biophysical chemistry principles and techniques

Biophysical Chemistry : Principles and TechniquesAvinash Upadhyay, PhD. Kakoli Upadhyay, PhD. Director Reader
Hislop School of Biotechnology, Hislop College,
Department of Biochemistry, Lady Amritabai Daga Women's College,
Shankamagar, Nagpur (M.S.) Civil lines, Nagpur (M.S.)
Nirmalendu Nath,PhD. Retired Professor,
Nagpur (M.S.).
MUMBAI- DELHI- NAGPUR - BANGALDRE - HYDERABAD - CHENNAI- PUNE - ~UCKNDW - AHMEDABAD - ERNAKULAM
© Author No part of this book shall be reproduced, reprinted or translated for any purpose whatsoever without prior permission of the Publisher in writing.
Published by
Branch Offices
REVISED EDITION: 2009
Mrs. Meena Pandey
HIMALAYA PUBLISHING HOUSE PVT. LTD., "Ramdoot", Dr. Bhalerao Marg, Girgaon, MUMBAI - 400 004. Ph. 2386 01 70 1 2386 38 63, Fax: 022-2367 71 78. E-mail: [email protected] + Website: www.himpub.com
·Pooja Apartments", 4-B, Murari Lal Street, Ansari Road, Daryaganj, NEW DELHI - 110 002. Ph. 23270392, Fax: 011-2325 62 86. Kundanlal Chandak Industrial Estate, Ghat Road, NAGPUR - 440 018. Ph. 0712-272 12 16/2738731, Fax: 0712-2721215. E-mail: [email protected] No.16/1, (Old 12/1), First Floor, Next to Hotel Highland, Madhava Nagar, Race course Road, BAN GALORE- 560 001. Ph. 2228 1541,2238 54 61, Fax: 080-2228 66 11. E-mail: [email protected] No.2-2-1 167/2H, 1st Floor, Near Railway Bridge, Tilak Nagar, Main Road, HYDERABAD - 500 044. Ph. 5550 17 45, Fax: 040-2756 00 41. No. 85/50, Bazullah Road, T.Nagar, CHENNAI - 600 017. Ph. 044 - 28 344020/32463737. Laksha Apartment, First floor, 527, Mehunpura, Shaniwarpeth, PUNE - 411 030 C-43, Sector - C, Ali Gunj, LUCKNOW- 226 024. Ph. 0522-4047594. 114, ·SHAIL" 1st Floor, Opp. Madhu Sudan House. C.G. Road, Navrang Pura, AHMEDABAD _- 380 009. Mob: 09327324149, 0931467413. 39/104 A, Lakshmi Apartment, Karikkamuri Cross Road., ERNAKULAM - 622011, Ph. 0484-2378012, 2378016, Mob: 09344199799. Geetanjali Press Pvt. Ltd., Ghat Road, NAGPUR- 440 018.
1.
2.
3.
4.
5.
6.
7.
CONTENTS
ACIDS AND BASES
Electrolytic Dissociation and Electrolytes - Ionization: Basis of Acidity and Basicity - Bronsted-Lowry Theory: Acid is a Proton Donor, Base is a Proton Acceptor - Strength of Acids and Bases - Acid-Base Equilibria in Water - Function and Structure of Biomolecules is pH Dependent - Measurement of pH : Use of Indicators - Electrometric Determination of pH - Buffers : Systems which Resist Changes in pH - Titrations : The Interaction of an Acid with a Base.
ION SPECIFIC ELECTRODES
Ion Selective Electrodes Measure the Activity of Metal Ions - Glass Membrane Electrodes - Solid-State Ion Exchanger Electrodes - Solid State Crystal Electrodes - Liquid-Membrane Electrodes - Gas-Sensing Electrodes.
THE COLLOIDAL PHENOMENA
DIFFUSION AND OSMOSIS
A Molecular-Kinetic approach to Diffusion - Methods of Determination of Diffusion Coefficient - Significance of Diffusion Coefficient -Diffusiop. of Electrolytes - Diffusion of Water Across Membranes : Osmosis - Measurement of Osmotic Pressure - Van't Hoff's Laws of Osmotic Pressure - Theories of Osmotic Pressure and Semipermeability -. Osmotic Behaviour of Cells - Molecular Weight Determination from Osmotic Pressure Measurements - Significance of Osmosis in Biology.
VISCOSITY
SURFACE TENSION
ADSORPTION
1 - 65
66 - 74
75 - 99
100 - 121
122 - 144
145 - 156
157 - 174
OTHER OPTICAL TECHNIQUES FOR MOLECULAR CHARACTERIZATION
Circular Dichroism and Optical - Rotatory Dispersion - Rotational Diffusion - Flow Birefringence - Electric - Birefringence - Polarization of Fluorescence - Light Scattering - X-ray Diffraction.
175 - 270'
271 - 300
10. CENTRIFUGATION
11. CHROMATOGRAPHY
12. ELECTROPHORESIS
301 - 343
344 - 421
422 - 488
Electrophoresis on Cellular Gels - 9. Capillary Electrophoresis - Electrophoresis in Genetic Analysis - 1. Restriction Mapping - 2. Southern Transfer - 3. Gel Retardation or Band Shift Assay- 4. DNA Sequencing- 5. DNA Foort printing.
13. ISOTOPES IN BIOLOGY
Radioactive Decay - Production of Isotopes - Synthesis of Labeled Compounds - Interaction of Radioactivity with Matter - Measurement of Radioactivity - I.Methods Based Upon Gas Ionization - A. Ionization Chambers - B. Proportional Counters - C. Fundamentals of Geiger Counters - 2. Photographic Methods - 3. Methods Based Upon Excitation - A. Liquid Scintillation Counting - Use of Stable Isotopes in Biology - The Tracer Technique - Use of Isotopes as Tracers in Biological Sciences - Some Information About Commonly Used Isotopes - Safety Aspects - Dosimetry.
14. CERTAIN PHYSICOCHEMICAL TECHNIQUES USEFUL IN BIOCHEMISTRY
Polymerase Chain Reaction - Enzyme-Linked Immunosorbent Assay (ELISA) - Flow Cytometry.
15. MASS SPECTROMETRY
Instrumentation and General Principles - 1. Sample Introduction 2. Ionization 3. Mass Analyzers 4. Detectors Applications of Mass Spectrometry 1. Protein - Characterization 2. Peptide Mass Fingerprinting 3. Determination of Higher Order Protein Structure 4. Analysis of Biological Noncovalent Complexes 5. Characterization of Small Biomolecules 6. Applications in Virology 7. Seqencing Polypeptides and Oligonucleotides.
-APPENDIX
-INDEX
1 ACIDS AND BASES
A history of the quest to understand the molecular basis of acid - base properties makes for a very amusing reading. For instance, in 1773 Doctor Samuel Jhonson averred that "acids are composed of pOinted particles which affect the taste in a sharp and piercing manner". Another attempt to explain the nature of acids was made by Lavoisier when he proposed that the characteristic behaviour of acids was due to the presence of oxygen. Stimulated by this observation, Sir Humphrey Davy went to great lengths to show that hydrochloric acid also contains oxygen. He, of course, failed in his attempt thereby disproving the theory of LaVOisier. Even the later history of acid - base research is not without its share of amusement, albeit in a manner different to the above described instances. In 1884 Svante August Arrhenius in his doctoral dissertation proposed the theory of electrolytic dissociation and ionization on which our current understanding of acid - base character is based. The doctoral dissertation was, however, greeted by the lowest possible pass-mark by the University of Uppsala, Sweden. For this same theory Arrhenius was awarded Nobel Prize in Chemistry in 1903.
ELECTROLYTIC DISSOCIATION AND ELECTROLYTES
FIgure 1.1. Experimental system for detennining electrical conductivity of a solution. The bulb does not light when there is a non electrolyte solution In the beaker. The bulb lights when the beaker contains electrolytes In solution.
Let us consider a simple experiment. A pair of electrodes is connected in series to a light bulb and to a source of electricity (Figure 1.1). As long as the electrodes hang separated in the air, no electric current flows through the circuit, and the bulb does not light. Ifhowever, the two electrodes are touched to each other, the circuit is completed and the bulb lights. If the electrodes are dipped into a beaker containing water purified by repeated distillations, the bulb does not light. This tells us that water is not a good conductor of electricity and is not capable of completing the
• circuit. Ifwe dissolve an acid, a base, or a salt in water in which the electrodes are dipped, the bulb lights up. Oqviously, these substances are able to carry the current and thereby complete the circuit. Substances producing solutions capable of conducting electricity are called electrolytes. On the other hand, substances producing solutions incapable of conducting electricity are known as non-electrolytes. Table 1.1 provides a few examples of electrolytes and non-electrolytes.
2 Biophysical Chemistry
~ ""'"':'''
Hydronium Ion
G:\C"I'
~ Chloride Ion
Figure 1.2. When gaseous hydrogen chloride is bubbled in water. HCI molecules coUide with water molecules. Collisions oj sufficient energy and proper orientation produce hydronium ions and chloride ions.
Going back to the experiment we discussed. a diligent observer would note that certain substances cause the bulb to be brightly lit. whereas other substances cause the bulb to be only dimly lit. This experimental observation pennits us to subdivide the electrolytes into two groups. Substances that dissociate almost completely and produce solutions that are very good conductors oj electricity are known as strong electrolytes; substances which dissociate only partially and produce solutions which are poor conductors oj ezectricity are known as weak electrolytes. The difference between strong and weak electrolytes was attributed by him to a difference in the degree of ionization.
IONIZATION: BASIS OF ACIDITY AND BASICITY
Arrhenius Theory: H+ Ion is the Acid, OIr Ion is the base From the experiment that we have discussed above, one can safely conclude that acid
base reactions are a function of ionization principle. Thus, based on ionization principle. Arrhenius defined acids and bases. These definitions are elaborated below.
Acids : Acids were described by Arrhenius as compounds containing hydrogen which upon addition to water become ionized to yield H+ ions. Nitric acid (HNO ). which is a soluble strong electrolyte or strong acid (Le .• it dissociates completely in water to p}oduce H+ ions). may be cited as an example.
HN0 3 ~H+ + NO;
Nitrous acid (HN0 2
) • a weak electrolyte (Le .• dissociates only partially to produce H+ ions). may be cited as an example of a weak acid.
+ -HN0 2 ~H +N02
(A single arrow ~ denotes reactions that go completely to the right; a double arrow ~ denotes reactions that go only partially to the right).
Acids and Bases 3
Strong Electrolytes
Hydrochloric acid. HCI [H+ + Cn Potassium chloride. KCI [K+ + Cn
Nitric acid. HN03 [H+ + NO;) Silver nitrate. AgNO 3' [Ag+ + NO:3)
Sulfuric acid. H2S0 4
[H+ + HSO ~ I Sodium chloride. NaCI [Na+ + Cn
Sodium hydroxide. NaOH [Na + + OI-r) Copper (II) sulphate. CuSO 4 [Cu2+ + SO~-l
Weak Electrolytes Nonelectrolytes
Lactic acid. CH3CHOHCOOH [CH3CHOHCOOH] Sucrose C12H22011 [C 12H22011 ]
Ammonia. NH3 [NH31 Ethyl alcohol. C2H50H [C2H5OH]
Hydrogen sulphide. H2S [H2S] Methyl alcohol. CH30H [CH3OH]
Mercury (II) chloride. HgCl2 [HgCI2 ] Acetone CH3COCH3 [CH3COCH3 ]
Species in parentheses are predominant in solution. The difference between weak and nonelectrolyte is that weak electrolytes dissociate very little (not shown in the table) whereas the nonelectrolytes do not dissociate at all.
Bases: According to the Arrhenius defmition. bases are compounds which upon ionization in water yield OH- (hydroxide) ions. Sodium hydrOxide. which dissociates completely to produce OH- ions. may be cited as an example.
+ - NaOH~Na +OH
The Arrhenius concept is important in that it has provided us with the first mechanistic approach to acid - base behaviour and has been instrumental for the development of more sophisticated theories. There are. however. two major shortcomings in the Arrhenius model.
(i) In the Arrhenius model the acid-base reactions are limited to aqueous solutions (this is not a problem as far as biological systems are concerned since all reactions must take place in aqueous solutions).
(iO The theory limits bases to hydroxide compounds. This is very unsatisfactory because it is well known that many organic compounds which are not hydrOxides. for example ammonia. show basic properties in their chemistry.
In the year 1923. two more theories defining acid-base character were proposed. The first theory. Bronsted and Lowry theory. is very satisfactory for understanding physiological processes and will therefore form the basis of all further discussions. The second theory. proposed by G. N. Lewis is much more general than the Bronsted - Lowry concept. A brief discussion of this theory is given in Box 1. 1.
Lewis Acids and Bases
As compared to the Arrhenius concept, the Bronsted and Lowry concept seems to be much more general in that any species which can donate proton is regarded as an acid. Proton binding, of course, is just a special example of forming a covalent bond by an electron - sharing process. Thus, all the Bronsted bases have an electron pair to share with a proton. The Bronsted acids then can be thought to donate something which is capable of sharing these electrons. Bronsted visualized this something to be just a single speci~s, a proton. Thus, the concept of acids is rather restricted in the Bronsted theory. This restriction was removed by G. N. Lewis when he proposed a much more general all inclusive concept according to which
- Acids are species which accept an electron pair.
- Bases are species which donate an electron pair.
If we apply this theory, automatically need arises to modify the term neutralization. It can no more be used in the sense in which it has been hitherto used. Since Lewis acid base interaction invariably results in the formation of a cova:ent bond, the word co-ordination is more appropriate than neutralization. However, one might still use the term neutralization.
The interaction of ammonia (a Lewis base) and boron trifluoride (a Lewis acid) is cited as an example of neutralization or coordination.
F H F H
I I I I F H F H
Boron Trifluoride Ammonia Boron - Ammonia (acid) (base) Trifluoride Complex
Boron trifluoride accepts a pair of electrons from ammonia. By this process boron trifluoride completes an octet of valence shell electrons.
On comparison with the previous two theories one would find that bases in Lewis concept are essentially the same as in Bronsted concept. The only difference is that in the Bronsted theory they could combine only with a proton; in the Lewis theory they can co-ordinate with any species that can accept a pair of electrons. Thus NH is a base if it shares its electrons with a proton or it shares it with boron trifluoride. It is evident tfiat the concept of acids has been made much more general in the Lewis concept; rather than being limited to just proton donating species, it now includes all species which have the capability of accepting a share in an electron pair. Thus, all metallic ions, which are by no means Bronsted acids, are certainly Lewis acids.
Bronsted - Lowry Theory: Acid is a Proton Donor, Base is a Proton Acceptor This theory defines an acid as any compound that yields protons (H+ ions) and a base
as any compound that combines with a proton. In other words, acids are proton donors and bases are proton acceptors. It should be noted that as far as acids are concerned, Arrhenius and Bronsted - Lowry theories are similar; in both cases acids give off H+ ions. However, the concept of a base is much broader in the Bronsted theory, hydroxyl ion being just one of the possible bases. Cited below are a few examples which will illustrate the point much better.
Acids and Bases 5
CH3COOH ~ H+ + CH3COO-...,--
HC0 3 ~ H+ C0 3-...,-- + ----">.
H 0+ -.;:---
-
Concept oj coryugate acid and conjugate base: Each of the compounds listed above as acid, upon ionization, produces H+ ions. Their ionization also produces ions or molecules which can combine with a proton (HSO~ , CC H2PO~, CH
3 COO-, etc) . According to the defmition, these
ions which can combine with a proton are bases. Thus, we can say that every acid dissociates into a proton and a base (if the reaction is reversed, a base can combine with a proton to produce an acid). The Bronsted -Lowry theory thus conceives of an acid - base 'pair' . An acid and its corresponding base are said to be 'conjugate', I.e., 'joined in a pair'. Thus, Cr- is the conjugate base of HCI, likewise H20 is the conjugate base of H30+.
An acid is a proton donor. Its strength would depend upon the ease with which it can donate a proton. An acid will yield a proton with comparative ease if its conjugate base is weak. Let us consider HCI as an example. Its conjugate base , CI- , is a weak base; it is not a very good proton acceptor. In solutions, therefore, HCI is completely ionized to produce H+ and CL HCl is a strong acid because its conjugate base is weak. Let us consider another example, that of 2H
3 COOH. Its conjugate base CH
3 COO- is stronger base compared to CI- . The acetate ion,
Lherefore, binds the proton much more tenaciously with the result that in solution acetic acid is .10t fully ionized . CH
3 COOH is a weak acid because its conjugate base is strong. Similar concepts
can be drawn for bases also and their strength would depend upon the strength of their conjugate acids. The Bronsted - Lowry theory gives us the following reciprocal relations:
- if an acid is strong, its conjugate base is weak.
- - if an acid is weak, its conjugate base is strong.
- if a base is strong, its conjugate acid is weak.
- if a base is weak, its conjugate acid is strong.
Concept oj an alkali : In the previous pages NaOH was regarded as an Arrhenius base because it ionized to produce OH- ions . NaOH , however, is not a Bronsted base because, as a molecule, it has little ability to accept a proton . NaOH can act as a base solely because upon lonization it gives rise to OH- ions which are very good proton acceptors. NaOH and other metallic hydroxides like KOH, therefore act as bases by proxy. Such compounds, under the 3ronsted theory, are known as alkalies.
Amphoteric substances: Substances which can behave both as an acid and as a base are referred to as amphoteric. Thus, under the Bronsted concept, liquid ammonia qualifies as an acid
and as a base too
Similar is the case with water which behaves as an acid
and as a base
HOH+ff ~ H30+
Salts : Under this theory salts are thought to be compounds which are formed by replacing the ionizable hydrogen with a metal ion or with any other positively charged group. Thus, CH3COONa is the sodium salt of CH3COOH formed by replacement of the proton by the Na+ ion. KCI is a salt of HCI formed by replacement of the proton by K+ ion.
CH3COO GJ CH3COO INa I Acid Ionizable
Hydrogen Salt Metal
STRENGTH OF ACIDS AND BASES
(Throughout the discussion acids will be treated as examples. However, the discussion applies equally well to bases, albeit, in a reverse manner).
In a preceding section we have said that the strength of an acid depends upon the strength/ weakness of its conjugate base. This, however, is not the only determinant of strength. Apart from strength of conjugate base, the strength of an acid depends upon (il the basic strength of the solvent, and (ii) the dielectric constant of the solvent. Both these factors are discussed below.
The Basic Strength of the Solvent So far we have been writing the ionization reaction of HCI as
HCI ~ H+ + CI-
HA ~ H++A-
It is, however, well known that H+ ions do not exist in acid solutions. This is because the H+ ions combine with the solv~nt molecules to give rise to 'lyonium ions'. Let us illustrate the case by considering a specific example, that of water, as a solvent. In water, the H+ ions (formed due to ionization of an acid) are known to combine with water molecules to give rise to H30+ , the hydronium ions (also known as the oxonium or hydroxonium ions) .
H+ +H 0 ~ H 0+ 2 --- 3
Acids and Bases 7
Recall that Bronsted - Lowry concept states that a base is a proton acceptor. Thus water in the above case (and solvents in general) is acting as a base.
We can now rewrite the general ionization reaction of an acid in water
~ + - HA + H2 ° -.;-- H3 ° + A
The strength of the acid. HA. now is a function of the competition between the two bases. \.- . and H
2 0 to accept the ionizable hydrogen.
Case 1 : A- is stronger than H 2 0. In this case A- is a stronger base and will bind to the
onizable hydrogen much more tenaciously than H 2 0. As a consequence. the dissociation of
he acid. HA. will be less and it will not be a strong acid in water.
Case 2: A- is weaker than H 0 . In this case. once the acid is dissolved in water. A- will lose he ionizable hydrogen to water w~ich is a stronger base. The dissociation of the acid. HA. will )e very high and the acid may even be completely dissociated. The acid. HA. will be a strong lcid in water.
We can now generalize the above observations. if the basic strength of the solvent is less than the strength of the conjugate base. the acid will be weak in that solvent. Ijthe basic strength of the solvent is greater than that of the conjugate base. the acid will be strong in that solvent.
To drive the point home. let us consider the strength of the same acid in two solvents.
Case 1 : Acetic acid in water. The acetate ion is a stronger base than water. Therefore. acetic acid is a weak acid in water.
° ° " " CH - C - ° - H + H - OH ( ) CH - C - 0- + H 0+
3 3 3
Case 2 : Acetic acid in liqUid ammonia . Acetate ion is a weaker base as compared to ammonia. Therefore. acetic acid which was a weak acid in water. is a strong acid in liqUid ammonia.
° ° II II CH -C-O-H+NH ( ) CH -C-0- +NH 4+
3 3 3
The above examples show the relative nature of the designations strong and weak. The statement that an acid is strong does not convey much sense unless we know in relation to what. The direction of proton transfer and its extent depend upon these relative proton - donating and proton-binding abilities of the potential acids and the solvent. It can thus be said that the strength of an acid is always relative to the basic strength of the solvent used.
Dielectric Constant of the Solvent Upon ionization the acid splits into two oppositely charged ions. H+ and A- . These ions
~an attract each other and recombine. However. solvents of high dielectric constant greatly reduce attraction between oppositely charged particles dissolved in them. This action of the 50lvent favours diSSOCiation of an acid and consequently is important for the strength of acid. \n acid in a solvent of high dielectric constant will dissociate greatly and will therefore be strong. The same acid. in a solvent which has a low dielectric constant. will not dissociate much
and will consequently be weak. Water is a solvent which has a very high dielectric constant at room temperature. almost 80. On the other hand. petroleum ether has a very low dielectric constant. just 2.2. A given acid can therefore dissociate to a much greater extent in water than in petroleum ether. The dielectric constant is thus of great importance in determining the strength of an acid.
Effect of Structure on the Strength of Acids It is a commonly accepted fact that carboxylic acids are stronger than other organiC acids.
Why is that so? The reason usually given is that the carboxylate anion (the conjugate base) formed upon dissociation is stabilized by resonance (two equivalent resonance structures) in such a manner that it is more stable than the original acid molecule.
o R-C~ --->.. '" ~ OH
Resonance stabilized anion
On the other hand. in the alkoxide ion. RO- . the negative charge is not delocalized and is concentrated on the single oxygen atom. This anion. therefore. is not as stable as the resonance stabilized carboxylate anion. The resonance stabilization promotes dissociation in the carboxylic acids making them stronger in relation to the organic acids where lack of resonance stabilization decreases dissociation.
If resonance stabilization were the only factor all carboxylic acids would have had the same strength. This is not so. Carboxylic acids which contain strong electron attracting groups (halogens) on the alpha - carbon are stronger than the un substituted acids. On the other hand. carboxylic acids bearing electron releasing groups (methyl) on the alpha - carbon atom are weaker than the unsubstituted acids. These electrostatic factors. in which electrons are either attracted to or repelled from one atom or group of atoms with respect to another are known as inductive effects. Electron attracting groups withdraw electrons from the carboxylate group. This weakens. the oxygen - hydrogen bond thereby facilitating iOnization and release of a proton. Moreover. these groups also help stabilization of the conjugate base by resonance.
CI 0 Cl 0
(1) CIE--l~c(! ~ i / ~--
l \ l '\'--- Cl O~H Cl 0
CH3 0 Cf-I 3
j '\, 3 t ~~, CH
0
Acids and Bases 9
Inductive effects are additive and increase with the number of substitutions by electron withdrawing or electron releasing groups. These effects also are sensitive to distance. Thus. substitution by a halogen on the beta carbon of a carboxylic acid is not as effective as one on the alpha - carbon.
What Do We Mean by 'Strength of an Acid'?
So far we have not reviewed this term critically. We. however. have been using the teml loosely to convey in essence the H+ ion concentration [H+] . Thus. when we said that HCI is a strong acid. what we meant was that HCI ionizes to give a high [H+]. When we said that CH COOH' is a weak acid. we meant that CH
3 COOH ionizes to only a little extent giving a low [H+]. Although
this is the way we are going to use this term subsequently in this chapter. we might as well understand its actual meaning.
The concept oj activity: The ions in solution. are separated from one another by shielding layers of solvent and thus have little attraction for each other. If. however. we increase the concentration of the solution. the intervening distances between different ions start decreasing. In a dilute solution. the ions move about freely without the hindrance of attractive forces from oppositely charged ions. In a concentrated solution. however. the ions can not move freely because they are closer to each other and therefore are affected by oppositely charged ions. The ions then assume a certain degree of orientation. Each ion is surrounded by an 'ion atmosphere' of opposite charge which reduces its movement. Thus the effective concentration of the ions is slightly less than its absolute concentration. This effective concentration is known by a better term. activity. Thus. in true sense. the strength of an acid is a measure of the activity ofH+ ions and not of its concentration. It may be said that the activity and concentration of H+ ions might be identical in dilute solutions. It is only in the concentrated solutions that they start to differ.
Activity coeffIcient: Activity is a measure of the effective concentration of the solutes in solution. The activities might be related to the absolute concentrations by a proportionality factor called activity coefficient. The symbol used for activity coefficient is y. The equation for the relationship is as follows
a=yC
where a is the activity and C the concentration. Units of both a and C are moles per litre. The activity coeffiCient approaches unity at infinite dilution.
Titration Does Not Reflect The Strength of an Acid We know that HCI is a considerably stronger acid as compared to CH
3 COOH. HCI ionizes
fully and almost all the hydrogen of HCI is present as H+ at any point of time. HCI also conducts the electric current much better than CH
3 COOH. The two acids. however. have Similar titration
profiles. ~5 ml of 0.01 N NaOH are required to fully titrate 25 ml of 0.01 N HC!. The same amount of O.OlN NaOH is required to fully titrate 25 ml of O.OlN CH
3 COOH. Both acids give
+
To achieve equilibrium with respect to dissociation. more acetic acid molecules dissociate to give rise to another 1.3 % H+. These too are removed as water in the manner described above. The process continues till all acetic acid has ionized to give up protons which get removed as water. A Similar process takes place with HCl also
HCI ~CI- + H+
1 H
2 O
The two acids therefore end up giving similar titration proffies. The acidity measured by titration is known as the total or the titratable acidity and :reflects the concentration of an acid in solution. It does not. however. reflect the strength of an acid or its actual acidity.
ACID-BASE EQUILmRIA IN WATER
The free hydronium ion concentration. [H 3 0+I. dominates chemical reactions in physiological
systems. Since all physiological fluids are aqueous based. the concentration of hydronium ions may determine the extent to which the reaction proceeds. the rate at which it goes. or the detailed mechanism of how it takes place in such solutions. For example. in both. living and in vitro physiological systems. specific enzyme activity is often quite dependent on the effective concentration of the hydronium ion.
Adjusting and controlling the free hydronium ion concentration is a necessity in any biochemical experiment. To understand the complex eqUilibria which are always present in an acid - base system is therefore of paramount importance.
The Law of Mass Action The law of mass action. evolved mainly by Guldberg and Waage. states that the. rate of a
chemical reaction at a given time is proportional to the active masses of reacting substances present at that time. The active mass for molecules is essentially equal to their molar concentrations. However. for ions. as one would recall. the active mass means the effective concentration or the activity (which might be equal to molar concentration in dilute solutions).
Let us conSider the reaction
A+B ~ C+D
in which two reactants A and B interact to form two products. C and D. Note that the reaction is reversible. According to the law of mass actiOI. :he rate of the reaction to the right will depend upon the molar concentrations of A and B (throughout the discussion we assume that the solution is dilute and thus activity is equal to concentration), Thus
V a [AI . [BI r
where [AI and [BI are expressions of molar concentrations of A and B. and V is the r
reaction velocity to the right. Apart from the molecular concentration. the ·chemical affiriities of the reactants should also be taken into account. The chemical affinities are constant at a given temperature and other reaction conditions. In the above equation. therefore. we might introduce a proportionality constant which corrects for the particular chemical affinity.
Acids and Bases 11
[A) . [B)
Since the reaction is reversible. the products e and D will react to give A and B. Writing an expression for the velocity of the reaction to the left
VI = K2 [e) . [D)
At equilibrium. the rate of the reaction to the right and that to the left will be equal. So that
and ~ [A) . [B) = K2 [e) . [D)
Rearranging
where Keq is the eqUilibrium constant and is an expression of the chemical affinities of the reactants. It would be obvious from the above eqUilibrium equation that if K eq is large the reaction to the right predOminates. which means that affinity between A and B is higher than e and D and that at equilibrium the concentration of e and D is higher than that of A and B. The reverse is true when Keq is small.
The eqUilibrium equation may be stated in words : at eqUilibrium the product of the concentrations of the substances formed in a chemical reaction divided by the product of concentrations of the reactants in that reaction is a constant referred to as the eqUilibrium constant. Keq• We may stress again that the activities of the reacting species will give the precise value and not the molar concentrations which are used only for the sake of simplicity.
The law of chemical eqUilibrium may be applied to virtually all reversible reactions and systems including the ionization of acids and bases.
The Ionization of Water As per the collision theory. it is expected that "vater molecules constantly collide with
neighbouring water molecules. It may further be expected that at any instant a minute fraction of these colliSions will be violent. These violent collisions might give rise to the following change:
H", /®", " '0' + O-H /' "
Floure 1.3. A coUision between two water molecules can result in the JOrTT''1tion oj a hydronium ion and a hydroxyl ion. The collision should be oj sufficient energy anl.i " roper orientation.
It is obvious from the above equation that for every single hydronium ion formed, a hydroxyl ion is also produced. Thus ionization of water forms these two ions in equal numbers thereby ensuring that pure water is essentially neutral. The dissociation of water has been confirmed by electrical conductivity experiments. These experiments also tell us that at eqUilibrium a very small percentage of water molecules becomes ionized; actually just slightly more than 10-7%. This means that water is almost a nonelectrolyte. At higher temperatures the number of collisions between water molecules will be higher producing a slightly higher number of hydronium ions. But the water will stay essentially neutral because an equally higher number of hydroxyl ions will also form.
The Equilibrium Constant and Ionization Constant of Water We have seen that water has only a very slight tendency to ionize. However, the products
of ionization, H30+ and OH- have very profound biological effects. It is therefore neces~~ that we express the extent of ionization of water quantitatively. "'"
We can represent the ionization of water simply as H - OH ~ H+ + OH-...-- \
(although we have said before that H+ ions do not exist as such and the correct representation would be H 0+, we can think that hydronium ion is the hydrated form ofH+ and take the libJrty to express it as H+ for the sake of Simplicity). The eqUilibrium constant of such a reaction according to the law of mass action would be
We have seen that water has a very slight tendency to ionize. This means that the concentration of water should be virtually unchanged by ionization. The concentration of water per litre in pure water is equal to the number of grams of H
2 0 in 1 L divided by the gram
molecular weight, i.e. 1000/18 = 55.5 M or 0.55 x 102 M. Substituting this value in the equilibrium constant expression we get
Acids and Bases 13
55.5
From electrical conductivity measurements of water the value of Keq has been calculated very carefully and has been found to be 1.8 x 10-16 at 25OC. Substituting this value for Keq in the above equation, we get
Rearranging
55.5
= [H+) [OH-) 1.0 X 10-14
The product of the equilibrium constant of water Keq, and concentration of water, 55.5, which is taken to be con8tant, is known as ionization constant or the dissociation constant or the ion product oj water and is symbolically denoted as Kw' Thus,
Kw :: 1.0 X 10-14 = [H+) [OH-) at 25°C.
The above equation is substantially true for water and for dilute aqueous solutions. In such solutions the product of hydrogen ion concentration and hydroxyl ion concentration is the constant value 10-14 (at 25°C) whether the solution is acidic, basic or neutral. Value of Kw varies widely with temperature as shown in Table 1.2. When concentrations of [H+) and 10H-) are exactly equal, as in pure water, the solution is said to be neutral. Under such cQnditions, the knowledge of the value of Kw allows us to calculate the concentration of H+ and OH-.
Kw = 1 X 10-14 = [H+) [OW)
= 1 x 10-14 = [H+)2
or
[H+) = 1 x 10-7
Table 1.2 Ionization Constant of Water at Various Temperatures
Temperature ("C)
3.13 X 10-14
Thus when a solution is neutral, the concentrations of H+ and OH- are both 10-7 M. On the other hand, if the solution is acidic, the concentration of H+ would be higher than 10-7 and
•
Thus. the ionization constant of water. Kw. is of great help to calculate the concentration of H+ if the concentration of OH- is known. and vice versa.
Box 1.2
The relationship [Hj [OW] = Kw= 1 X 10-14 helps in calculation of [Hj if [OHl is known and vice versa. The following examples demonstrate it.
(1) Calculate the [H+] of the solution which is 0.01 Nfor NaOH at 24·C.
Ans. NaOH is a strong alkali and by definition dissociates fully. Thus a solution which is 0.01 N with respect to NaOH is also 0.01 N with respect to OW. Therefore [OHl of the solution is 0.01 g mol per litre or 1 x 10-2 g mol per litre. Putting this value into the equation
[Hj [OHl = Kw = 1 X 10-14
we get
Therefore
+ x10 -12 H = = 1 x 10 g mol per litre
1 x 10- 2
(2) Calculate the [OHl of the solution which is 0.001 N for HCI at 24·C.
Ans. HCI is a strong acid and by definition dissociates fully. Thus a solution which is 0.001 Nwith respect to HCI is aiso 0.001 Nwith respect to H+. Therefore, [H+] of the solution is 0.001 g mol per litre or 1 x 10-3 g mol per litre. The [OHl of this solution will be
[ _] 1x10-
14
9 mol per litre 1 x 1 0-3
(3) Calculate the [OHl for each of the following and state whether the solution is acidic, basic, or neutral. The temperature is 24·C.
(i) [Hj 1 x 10-9 molellitre.
(ii) [Hj 4 x 10-9 mole/litre.
(iii) [Hj 2.5 x 1041 mole/litre.
(iv) [Hj = 2 x 10-2 mole/litre.
Ans. (i) 1 x 10-5 mole/litre. (ii) 2 .5 x 10-6 mole/litre . (iii) · 4 x 10-9 mole/litre. (iv) 5 x 10-13 mole litre.
Simple Way of Denoting H+ and 011 Concentrations: The Concept of pH
Because of the importance of trace concentrations of hydrogen and hydroxyl ions, scientists routinely have to make hundredb and thousands of measurements. The manipulation of such
Acids and Bases 15
awkward figures as negative exponents (e.g .. 10-7 ) or even their decimal equivalents (0.0000001)
is cumbersome and tedious. As a matter of simple convenience. the chemists. chiefly Sorensen. long ago devised a shortcut. This shortcut is the pH scale which is a convenient tool to designate the actual concentration of H+ (and therefore of OH-) in any aqueous solution in the range of acidity between 1.0 MH+ and 1.0MOH-. Mathematically. the term pH is defined by the equation
pH= log [~, f -log [ H' ]
Let us see how convenient is the pH scale. We know that the hydrogen ion concentration in a neutral solution at 25° is 1 x 10-7 M. The pH of this solution would be given by
1 pH = log---
1 X 10-7
=0+7
pH= 7
Thus the cumbersome figure of neutrality. hydrogen ion concentration of 10-7 M. is translated into the simple pH value of 7. Solutions which are acidic will have pH values less than 7. and conversely. the solutions which are alkaline will have pH values larger than 7. Since Kw. ion product of water (1 x 10-1
,\ forms the basis for the pH scale. the scale ranges from o to 14 (Table 1.3).
Table 1.3 The pH Scale
pH [H+I,M pOH [OH-I,M
0 1.0 14 10- 14
1 10- 1 13 10- 13
2 10 2 12 10-12
3 10-'3 1 1 10-11
4 10-4 10 10-10
6 10-6 8 10-8
7 10-7 7 10-7
8 10-8 I) 10-6
9 10-9 5 10-5
11 10- 11 3 10<1
12 10-12 2 10-2
14 10-14 0 1.0
It is necessary to understand that the pH scale is logarithmic and not arithmatic. Thus. when it is said that two solutions differ from each other by 1 pH unit. It means chat one solution has 10 times the hydrogen ion concentration of the other. Thus. vinegar (pH 3.0) has H+ concentration approximately 10.000 times greater than that of blood (pH 7.4), Table 1.4 list~ the pH values of some important and commonly used aqucous fluids.
16
Table 1.4 Place of Various Materials in the pH Scale
Material
Household bleach Household ammonia Baking soda Sea Water Egg white Hepatic duct bile Intestinal juice Pancreatic juice Blood (human) Tears (human) Cerebrospinal fluid Saliva Urine Milk Kupffer cells (intracellular) Black coffee Beer Tomato juice (ripe) Orange juice Vinegar Cola Lemon juice Pure gastric juice
If we take the negative logarithm of the equation
Kw = [H+] [OH-] = 10-14
BwphyskalChentiSUy
pH value
12.7 12.0 9.0 8.0 8.0 7.4 - 8.5 7.5 - 8.0 7.5 - 8.0 7.35- 7.45 7.4 7.4 6.35- 6.85 4.8 - 7.5 6.6 - 6.9 6.4 - 6.5 5.0 4.2 - 4.9 4.3 2.6 - 4.3 3.0 3.0 2.0 0.9
but. - log [H+] = pH. Similarly - log [OH-] = pOH. and - log Kw = pKw
Thus
pH + pOH = pKw (at 24°C)
Sometimes the expression pOH is used to denote basicity (OH- concentration) of a given solution.
It is important to note that the pH scale is applicable accurately only to solutions at ordinary temperature (approxinlately 24"C) where the value for pKw is 14. Only at this temperature pH of neutral solutions will be 7.
Measurement of pH is of utmost importance to biologists in general and to biochemists in particular. This is so since pH determine:: not only the activity ofbiomolecules such as enzymes. but may also be important for the stability oftheir structures. Moreover. measurement of pH of blood and urine can give us important diagnostic information.
Acids and Bases 17
It must be emphasized that the actual meaning of pH is the negative log of hydrogen ion activity and not the hydrogen ion concentration. However. in dilute solutions with which we usually deal. activity is essentially equal to the concentration.
Measurement of pH of an aqueous solution can be performed by using such indicator dyes (see later) as phenolphthalein. phenol red. litmus. etc. Accurate measurements. however. require the use of electrodes. specially glass electrodes which are very accurate (see later).
Box 1.3
(1) Calculate the pH of a solution in which [W] = 4.5 x 10-6. State whether the solution is acidic, basic or neutral. The temperature is 24"C
Ans. pH = - log [H+]
The solution is acidic.
(2) Calculate pH of a solution which is 0.01 N for NaOH at 24"C.
Ans. From problem (1) Box 1.2 we know that the [HJ for this solution is
1 x 10-12 molesllitre
=-(-12+0)
pH = 12
(3) Calculate the pH of each of the following solutions and state whether the solution is acidic, basic, or neutral. Temperature is 24"C.
.
Ans. (i) 7.82. (ii) 5.96. (iii) 7.4.
(4) Normal body temperature is 37"C. Calculate (i) [Hl for pure water at this temperature in moles per litre, and (ii) pH of pure water at this temperature. State whether water is acidic, basic, or neutral at this temperature giving reasons for the answer.
Note: The value of Kwat this temperature can be taken from Table 1.2.
Ans. (i) 1.76 x 10-7 , (ii) 6.75, (iii) Neutral, of course. since [H+] = [OHl.
Ionization of Weak Acids A biologist is more concerned with the behaviour of weak acids which are not completely
ionized when dissolved in water. Weak acids 'and weak bases) occur commonly in biological systems ad are responsible for metabolic regulation.
The law of mass action can be applied to formulate equilibrium equations for the dissociation of weak acids. If weak acids are given the general formula HA. their dissociation equation can be written as
According to the law of mass action the equilibrium expression for this dissociation may be written as
where Ka is the dissociation constant or the ionization constant of weak acid. A higher value of Ka obviously means higher degree of ionization. Thus, lactic acid with a Ka of 1.38x 10-4 is much more ionized than acetic acid which has a Ka value of 1. 74 X 10-5• This automatically provides the information that lactic acid is a stronger acid as compared to acetic acid. The dissociation constant thus defines the tendency of any acid, HA, to lose its proton.
As discussed earlier in the section on pH, it is cumbersome to handle negative exponent values. These values can be better handled if they are converted to their negative logarithms. Thus.
-log Ka = pKa
While making use of pKa' it should be remembered that this value would be less for a stronger acid and more for a weaker acid. Thus, lactic acid which is stronger than acetic acid has a pKa value of 3.86 as compared to 4.76 of acetic acid. Table 1.5 lists the Ka and pKa values of some common weak acids.
Table 1.5 Dissociation Constant and pKQ of Some Weak Acids at 25°C
Acid Ka(M} pKa Phosphoric acid (H
3 PO 4) 7.25 x 10-3 2.14
Formic acid (HCOOH) 1.78 x 10-4 3.75 Lactic acid (CH
3 CHOHCOOH) 1.38 x 10-4 3.86
Acetic acid (CH COOH) 1.74 x 10-5 4.76 Propionic acid (CH
3 CH
Carbonic acid (H 2 C0
3 ) 7.9 x 10-7 6.1
Ammonium ion (NH 4) 5.62 X 10-10
i 9.25
We have so far conSidered the dissociation of monobasic acids only. However, there are certain polybasic acids, like H 2C03 , H3P04 etc., whose dissociation should also be considered. Polybasic acids dissociate in stages and an equilibrium expression for each stage, involving a dissociation constant for each stage. may be written. We will take H2C03 as an example. The dissociation of H2C03 takes place as follows:
CO - ~ + CO 2-H 3 ~H + 3
We can write equilibrium expressions for each of the two stages
[H+J[ CO~- ] ---~--_-.,---- = K = 6.31 X 10-11
[HC03J 2
where KI and K2 are the first and the second dissociation constant ofthe acid. The dissociation of the first hydrogen ion from H? CO 'I is opposed by the force of attraction of its linkage to the
Acids and Bases 19
molecule. The dissociation of the second proton is more difficult. It is held not only by the primary union with the molecule but also by the attraction of the negative charge left on the molecule by the dissociation of the first proton. The value of K2 is therefore less than K
1 .
The dissociation constant of a weak acid may be employed to calculate the pH of its solution of a known concentration. The procedure for such calculation is enumerated below.
For the dissociation of a weak acid HA
HA ¢H++A-
the eqUilibrium expression may be written as
The concentrations of H+ and A- would be equal as they are formed in equal amounts.
Therefore. [H+ r = Ka [HAl or [H+ ] = JKa[HA]
We know that weak acids are only slightly ionized. Thus. we can safely assume that not more than 1% exists as H+ and A-. One can therefore assume that the concentration of the undissociated acid. HA. is equal to the normality of the acid. This value can then be substituted in the above equation and the hydrogen ion concentration can be calculated. The value of hydrogen ion concentration so calculated will be apprOximate as we have not corrected it for the slight dissociation which the weak acid has undergone.
Box 1.4
(1) Calculate the pH of 0.1 N lactic acid. Temperature is 24°C.
Ans. We know that [ H+ J = ~Ka [HA]
K for lactic acid is 1 .38 x 1 0-4. a
Therefore.
-log ( 1.38 x 10- 5 )
2
-0.1399+5 ;:: =2.43
2 The pH of 0.1 N lactic acid is 2.43 at 24°C
(2) Calculate the pH of 0.01 N solutions of (i) formic acid, Ka = 1.78 X 10-4, (ii) acetic acid, Ka = 1.74x 10-5, (iii) phosphoric acid, Ka = 7.25x 10-3. Temperature is 24°C
Ans. (i) 2.88, (ii) 3.38, (iii) 2.07.
20 BwphyskalCherrtisOy
Ionization of Strong Acids Strong acids (and bases) dissociate completely or almost completely in dilute aqueous
solutions (HCI.' H 2 SO / Thus. a 0.1 N solution of HCI is essentially 0.1 N in hydrogen ion
\
I .
pH of a 0.1 N solution of HCI would be 1 if the IpH depehded on the concentration of W ions. However, pH actually depends upon the activ~y of H+ ions. pH of 0.1 N solution of HCI is experimentally found to be 1.09. .
We can write pH = - log [H"J as pH = - log aH+I ~here a is equal to the activity. Substituting the
experimentally determined pH into this equation ~e get I
1.09 = - log a H + '
a H + = 8.1 x 10-2 mole/litre
Thus although the concentration of H+ ion in 0.1 N Hel solution is 0.1 moles per litre, the activity of H+ ion is only 0.081 moles per litre and the pH tak~s this value into consideration and not the concentration. From this value we can calculate the a9tivity coefficient, y .
0.081
0.1
:: 0.81
It should, however, be emphasized that in very dilute solutions and also for weak acids, the activity is equal to the concentration. It is only for concentrated solutions and for strong acids and bases that activity considerations assume importance.
(See "What do we mean by strength of an acid 1").
Hydrolysis of Salts There are numerous salts which. from an inspection oftheir chemical fonnulae. cannot in
any possible way provide either hydrogen ions or hydroxyl ions in water. Yet. in solution. many of these salts test either acidic or basic. Thus sodium acetate. CH
3 COONa. t~sts basic when it
Acids and Bases 21
is dissolved in water. Obviously sodium acetate solution has more OH- ions than it has H30+ . Similarly, ammonium chloride, NH Cl, tests acidic in water which means that this solution has more H 0+ ions than it has OH-. In~pection of the formulae of these salts tells us that they can not pos~ibly provide H30+ or OH- ions. What then is the mechanism by which extra OIr or extra H30+ ions are being produced in such salt solutions?
To answer this question let us find out which ions will be present in a solution of these salts in water. First let us conSider sodium acetate: Upon dissolution in water, sodium acetate completely dissOCiates into the Na+ ions and acetate, CH COO-, ions. Apart from these two ions, some H 0+ and OH- will also be present through di~sociation of water. This inspection tells us that tfie only way sodium acetate can test basic is by decreasing the H 0+ concentration _ 3 and thus relatively increasing the OH concentration. Let us find out whetlier any of the two ions, CH3COO- and Na+, produced by sodium acetate, have the ability to combine with protons (H30+) and effectively redu..ce their concentration. Can Na+ ions bind H30+? Obviously no. Can Na+ ions combine with OH ions? No. Because NaOH is a strong base (alkali), and by definition sodium ions readily release OH- ions. The answer, thus, does not lie in Na+ ions. If now we consider CH3COO- ions, we will see that this ion is derived from a weak acid, the acetic acid. We have already seen that weak acids are weak because their conjugate bases are strong and bind with protons rather tenaciously reducing the extent of diSSOCiation. The strong conjugate base, CH3COO- ion in this case, can therefo~e bind with protons (H30+) and effectively remove them from solution leaving an excess of OH ions. This makes a soClium acetate solution test baSic (Figure 1.4). Is it that all salts of weak acids and strong bases (sodium acetate is an example) test basiC in solution? Yes, by definition all of them have strong conjugate bases which can remove protons from solution. We therefore can generalize the situation. Salts of weak acids and strong bases test basic when dissolved in water.
Ions from the salt: Na +
Ions from water: H+
... t---------~~~ Tendency to combine
~ No possibility of Interaction
Figure 1.4. Hydrolysis ojsodium acetate (salt ojstrong base and weak acid). Na+ and Of1 do not have a tendency to combine because they are derivedjrom strong alkali. CH
3 COO-. however. has a tendency to combine
with W oj water berause it is a base coryugate to a weak acid. This depletes W ions oj water while Of1 remain unchanged. The solution becomes alkaline. (H
3 0+ shown as W jar the sake oj SImplicity)
The same train of logic can be adapted to find out what will happen when salts of strong acid and weak base (Figure 1.5). and salts of strong acid and strong base (Figure 1.6) are dissolved in water. We can generalize these situations also and state that (i) salts oJstrong acids and weak bases test acidic when dissolved in water. and (ii) salts oj strong acids and strong bases test neutral when dissolved in water.
Ions from salt:
Ions from water:
ow
Figure 1.5. Hydrolysis oj ammonium chloride (salt oj strong acid and weak base). CZ- and W have no tendency to combine. NHt on the other hand can combine with OIr ions. This depletes 011 ions oj water while H+ ions remain constant. The solution becomes acidic
Ions from salt: Na+
Ions from water:
Figure 1.6. Hydrolysis oj sodium chloride (salt oj strong acid and strong base). As evident from the figure. none oj the salt ions has any tendency to combine with either W or 011 provided by ionization oj water. The solution remains neutral.
If any ion from the salt interacts with water in such a manner as to change its pH. hydrolysis is said to occur.
The Effect of Salts Upon the Dissociation of kids Let us see what happens when a salt of a weak acid is mixed with the weak acid in
solution. Experimental results with such mixed solutions tell us that the pH of such solutions increases as compared to the pH when only the acid was present. This obviously means that the addition of salt to acid solution has decreased the dissociation of the acid. If we apply the same principles which we considered in the above section. we can provide an answer for this decrease in dissociation. Let. us consider the solution of acetic acid and its salt. sodium acetate as an example. From our discussion above we know that sodium acetate is completely dissociated in solution. whereas acetic acid is only weakly dissociated. We. therefore. have the following dissociation equations :
We have seen that acetic acid is a weak acid and dissociates very little. This is because its conjugate base. CH
3 COO-. is very strong and binds protons tenaCiously. Since sodium acetate
dissociates completely. by adding this salt we are further increasing the concentration of the conjugate base, i.e .• the acetate ion. These extra ions then combine with the small number of protons dissociated from acetic acid. Thus. the H+ ion concentration gets reduced and the pH increases. We can therefore say that the pH oj a solution oJweak acid and its salt is determined by the ratio oj salt to acid in the solution. The higher the salt concentration. the higher the pH. Table 1.6 elaborates the effect of changing salt to acid ratio on the pH of salt-acid solution.
Acids and Bases 23
Table 1.6 Effect of Changing Salt/Acid Ratio on the pH of Salt-Acid Solution
Sodium Acetate Acetic Acid Ratio pH (Molar) (Normal) Salt/Acid
0.00 0.2 0.00 2.7 0.05 0.2 0.25 4.6 0.10 0.2 0.50 4.4 0.15 0.2 0.75 4.6 0.20 0.2 1.0 4.7
The same set of prtnciples discussed above apply in the case of solutions of weak hydroxides and their salts also. We might cite the example of NH 4 OH and NH 4 CI, where the dissociations are
NH4CI~NH~ +CC
while NH OH is only partially dissociated, NH CI dissociates completely. The extra NH: ions due to th~ dissociation of NH4CI depress the dissociation of NH40H thereby decreasing OH concentration and thus a drop in pH results. The higher the salt concentration the lower the pH.
BUFFERS: SYSTEMS WHICH RESIST CHANGEs IN pH
Solutions which contain both weak acids and their salts are known as buffer solutions (by the same logic, solutions containing weak bases and their salts are also buffer solutions) because they have the capacity to resist changes in pH when confronted with either an acid or a base. The prtnciple behind this resistance of pH by buffers remains the same as described in the previous section. However, we will consider it once again in a more expliCit manner. Let us consider a system of acetic acid and sodium acetate. From the discussion in the previous section we know that sodium acetate dissociates fully and acetic acid dissociates only a little. The solution therefore contains undissociated acetic acid molecules, CH COOH, acetate ions, CH3COO-, and Na+ ions. Let us now see what happens when an acid or a
3 base is added to this
solution. When an acid (HCl) is added:
CH3COO- +H+ +CC ~CH3COOH+CC
In solution HCI dissociates ccmpletely to produce hydrogen ions and chlOride ions. The free hydrogen ions which could have decreased the pH, combine with the strong conjugate base CH3 COO- and are thus removed. The pH of the solution does not decrease appreciably (it falls in proportion to the change in ratio of salt to acid in solution).
When an alkali (NaOH) is added:
CH3COOH+Na+ +OH- ~CH3COO- +Na+ +H 2 0
The strong alkali, NaOH, dissociates completely into its constituent ions Na+ and OH-. OH- could have increased the pH, but in the buffer solution they react with CH3COOH to give rise to water and acetate ions. The pH does not increase appreciably (it increases only in proportion to the change in the ratio of acid to salt in the solution).
To what extent can a buffer solution resist change in pH ? A simple example will be cited. If 10 ml of 0.1 N HCI is added to 990 ml of pure water (pH 7.0). the pH of water drops 4 units and becomes 3. Similarly. if 10 ml of 0.1 N NaOH is added to 990 ml of pure water. the pH increases by 4 pOints and becomes 11. However. if 10 ml of 0.1 N HCl is added to 990 ml of a buffer consisting 0.1 N acetic acid and 0.1 M sodium acetate (pH 4.76). the drop in pH is only 0.0 1 points. The pH changes merely to 4.75. Similarly. addition of 10 ml of 0.1 N NaOH to-990 ml of above buffer solution elicits a rise of merely 0.0 1 units on the pH scale. The pH becomes 4.77. We thus see that buffer solutions resist changes in pH to a very significant extent (we will consider the same example quantitatively a little later).
We have seen that the conjugate base provided by salt dissociation is actually involved in the buffering action. The metal ions (like Na+ in sodium acetate) are not involved. We should therefore rewrite the definition of buffer solutions. Buffers are mixtures oJweak acids and their conjugate bases.
The Henderson-Hasselbalch Equation Henderson-Hasselbalch equation is important for understanding buffer action and acid
base balance in the blood and tissues of the mammalian system. The equation is derived in the follOwing way. Let us denote a weak acid by the general formula HA. and its salt by the general formula BA (B+ being the metal ion and A- being the conjugate base). The salt dissociates completely. while the weak acid dissociates only partly. We can write the eqUilibrium reactions for the dissociation of HA and BA in the buffer solution as follows:
HA r H++A
BA ~ B++A-
We will soon find that Henderson-Hasselbalch equation is simply another way or writing the expression for the dissociation constant of a weak acid.
Solving for (H+]. we get
Taking the negative logarithm of both sides. the equation becomes
However. - log [H+] = pH. and - log K = pK . Therefore. a a
[HA] pH= pKa -IOg~
Acids and Bases 25
To change the negative sign. we invert -log [HAJ/[A-] and obtain
This is Henderson-Hasselbalch equation. Now. the weak acid. HA. is only slightly dissociated even in the absence of the salt. Thus very little of the A- ions come through the dissociation of weak acid. On the other hand. we have seen that the salt BA is completely dissociated and gives a high concentration of A- ions. It can. therefore, be safely assumed that the concentration of the undissociated acid [HAl is equal to the total acid concentration. W~ can also assume that all A- has dissociated from BA and therefore the concentration of the conjugate base. [A-l is equal to the concentration of the salt. [BAl. Taking into consideration these assumptions. the Henderson-Hasselbalch equation can take many different forms.
or
or
[conjugate base] pH = pKa + log [aCid]
pH = pK + log a
[proton acceptor]
[proton donor]
As With all the equations considered so far. the Henderson-Hasselbalch equation also applies more accurately when concentrations are converted to activities by multiplying With appropriate activity coeffiCients. This is necessary because the values of pK and activities vary With ionic strength. The value of pK on the basiS of activities can be calculated With the help of
a the folloWing relationship :
pK (activity) = pK (concentration)-1.018 r;; a a "M
where ~ is the ionic strength of the solution. For most calculations. however. concentrations can provide fairly accurate results. Now, that we have derived an equation which relates pH to the ratio of salt concentration (conjugate base concentration) and the weak acid concentration. let us see the quantitative basis of buffer solution8 re'sisting a large change in pH. We have seen that addition of 10 ml 0.1 N Hel to 990 ml of pure water brings its pH down from 7 to 3. Let us see wbat happens if we add this acid to 990 ml of 0.1 N acetic acid and 0.1 M sodium acetate buffer solution. The H+ ions dissociating from Hel are neutralized by the acetate ions.
The addition of Hel therefore lowers the concentration of the acetate ion slightly and raises the concentration of acetic acid by the same amount. Ifwe assume that all H+ ions have been neutralized. the drop in acetate ion concentration will be 10-3 mole/litre. The concentration of acetic acid would rise by the same amount.
26
[ ] mole mole mole
Biophysical Chemistry
Substituting the final salt and acid concentrations in the Henderson-Hasselbalch equation we get
0.0999 pH = pK + log---
0.0999 pH = 4.76 + log---
0.101
= 4.75
The pH of the buffer solution after addition of 10 ml of 0.1 NHCl changes from 4.76 to 4.75; a drop of merely 0.01 units of pH.
Henderson-Hasselbalch equation gives a very important relationship which makes it possible to calculate the pK of any given acid with extreme ease. The relationship is, that if the
a molecular ratio of salt to acid is unity in a solution, the pH of that solution will be equal to the pK of the acid used.
a
pH = pK + 0 a
pH =pK a
Thus to calculate the pK of any acid one only needs to dissolve that acid and its salt in a
equal concentrations and then experimentally determine the pH of the solution. It will be equal to the pK of the acid. Some extremely important probleI1~s about buffers which can be solved
a using Henderson-Hasselbalch equation are provided for in Box 1.6.
Henderson-Hasselbalch equation makes it clear that the pH of a buffer solution depends upon the pK of the acid and upon the salt to acid concentration ratio. The lower the pK of the
a a acid the lower will be the pH. The buffer pH will increase with increasing salt concentration. Again, according to Henderson-Hasselbalch relationship, the actual salt and acid concentrations can be varied widely without any change in pH if the ratio between the two is unity. Thus, a lactate buffer containing 0.01 M lactate and 0.01 N lactic acid will have the same pH even if the buffer is diluted 10 times or even 20 times. In actual cases, however, the pH of the diluted buffer increases slightly. This increase is not significant enough.
Acids and Bases
Box 1.6
(1) Calculate the pK of acetic acid, given the fact that the concentration of free acetic acid is 0.1 N and that of sodiurfl acetate is 0.2 M. The pH of the solution is 5.06.
Ans. [acetate]
[acetate] pK = pH -log -=------=
0.1 = 4.76
pK a
of acetic acid is 4.76 (2) Calculate the pH of a mixture of 0.01 N lactic acid and 0.087 M lactate. The pK of lactic acid is 3.86. a
Ans. [lactate]
0.087 = 3.86 +Iog-- = 3.86 + log 8.7 0.01
= 3.86 + 0.94 = 4.8
pH of the above solution is 4.8. (3) Calculate the ratio of concentrations of lactate and lactic acid in a buffer system whose pH is 4.50. pK of lactic acid is 3.86.
a
n . [lactic acid]
[lactate] log = pH-pK
[lactic acid] a \
= 4.5 - 3.86 = 0.64
lactic acid
The ratio of concentration of lactate and lactic acid in the above buffer is 4.37.
(4) Can you calculate the ratio of concentrations of HCO; to H2 CO 3 at the pH of blood? lake the pK
a of H2C0
Buffer Capacity By buffer capacity we mean the capacity of the buffer to resist changes in pH. The capacity
to resist changes in pH depends upon (i) the actual concentrations of salt and acid present in the buffer. and (ii) the salt to acid concentration ratio.
First. let us consider the effect of actual salt and acid concentration on the buffer capacity. Let us add 1 ml of 0.1 N HCl to a lactate buffer solution containing 10 ml of 0.1 M lactate and 10 ml of 0.1 N lactic acid (pH ofthis buffer will be equal to the pK oflactic acid. 3.86. since the ratio of salt to acid is unity). What will be the change in pH of the ~uffer solution? The HCl will convert 1 ml of the salt to 1 ml of acid. The pH of the solution will therefore be
9 pH = 3.86+ log- = 3.86+log 9-log 11
11
= 3.86 + (0.9542 - 1.0414) = 3.77 (App.)
the change in pH of the buffer solution is therefore 3.86 - 3.76 = 0.09. Thus. one ml of 0.1 N HCl causes a decrease of about 0.09 pH unit.
Suppose we add 1 ml of 0.1 NHCl to a buffer solution containing 10 ml of 0.025 Mlactate and 10 ml of 0.025 N lactic acid. What will be the change in pH ? The HCI. in this case. will convert 4 ml of salt to acid. The pH of the solution will therefore be
6 pH=3.86+log-=3.86+log6-log 14
14
= 3.86 + (0.7782 - 1.1461) = 3.49
the change in pH of the buffer solution is therefore 3.86 - 3.49 = 0.37. Thus. in this case. 1 ml of 0.1 N HCI causes a decrease of about 0.37 pH unit.
The above example tells us that the first buffer has a higher buffer capacity than the second. This means that buffers containing higher concentrations of salt and acid have a higher buffer capacity as compared to solutions with lower salt and acid concentrations.
Let us now consider the effect of salt to acid concentration ratio upon the buffer capacity. To understand this. let us consider a lactate buffer composed of 15 ml of 0.1 Mlactate and 5 ml of 0.1 IV lactic acid. The pH of this buffer would be
15 pH = 3.86 + log - = 3.86 + (1.176-0.6989) = 4.34
5
Let us now add 1 ml of 0.1 N HCl to this buffer. The HCl would convert 1 ml of salt to 1 ml of acid. The pH of the buffer will be
14 pH = 3.86+log- = 3.86+(1.1461-0.7782)= 4.23
6
Thus the pH of the buffer is lowered by 0.11 pH unit. As shown previously. 1 ml of 0.1 N HCI added to a buffer composed of 10 ml of 0.1 M lactate and 10 ml 0.1 Nlactic acid changes its pH by 0.09 pH unit. This example elaborates the effect of salt to acid concentration ratio on buffer capacity. The generalized statement based on tl-.e above example can be that when the ratio of salt to acid concentration is unity. the buffer has maximum efficiency.
Acids and Bases 29
The buffer range of any given buffer is about 2 pH units. It consists of one pH unit on either side of the pK of the buffer acid. Thus. lactate buffer should be a good buffer in the pH range 2.86 - 4.86. I~we increase the concentration of buffer solution. we can also increase its buffering range to a little extent. The selection of a proper buffer system for a given experimental condition is a common problem. Some examples are provided. For the pH range 3 to 4. phthalic acid-potassium acid phthalate can be used; for the pH range 4-6. acetic acid-sodium acetate buffer is satisfactory; for the pH range 6 to 8. monosodium dihydrogen phosphate (acid) - disodium monohydrogen phosphate (salt) buffer is useful (see Appendix).
How important buffers are for normal functioning of a body can be understood from the fact that the pH of blood is maintained strictly within the range 7.3 to 7.5. Death is more or less certain below a pH of7.0 and above a pH of7.9. In the laboratory. buffers are used for two main purposes: (i) as reference standards for pH determination. and (ii) to maintain optimum acid base reaction of a medium such as bacteria or tissue culture or an enzymatic reaction mixture. We will discuss more about some important biological buffers in a later section.
SOME PRECAUTIONARY INFORMATION ABOUT COMMONLY USED BUFFERS
As mentioned earlier. it is the pK value that is of utmost importance when deciding about which buffer has to be used. However ~ each buffer has other chemical characteristics peculiar to it which must be borne in mind. Several buffers may fit the pH range one is working in. However. a few of them may have characteristics that are detrimental to the experimental setup. This becomes even more important considering the fact that most of the commonly used buffers were not designed for biochemical use. The most common problems that plague these buffers are inhibition of some enzymes. precipitation of polyvalent cations. tOxiCity. absorption of ultraviolet light. strong effect of concentration and temperature on pH. and lack of good buffering activity in the most used pH range in biochemistry. A few most commonly used buffers are discussed below individually.
Phosphate Buffers The advantages of phosphate buffers are numerous. They have a high buffering capacity.
Both. Na and K salts are very highly soluble and thus any ratio of Na + and K+ ions can be selected. Because the ions are highly charged. high ionic strength can be obtained without the need for high molarity.
The last named advantage can become a disadvantage too. It is impossible to prepare a phosphate buffer with a high buffering capacity and a low ionic strength!
The actual disadvantage of the phosphate buffers are as follows. They may bind polyvalent cations. Chiefly. they bind Ca2+. and to a lesser extent. Mi+. More importantly. phosphate buffers are known to be toxic to mammalian cells. Another disadvantage is the lack of buffering capacity in the range 7.5 to 8.0.
They are good buffers between the pH range 12.0 -12.5.
Carbonate Buffers The principal disadvantages of these buffers result because of relative insolubility of most
metal carbonates and because of .he sensitivity of pH to temperature changes. High temperatures cause extreme pH changes due to loss of CO
2 ,
The buffering range in which these buffers work well is 10 - 10.8.
Trls Buffer This buffer is probably the most used in biochemistry and for obvious reasons. Consider
the advantages. (1) Since the pK is 8. it has a high buffering capacity between 7.5 and 8.5. a
(2) Very low toxicity. (3) Does not interfere with most biochemical reactions. (4) Available in very pure forms.
The disadvantages are as follows: (1) Like carbonate buffers, its pH varies with tem~erature to a very high extent. (2) Like phosphate buffers, it reacts with a few metal ions like Cu +, Ca2+, Ni2+, Ag+ etc. (3) It reacts with some glass electrodes and thus may lead to erroneous pH readings.
EDTA Buffers EDTA (ethylenediaminetetraacetate) is not normally used for its buffering. It is a good
chelating agent of divalent cations and is added to other buffers mainly to reduce the concentrations of the divalent cations. Thus, one finds that EDTA buffers are used very frequently when working with nucleic acids; the reason is that Mg2+ is a cofactor for nucleases and the use of EDT A therefore abolishes the activity of these enzymes. This is exactly why EDTA buffers are used when nucleic acids are to be stored. One precaution here. EDTA suffers from the disadvantage of absorbing very highly in the UV range. As such, if nucleic acid concentration has to be estimated, the concentration of this buffer should be kept very low (0.001 M).
Another buffer that suffers from high absorbance in the UV range is the barbiturate buffer.
Boric Acid and Glycine Buffers Borate has weak toxicity and glycine, of course, has none. Both these buffers have a low
UV absorption. Borate is good between pH range 8.7 to 9.7 and glycine between 9.5 to 10.3. Additionally, borate is chosen for work with bacteriophages since it stabilizes them somehow.
Glycylglycine Buffer This is often a buffer of choice for enzymological work and works well in the pH range 7.5
to 8.0. It also has very low UV absorbance. This is another major plus since enzyme activity assays in the UV range will not be impeded. One more great advantage is that it has no affmity for the divalent cations Ca2+ and Mg2+. These are precisely the cations that are used very often for enzymological work.
The disadvantage with glycylglycine springs from its being a peptide : it is cleaved by proteases and as such cannot be used with these enzymes. Additionally, it cannot be used with crude protein preparations since such preparations may have protease contamination.
Triethanolamine Buffer This is another favorite for enzymological work. It has all the advantages listed above for
glycylglycine. It buffers at the same pH range and it doesn't suffer from the limitation of glycylglycine, namely protease susceptibility. Also, it is a volatile buffer and therefore may be chosen for purification work where the buffer is to be subsequently removed.
The Good Buffers These buffers are so named after their discoverer, Norman Good. Because of several
problems with the buffers just discussed, Good looked at a large number of zwitterionic buffers. The buffers that he found good lack the drawbacks mentioned above. They are not toxic, they do not absorb appreciably in the UV range, they do not preCipitate divalent cations, their pH is not sensitive to temperature changes, and they are quite soluble. These buffers are given below in a tabulated form (Table 1. 7). Since they have very long names, they are usually known by their abbreviations. However, their full names are being provided in the table.
Acids and Bases 31
Table 1.7. Good's Buffers
N-(2-acetamido)-2- ACES 6.88 6.4 - 7.4 aminoethanesulfonic acid; 2-[(2-amino-2-oxoethyl)amino]- ethanesulfonic acid
N-(2-acetamido)iminodiacetic ADA 6.62 6.2 - 7.2 acid; [(carbamoylmethyl)imino]- diacetic acid
2-[bis(2-hydrosyethyl)amino]- BES 7.15 6.6 - 7.6 ethanesulfonic acid
N ,N -bis(2-hydroxyethyl)glycine Bicine 8.35 7.8 - 8.8
3-(cyc1ohexylamlno)propane- CAPS 10.40 9.7 - 11.1 sulfonic acid
2-(cyc1ohexylamino)ethane- CHES 9.55 9.0 - 10.1 sulfonic acid
4-(2-hydroxyethyl}-1-piperazine- HEPES 7.55 7.0 - 8.0 ethanesulfonic acid
4-(2-hydroxyethyl}-I-piperazine- HEPPS* 8.0 7.6 - 8.6 propanesulfonic acid
2-(N-morpholino)ethanesulfonic MES 6.15 5.8 - 6.5 acid
3-(N -morpholino)propanesulfonic MOPS 7.20 6.5 - 7.9 acid
l,4-piperazinediethanesulfonic PIPES 6.80 6.4 - 7.2 acid
3-i[2-hydroxy-I,I-bis(hydroxy- TAPS 8.40 7.8 - 8.8 methyl-ethyIJ-aminoyPropane- sulfonic acid
N-tris(hydroxymethyIJmethyl-2- TES 7.50 7.0 - 8.0 aminoethanesulfonic acid
N -tris[(hydroxymethyl)methylJ Tricine 8.15 7.6 - 8.8 glycine;N-[2-hydroxy-1, I-bis- (hydroxymethyl-ethyl)glycine
* Also known as EPPS.
TITRATIONS : THE INTERACTION OF AN ACID WITH A BASE
The old definition of neutralization states that an acid and a base react with each other to form salt and water. The Bronsted -Lowry concept offers a much broader view of the process of neutralization. According to this concept. neutralization is a process of proton transfer from an acid to a base. Neutralization need not result in the formation of a recognizable salt and may not involve water.
32
(conjugate basel
Although, in the following pages, we shall be considering acid-base interactions in aqueous media, the above discussion will help us in identifying the conjugate acid and base produced in any neutralization process.
Titration is normally used to determine the amount of an acid in a given solution. In this procedure a known volume of an acid is titrated with a base (usually NaOH) whose concentration is accurately known. Small aliquots ofthe base are added till the acid is totally neutralized. The titration can be followecj. by adding an indicator to the acid solution or by continuous measurement of the pH by a pH meter. The concentration of the base and the volume required for fully neutralizing the acid are sufficient for calculations which will reveal the concentration of the acid in solution.
Titration Curves of Weak Acids Let us again take the example of acetic acid. Figure 1.7 represents the characteristic
titration curve of acetic acid when it is titrated against a strong alkali. The figure traces the course of titration of a 0.1 N solution of acetic acid with 0.1 N NaOH at 25°C. Before the titration is started (Le. before any NaOH is added), the acetic acid is slightly ionized and the pH of the solution is due to acid alone. When successive aliquots of NaOH are added, the OH- from dissociation of NaOH will combine with the free H+ in solution to form water. As soon as the free H+ is neutralized by OH- to water, some of the undissociated acetic acid immediately dissociates further to satisfY its dissociation constant. Thus with each addition of NaOH, more water is formed and more and more acetic acid gets converted to the acetate anion.
+ - - + CH3 COOH + Na + OH ~ CH3 COO + H20 + Na
As the titration progresses, the concentration of acetate ion increases continuously and that of acetic acid decreases. Have we come across this situation before? Yes. We know that solutions of weak acids and their conjugate bases are known as buffers. With the progress of titration, the solution is fast becoming a mixture of the conjugate base, acetate, and the weak acid, acetic acid. The pH of this solution will now change in accordance with the Henderson Hasselbalch equation, i.e., at any stage of titration, we should be able to calculate the pH of the solution using the Henderson-Hasselbalch relationship. If we plot the pH values against the volume of alkali added we get the characteristic curve shown in Figure 1.7. The titration curves of all weak acids have similar shape (Figure 1.7). They differ only in their location on the pH scale. The position of the curve on the pH scale depends upon the pK of the acid being titrated.
a While dealing with the Henderson-Hasselbalch relationship, we have already considered that the pK of an acid is equal to the pH of the solution containing equal concentrations of both the
a salt and the acid. Such a situation will clearly be present at the mid-point of the titration. Thus the pH of the solution when the acid is half titrated represents the pK of the acid being titrated
a (Figure 1. 7).
The titration curve of a weak acid is usually spread over about 4 pH units. Thus, for a weak acid whose pK is 5, the titration begins at around pH 3. This acid will be half titrated at pH 5 and will stand completely titrated at around pH 7. If the pK of the acid being titrated is 7,
a the titration begins at pH 5, is half completed, by pH 7, and is complete at around pH 9. The titration curves of these two acids will be displaced along the pH scale according to their respective pK.
a
1.0
33
Figure 1. 7. Characteristic titration curoes oj weak acids. TIl.e midpoints oj the titrations have been indicated. Also indicated are the predominant ionic species at the beginning. midpoint and end qf the titrations. The b41fering zones have been shown.
From Figure 1.7. we note that the titration curves are relatively flat in their centre sections. These flat zones are the buffering regions of the acid -conjugate base pair (Figure 1. 7). On the basis of these curves one can select the salt acid concentrations that will give a good buffer capacity. One can see that the titration curve assumes greatest degree of flatness at its pK
a where the acid to conjugate base concentration ratio is unity. This ratio obviously has the highest buffer capacity. This is the proof for what we have already considered mathematically in a previous section: the buffer is most efficient in reSisting pH changes when the ratio of salt to acid concentration is unity. Figure 1.7 also shows that at both the ends the titration curve breaks sharply. This means that the composition of the acid-conjugate base solution in these regions is not good for a buffer. It is obvious that at both the ends the ratio of conjugate base to acid concentration is far removed from unity.
Titration curves of weak bases follow the same pattern as seen for weak acids. but in a reverse order as evident from Figure I.B.
34
14
.~ .. -M Aniline I pkb=.ct·74 ~ pkw - rkb = 9.26 = pka
PH 7 1\ . :
hYdrOChloride
fJ Aniline F I I hydrochloride I I ,
0.5
Titration of a Strong Acid with a Strong Base
14 I
I I
I i :
I ./ I
100% - Equivalents of OH~ 100% Acid 0.1 N NaOH Salt
Figure 1.9. Titration oj a strong acid with strong base (0.1 N HCl against 0.1 N NaOH).
Figure 1.9 represents the titration curve of 0.1 N HCI titrated against 0.1 N NaOH. The striking thing about this titration curve (in general for titration curves of all strong acids) is the very sluggish change in pH as successive aliquots of NaOH are added. To change the pH by one unit, almost 80% of the NaOH is required. However, at the later stages the titration curve shows a sharp break and the pH changes rapidly. Thus the HCI solution has a good buffering capacity between pH 1 and 3. As this pH range is seldom used in biology, titration curves of strong acids are not so important to a biochemist.
Titration Curves of Polybasic Acids Let us now consider titration curves of polybasic acids which can donate more than one
proton and can consequently possess more than one pK corresponding to the successive dissociation of each of the protons. A good example is afforaed by phosphoric acid, H
3 PO 4' for
which three ionization steps and there corresponding pK are a
Acids and Bases 35
4 +H. pKa = 12.4
Thus. in a titration of phosphoric acid the first stage consists of titration of H3P04 to H2P04• the second in the titration of H2PO 4 to HPO i-. and the third in titration of HPO i- to PO!: For phosphoric acid the three pKa are much separated from each other. The titration curve. therefore. shows a sharp break after each pKa and at these regions the buffering capacity of the solutions is very poor (Figure 1.10). However. there are three different pH zones at which the phosphoric acid system can act as a very good buffer. This example of phosphoric acid has been deliberately chosen because many biological molecules contain phosphate-related groups. These groups enter into multistep acid-base processes closely analogous to those of phosphoric acid itself.
---for HP02 - - P03-- + H+ prJ' = 12.4 : 4""""'-- 4 Ha
I I
244
--for H PO ~ H PO-4 + H+ pKa = 2.24 34 2
O~ __ ~~~~ __ ~ o 25 _ 50 _ 75
ml ofO.IN NaOH
FYgure 1.10. Titration of25 mIs of 0.1 N H 3 PO solution by 0.1 N NaOH solution. pKa of three dilferent stages are
slwwn. 7hree buffering zones, although not slwwn. are self evident.
What happens if the polybasic acid happens to have different pKa values very close to each other? Let us answer this question with the help of an example of citric acid. Citric acid has three PKa values which are relatively close to each other (pK\ = 3.1. pK2 = 4.7. pKs = 6.4). In such a case what will happen is that by the time the first H+ is fully titrated the second H+ also starts titrating. Likewise. the titration of the second H+ is not complete before the third H+ starts titrating. In such cases there are no sharp breaks in the titration curve between successive pKa and one observes a relatively flat curve throughout. Such systems are well buffered over a big range of pH. This is evident from the titration curve of Citric acid shown in Figure 1.11. If three acids having pKa values not far away from each other are mixed together. one would observe similar type of curve for such a mixture also. This is what happens in the body. The physiological buffers have their PKa relatively close to each other. Their titration curves therefore overlap thereby enhancing their effiCiency in the pH range maintained by the body fluids.
t! :r: 5 0..
NaOH
Figure 1.11. Titration oj citric acid by NaOH equivalent strength. Compare this CW1Je with Fig.1.10. Citrate titration gives a characteristic flat curve because oj overlapping first. second. and third stages oj hydrogen ion dissociation. Citric acid thereJore has a large buffering zone.
FUNCTION AND STRUCTURE OF BIOMOLECULES IS pH DEPENDENT
The death of a human being below a blood pH of 7.0 and above a pH of 7.9 is enough testimony for the importance of pH to life in general. Examples may also be cited of death of tissue cultures and bacterial cultures in inadequately buffered media. It is therefore a very obvious conclusion that biomolecules are profoundly affected by changes in pH. In any case, most of the important conponents of the living cell are acidic, basic, or amphoteriC and any alteration in the pH of the environment profoundly affects their state of ionization and thereby their conformation and biological activity.
In this section we will deal with pH-dependent properties of proteins and their building blocks, amino acids. We will also discuss in brief the pH-dependent properties of other biomolecules.
Ionization of Amino Acids is pH-Dependent All amino acids are amphiprotic compounds and can be denoted by the general formula
R
I H-C-NH
I 2
COOH Their a-amino group is weakly baSic and has a pK in the range 9-10.5. The
a a-carboxyl is acidic with the pK in the range 1.7 to 2.4. All amino acids are therefore ionized in
a an aqueous solution depending on the preVailing pH.
The amino acids which do not possess any dissociable group in the side chain exist in three ionic forms :
R
Acids and Bases 37
At a low pH only the a-amino group is ionized and the amino acid is a cation. If the pH is raised the a-carboxyl group starts dissociating. This process leaves a negative charge on the amino acid which already has a positive charge due to the amino group. The charges cancel out and the amino acid possesses no net charge. This state is known as the zwitterionic state and the amino acid may be called a zwitterion. If the pH is still further raised. the hydrogen ion from amino group dissociates. This leaves only the negative charge on the amino acid due to the carboxyl group dissociation and the amino acid behaves as an anion.
Thus. on the basis of the principles we have discussed earlier (Henderson-Hasselbalch relationship), it can be said that at a pH equal to the pKa of the carboxyl group (pKa1 ) the amino acid will exist as partly cation. partly zwitterion. Similarly. at pH equal to the pKa of the amino group (PKa2) the amino acid will exist partly as anion and partly as zwitterion. In a solution in pure water the amino acid exists mostly as a zwitterion. Let us take the example of alanine.
CH 3
CH 3
I COO-
If we add an acid. HCI. to this solution of alanine in water it will behave as a base. The reaction (neutralization) can be represented by the equation
CH I 3
CH I 3
H+ CI- ~ +H N - CH - COOH + + ~ 3 + cr
On the other hand. if an alkali is added. alanine solution behaves as an acid. The reaction (neutralization) can be expressed by the equation
CH I 3
+Na++ OH- ~ H2N-CH-COO- + Na+ + H20
Thus. in the zwitterionic alanine. a-amino group behaves as an acid and the a-carboxyl group as a base.
9.69
Equivalents of OH- -+ Figure 1.12. TItration curve Jor alanine.
PKaI isJora·COOH andpKa2 is for the a·NH; .
What would the titration curve of alanine look like? Figure 1. 12 shows that the titration curve for alanine looks like that of a diprotic weak acid. From the midpoint of the first titration curve we can calculate the pKal (for the dissociation of carboxyl group) and from the mid-point of the second titration curve we can calculate the PKa2 (for the dissociation of the amino group). From these two pKa values we can calculate th

biophysical chemistry principles and techniques

Documents