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.).
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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.
4 Biophysical Chemistry
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.
6 Biophysical Chemistry
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
8 Biophysical Chemistry
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
+
10 Biophysical Chemistry
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 /' "
12 Biophysical Chemistry
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
14 Biophysical Chemistry
•
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
18 Biophysical Chemistry
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)
22 Biophysical Chemistry
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).
24 Biophysical Chemistry
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
28 Biophysical Chemistry
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
30 Biophysical Chemistry
(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
Biophysical Chemistry
(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
Biophysical Chemistry
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.
36 Biophysical Chemistry
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