titer Determination

The titer of this NaOH (1.0 mol/L) was determined against the primary standard potassiumhydrogen phthalate (dried for 2 h at 150 °C). The following results were obtained:

Comment:

The standardization is highly reproducible and linear. Results do not depend on the sampleweight.

Number of samples: 22

Mean value x: 1.0012

Standard deviation: 9.06 • 10-4

Relative Standard Deviation: 0.0905 %

Results:

Number Size Result[ g ] [ — ]

1 0.94376 1.00112 0.69729 1.00143 1.44905 1.00154 0.76393 1.00035 1.28186 1.00126 0.91697 1.00027 1.09282 1.00158 0.61858 1.00449 1.73847 1.002410 1.32274 1.001111 1.63289 1.000812 1.17670 1.001113 0.64051 1.001814 1.52071 1.001715 1.30135 1.000416 0.72725 1.001217 1.04305 1.001018 0.62867 1.002419 1.79993 1.000920 1.68623 1.001721 1.77458 1.001022 1.38162 1.0024

Titer vs. Sample Size

0.0 0.3 0.6 0.9 1.2 1.5 1.8

0.980

0.985

0.990

0.995

1.000

1.005

1.010

1.015

1.020

1.025

1.030

1.035

1.040

1.045

1.050

y = 1.0019 - 4.160e-4x

Sample Size [g]

Tite

r


8.3 Precision and Accuracy

To assess precision and accuracy of the method, a commercially available H2SO

4 solution,

c(H2SO

4) = 0.05 mol/L, was titrated with the titrant standardized in the previous chapter,

c(NaOH) = 1 mol/L.The results were compared with the true value (compensated for a temperature of 21°C) todetermine the ACCURACY, and the PRECISION was evaluated with the standard deviationobtained from the measurements.

Comment:

Precision as well as accuracy are excellent. The requirements are easily met.

Number of samples: 12

Theoretical value: 4.9030 g/L

Mean value found: 4.90529 g/l

Deviation to theoretical: 0.00229 g/L

Relative deviation to theoretical: 0.0467%

Standard deviation: 0.04752 g/L

Relative standard deviation: 0.0968%

Results:

Number Size Result[mL] [g/L]

1 75 4.901432 34 4.908283 44 4.898034 60 4.900465 35 4.908706 44 4.906727 77 4.899128 32 4.902739 52 4.9099510 91 4.9058411 31 4.9110912 42 4.91117

123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678

Theoretical contentMean value± 0.3% from theor.content± S from meanvalue

123412341234

2 0 4 0 6 0 8 0 100

850

855

860

865

870

875

880

885

890

895

900

905

910

915

920

925

930

935

940

945

950

y = 4.9106 - 1.030e-4x R = 0.43Temperature: 21 °CTheoretical Content: 4.9030 g/LNo. of Samples: 12Mean Value: 4.90529 g/LStand. Dev.: 0.004752 g/LRel. Stand. Dev.: 0.0968%

Sample Size [mL]

H2S

O4

[g/

L]

Result H2SO4 vs. Sample Size [g/L]


8.4 Systematic Errors, Linearity

The equivalence volumes (VEQ) were plotted versus the sample size. A linear regression wasperformed on these data to determine systematic errors. In case, systematic errors manifestthemselves in a significant deviation of the y axis intercept of the regression line from thezero point coordinates (see diagram below).

Size VEQ Result [mL] [mL] [g/L]

75 7.4871 4.9014334 3.3989 4.9082844 4.3894 4.8980360 5.9885 4.9004635 3.4492 4.9087043 4.3972 4.9067277 7.6831 4.8991232 3.1953 4.9027352 5.2001 4.9099591 9.0925 4.9058431 3.1008 4.9110942 4.2011 4.91117

To determine the linearity there are two practicalways, as we said in chapter 3.3.2.

The first one is to check the regression coefficient(R2) of the linear regression above, which has tobe better than 0.995 to prove linearity. Theachieved R2 of 0.9999 proves an excellent linear-ity of the method.

The second way to determine the linearity is toplot the results of the titration (H

2SO

4 in g/L)

against the sample size, as one can see in the graphnearby. Then a linear regression is performed onthese data. A significant positive or negative slopeb of the regression line y = a + bx indicates non-linearity of the titration method, i.e. that the re-sult depends on the sample size.

2 0 4 0 6 0 8 0 100

4.85

4.86

4.87

4.88

4.89

4.90

4.91

4.92

4.93

4.94

4.95

H2S

O4

[g/

L]

y = 4.9106 - 0.000103 x

Sample Size [mL]

Result vs. Sample Size

Equivalence Volume vs. Sample Size

Equi

vale

nce

Volu

me

[m

L]

y = -0.00839 + 0.09997 xR2 = 0.9999

Sample Size [mL]0 2 0 4 0 6 0 8 0 100

0

1

2

3

4

5

6

7

8

9

10


8.5 Robustness and Ruggedness

In this example the ruggedness of the method was tested against the carbon dioxide uptake ofthe titrant only.

The uptake of carbon dioxide CO2 from ambient air is the major threat of alkaline titrants.

CO2 reacts to CO

32-. Carbonate precipitation and reduction of the strength of the titrant are

the consequences.

Other analytical influences as well as the robustness (see chap. 3.4) can be checked in asimilar way.

The ruggedness of the sulphuric acid method was evaluated by exposing the titrant to air andthereby also to CO

2. Batches of NaOH titrants were exposed to air for 1, 2, 3, 4, 5, 6, 7 days.

The CO32- content of each sample was determined by titration with sulphuric acid.

CO32--Content

Air exposure Result CO32-

[day] [mg/L]

1 25262 50263 87934 144226 206847 24568

0 2 4 6 8

0

10000

20000

30000

Air exposure [days]

Res

ult C

O 32-

[mg/

L]

Comment:

The results show a systematic error (SE) and non-linearity (NL). Presumable causes arepipetting errors when preparing the samples.

SE as well as NL are very small and well below the recommended limits.

Systematic error: 8.4 µL

Correl. coefficient R2 : 0.9999

Non linearity: 1 • 10-4 (g/L)/mL


The uptake of carbon dioxide is almost linear and very fast! After 2 days already 5 g/L CO32-

are present in the NaOH titrant. The NaOH concentration (as to OH-) thereby is reduced fromthe initial 40 g/L to ca. 37 g/L in these two days.

Each NaOH batch was then standardised against potassium hydrogen phthalate. Then it wasused as the titrant to determine the H

2SO

4 concentration. The following table shows the cor-

responding results.

Air exposure Result Theoretical Systematic Reproducibility[day] [g/L] content Deviation [%] (RSD) [%]

1 4.837 4.9017 1.31 0.0512 4.586 4.9017 6.44 0.1393 4.308 4.9020 12.11 0.1784 4.152 4.9017 15.20 0.1086 3.906 4.9040 20.35 0.162

Comment:

The method was found not to be rugged at all against exposure to air. Even the NaOH sampleexposed to air for only one day did not allow correct determinations any more.

Reason: When titrating strong acids with NaOH that contains CO32-, a typical double

jump of the titration curve is found, caused by the following reactions:

1. EQP: NaOH + H3O+ --> Na+ + 2 H2O

Na2CO3 + H3O+ --> NaHCO3 + H2O + Na+

2. EQP: NaHCO3 + H3O+ --> Na+ + 2 H2O + CO2

However, this double jump does not occur when titrating weak acids such as potassium hy-drogen phthalate, which is mainly used for the titer determination. Therefore, the carbonateerror cannot be compensated for by frequent standardization of the titrant. It is advisable toperiodically check the carbonate content by a specific titration and dispose of the titrant if asignificant amount of carbonate is found.


8.6 Determination Limit

The determination limit was examined using 0.005 mol/L NaOH. Series of 5 to 6 sampleswere run, in order to check the reproducibility (RSD) with a low amount of sample.

The results show, that in the sample with less than 0.01 mmol sulphuric acid the RelativeStandard Deviation RSD increases drastically and continuously, while the absolute standarddeviation s remains more or less constant. The uptake of CO

2 from the air is very severe in

this concentration range. Therefore the titrant has to be protected from air intake with anabsorption tube filled with NaOH on a carrier. Even then, it remains usable only for one day.

The smallest amount of sub-stance, which can be titrated witha good reproducibility of ≤ 0.3% RSD, was determined byintrapolation. As the followinggraph shows, that is about 0.01mmol H

2SO

4 per sample.

Comment:

The determination limit wasobtained with a titrant of verylow concentration, c(H

2SO

4) =

0.005 mol/L. When using thestandard NaOH solution of 1mol/L, which was employed inthe other titrations in this bro-chure, the determination limit isdefined by the resolution of theburette and not by the chemistry.

No. of Mean Value Standard Relative StandardSamples [mmol] Deviation [mmol] Deviation [%]

3 0.013135 0.000012 0.0925 0.005380 0.000022 0.4085 0.004065 0.000038 0.9446 0.002735 0.000037 1.3696 0.001335 0.000048 3.5815 0.000785 0.000031 3.945

mmol H2SO4

0.000 0.0150.0100.005

0

3

2

1

4

RSD

[%

]


8.7 Closing Remarks

It has been shown with this example how a titration method can be validated. The chosenacid/base titration gave excellent results in all areas.

The limits for different parameters or the set up of priorities in the validation process have tobe adapted by the user depending on the method and the specifications for a given task (e.g.other tests for the determination of ruggedness).

Anyway the basic course of a method validation remains the same. Thus, this example maywell serve as a guideline for further validations.


9 Appendix 1:

Standardisation of TitrantsTitrant Standard Substance Merck

OrderNo.

Solvent andAuxiliaryReagents

Intervall Protection ofTitrant / GeneralRemarks

Alkalimetry

Sodium hydroxidec(NaOH) = 1.0 mol/L

Potassium hydrogenphthalateC8H5KO4; M = 204.23Dry at: 150 °C

104876 Deion. H2O weekly Protect from CO2

(tube filled withNaOH on carrier).

Sodium hydroxidec(NaOH) = 0.1 mol/L

Potassium hydrogenphthalateC8H5KO4; M = 204.23Dry at: 150 °C

104876 Deion. H2O weekly Protect from CO2


Tetrabutyl ammoniumhydroxidec(TBAH) = 0.1 mol/L

Benzoic acidC7H6O2; M = 122.12Dry at: 105 °C

100135 Isopropanol weekly Protect from CO2


Sodium methylatec(NaOCH3) = 0.1 mol/L


100135 Methanol daily Protect from CO2


Potassium hydroxidec(KOH) = 0.1 mol/L


100135 Ethanol weekly Protect from CO2


Acidimetry

Sulfuric acidc(1 /2 H2SO4) = 0.1 mol/L

Tris(hydroxymethyl)-aminomethane [THAM]C4H11NO3; M = 121.14Dry at: 105 °C

108365 Deion. H2O Every 2weeks

Hydrochloric acidc(HCl) = 0.1 mol/L


108365 Deion. H2O Every 2weeks

Perchloric acidc(HClO4) = 0.1 mol/L


108365 Acetic acid weekly

Precipitation

Silver nitratec(AgNO3) = 0.1 mol/L

Sodium chlorideNaCl; M = 58.44Dry at: 105 °C

106405 Deion. H2Oacidify to pH3.5

Every 2weeks

Keep bottle in dark.

Barium chloridec(BaCl2) = 0.1 mol/L

Sodium sulfateNa2SO4; M = 142.05Dry at: 105 °C

106649*1)

Deion. H2OBuffer pH 4Thorin

weekly

Complexometry

Complexone IIIc(EDTA) = 0.1 mol/L

Calcium carbonateCaCO3; M = 100.09Dry at: 105 °C

102060 Deion. H2OIndicator-buffer-tablet

Every 2weeks

Use PE bottles.

Complexone VIc(EGTA) = 0.1 mol/L

Calcium carbonateCaCO3; M = 100.09Dry at: 105 °C

102060 Deion. H2OIndicator-buffer-tablet

Every 2weeks

Use PE bottles.


Titrant Standard Substance Merck

OrderNo.

Solvent andAuxiliaryReagents

Intervall Protection ofTitrant / GeneralRemarks

Redox - Titration (Reducing titrants)

Sodium thiosulfatec(Na2S2O3) = 0.1 mol/L

Potassium iodateKIO3 M = 214.00

105053 Hydrochloricacid 0.1 M

biweekly

Hydroquinonec(C6H6O2) = 0.1 mol/L

Potassium dichromateK2Cr2O7 M = 294.19

104868 Sulfuric acid5%

weekly Keep bottle in dark.

Ammonium ferrous (II)sulfatec(FAS) = 0.1 mol/L

Potassium dichromateK2Cr2O7 M = 294.19


daily Protect fromOxygen.

Redox - Titration (Oxidizing titrants)

Iron(III) chloridec(FeCl3) = 0.1 mol/L

Ascorbic acidC6H8O6; M = 176.13

100127*1)

Deion. water biweekly

Potassium dichromatec(1 /6 K2Cr2O7) = 0.1 mol/L

(CH2NH3)2SO4 • FeSO4•4H2O; M = 382.15


biweekly

Iodinec(1 /2 I2) = 0.1 mol/L

di-Arsenic trioxideAs2O3; M = 197.84

100120 Deion. waterNaHCO3

daily Keep bottle in dark.Keep in PE bottles.Keep cool.

Cerium sulfatec(Ce(SO4)2) = 0.1 mol/L

di-Sodium oxalateC2Na2O4; M=134.00

106556 Deion. waterSulfuric acid5%

biweekly

Potassium permanganatec(1 /5 KMnO4) = 0.1 mol/L

di-Sodium oxalateC2Na2O4; M=134.00

106556 Sulfuric acid5%; 70 °C

biweekly Keep bottle in dark.

Sodium nitritec(NaNO2) = 0.1 mol/L

Sulfanilic acidC6H7NO3S; M = 173.19

100686*1)

HBr0.5 mol/L

weekly

Fehling solution Glucose 1% in waterC6H12O6; M = 180.16

108337*1)

Deion. water weekly Prepare Glucosesolution daily.

2,6-Dichlorophenol-indo-phenol sodium saltc(DPI) = 0.01 mol/L

Ascorbic acidC6H8O6; M = 176.13

100127*1)

Deion. water daily Keep bottle in dark.Keep in PE bottles.Keep cool.

Turbidimetric Titrations

Sodium dodecylsulfatec(SDS) = 0.01 mol/L

N-Cetylpyridinium chlo-ride [CPC] monohydrate;M = 358.01

102340*1)

Deion. water biweekly Rinse bottle andbeakers with deion.water before use.

Hyaminec(Hyamine) = 0.01 mol/L

Sodium dodecylsulfate[SDS]; M = 288.4

112012*1)


N-Cetylpyridinium chloridec(CPC) = 0.01 mol/L

Sodium dodecylsulfate[SDS]; M = 288.4

112012*1)


. * 1) These substances can not be acchieved as guaranteed primary standard substances from MERCK.So the highest aviable quality is indicated.


10 Appendix 2

10.1 Assessment of Results

E r r o r s

Deviations from the correct or expected value

Gross errors Systematic errors Random errors

Avoid Accuracy Precision

The measurement The measurement result is wrong result is unreliable

C o r r e c t n e s s

10.2 Precision versus Accuracy

high accuracy low accuracy (found = true) (found ≠ true)

high precision(small RSD)

low precision(big RSD)


11 Glossary

Validation: A check whether or not correct results can be obtained with a givenmethod under all circumstances.

Correctness: The sum of accuracy and precision.

Accuracy: Deviation of the found value from the true (theoretical) value.

Precision: Also called repeatability. The results of a multiple determinationof a sample (e.g. 10 times in a row) do not diverge to much fromthe found mean value (small relative standard deviation).

Systematic Errors: Result offsets due to method inherent parameters. Shows itself inthe linear regression “titrant consumption versus sample size” bya y axis intercept, which is clearly different from zero.

Linearity: There has to be a linear correlation between the amount of samplepresent and the titrant volume consumed. Therefore the correla-tion coefficient of this regression has to exceed a certain value(i.e. R2 ≥ 0.995).

Or in the plot “result of titration versus sample size” of a singlesample the slope of the regression line should be zero. This showsthat the results do not depend on the sample size (i.e. dilution vol-ume).

Robustness: Also called reproducibility. Closeness of the agreement betweenthe results of measurement of the same sample carried out underchanged conditions of measurement, such as different days, in-struments, operators, laboratories, methods. Expressed as the rela-tive standard deviation of the different results obtained.

Ruggedness: Inertness against chemical/physical influences likely to occur (sol-vents, reagents, temperature, etc.).

Detection Limit: The smallest amount of substance giving a detectable potentialchange and a quantifiable titrant consumption.

Determination Limit: The smallest amount of substance that can be titrated with a goodprecision.

Sample: Sample to be analysed (liquid or solid).

Sample size: Exact volume or weight (of sample) used for the titration.

Analyte concentration: Concentration of the substance to be analysed in the titration beaker.


12 Literature

[1] METTLER TOLEDO: Fundamentals of Titration, ME-704153A (1993).

[2] METTLER TOLEDO: Standardization of Titrants, Applications Brochures No. 8 and9, ME-51724650 resp. ME- 51724652 (1994).

[3] MERCK: Primary Volumetric Standards; E. Merck AG, Darmstadt, D.

[4] Analytical Methods Committee: Uses (Proper and Improper) of Correlation Coeffi-cients; Analyst, Vol. 113, pp 1469 - 71 (1988).

[5] METTLER TOLEDO: Encyclopedia of Weighing; ME-720113.

[6] G. Mücke: How Little is “Nothing”?, Fresenius Z Anal Chem, Vol. 320, pp 639 - 641(1985).

This application bulletin represents selected, possible application examples. These have been tested with all possiblecare in our lab with the analytical instrument mentioned in the bulletin. The experiments were conducted and theresulting data evaluated based on our current state of knowledge.

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