PKa
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The weak acid acetic acid donates a proton to water in an equilibrium reaction to give the acetate ion and the hydronium ion.
The weak acid acetic acid donates a proton to water in an equilibrium reaction to give the acetate ion and the hydronium ion.

An acid dissociation constant (aka acidity constant, acid-ionization constant) is an equilibrium constant for the dissociation of an acid. It is denoted by Ka. For an equilibrium between a generic acid, HA, and its conjugate base, A-,

H A \rightleftharpoons A^- + H^+,

Ka is defined, subject to certain conditions, as

K_a = \frac{[A^-][H^+]}{[HA]}

where [HA], [A^-] \, and [H^+]\, are equilibrium concentrations of the reactants.

The term acid dissociation constant is also used for pKa, which is equal to -log10 Ka. The term pKb is used in relation to bases, though pKb has faded from modern use due to the easy relationship available between the strength of an acid and the strength of its conjugate base. Though discussions of this topic typically assume water as the solvent, particularly at introductory levels, the Brønsted-Lowry acid-base theory is versatile enough that acidic behavior can now be characterized even in non-aqueous solutions.

The value of pKa indicates the strength of an acid: the larger the value the weaker the acid. In aqueous solution, simple acids are appreciably dissociated in in the pH range pKa \pm 2. The actual extent of the dissociation can be calculated if the acid concentration and pH are known.

A knowledge of pKa values is essential for the understanding of the behaviour of acids and bases in solution. For example, many compounds used for medication are weak acids or bases, so a knowledge of the pKa and log p values is essential for an understanding of how the compound enters (or does not enter) the blood stream. Other applications include buffer solutions, acid-base homeostasis and certain kinds of enzyme kinetics, such as Michaelis-Menten kinetics, which involve a pre-equilibrium step. Also, knowledge of pKa values is a prerequisite for a quantitative understanding of the interaction between acids or bases and metal ions to form complexes in solution .

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Contents

Definitions

Concepts in
Chemical Equilibria
Acid dissociation constant
Binding constant
Buffer solution
Chemical equilibrium
Chemical stability
Dissociation constant
Distribution coefficient
Distribution ratio
Equilibrium constant
Equilibrium unfolding
Equilibrium stage
Liquid-liquid extraction
Phase diagram
Phase rule
Reaction quotient
Relative volatility
Solubility equilibrium
Stability constant
Thermodynamic equilibrium
Theoretical plate
Vapor-liquid equilibrium

According to Arrhenius's original definition, an acid is a substanstance which dissociates in solution, releasing the hydrogen ion.

H A \rightleftharpoons A^- + H^+

The equilibrium constant for this "dissociation" reaction is known as a dissociation constant. However, since the liberated proton combines with a water molecule to give an hydronium ion, Arrhenius proposed that the "dissociation" reaction should be written as an acid-base reaction.

H A +H_2O \rightleftharpoons A^- + H_3O^+

Brønsted and Lowry generalized this definition as follows.

acid + base \rightleftharpoons conjugate base + conjugate acid

For aqueous solutions an acid, HA, reacts with the base, water, to give the conjugate base, A-, and the conjugate acid, the hydronium ion. The Brønsted-Lowry definition is particularly useful when the solvent is a substance other than water, such as DMSO; in that case the solvent, S, acts as a base, accepting a proton and forming the conjugate acid SH+. It also puts acids and bases on the same footing as being, respectively, donors or acceptors of protons. The conjugate acid of a base, B, "dissociates" according to

BH^+ +OH^- \rightleftharpoons B+H_2O.

Examples

H_2CO_3^{2-} +H_2O \rightleftharpoons HCO_3^{-} + H_3O^+ The bicarbonate ion is the conjugate base of carbonic acid.
HCO_3^{-} +OH^- \rightleftharpoons CO_3^{2-} +H_2O The bicarbonate ion is the conjugate acid of the base, the carbonate ion.

In fact the bicarbonate ion is amphoteric. These reactions are important for acid-base homeostasis in the human body (see carbonic acid).

Equilibrium Constant

Main article: Equilibrium constant

An acid dissociation constant is a particular example of an equilibrium constant. For the specificic equilibrium

HA +H_2O \rightleftharpoons A^- +H_3O^+

the equilibrium constant can be defined by[1]

K=\frac{{\{A^-\}} {\{H_3O^+\}}} {{\{HA\}} {\{H_2O\}}}

where {A} is the activity of the chemical species A etc (activity is a dimensionless quantity). It is conventional, for a dissociation constant, to put the activities of the products in the numerator and those of the reactants in the denominator. See Chemical equilibrium for a derivation of this expression.

Since activity is the product of concentration and activity coefficient the definition could also be written as

K_a = \frac{[A^-][H_3O^+]}{[HA][H_2O]}\times \frac{\gamma_{A^-}\gamma_{H_3O^+}}{\gamma_{HA}\gamma_{H_2O}} =\frac{[A^-][H_3O^+]}{[HA][H_2O]}\times\Gamma

where [HA] represents the concentration of HA and Γ is a quotient of activity coefficients. According to this definition Ka is not constant, but will vary with the concentrations, when Γ also varies.[1]

In order to avoid this complication dissociation constants are usually determined in a medium of high ionic strength, that is, under conditions in which Γ can be assumed to be always constant.[1] For example, the medium might be a solution of 0.1 M NaNO3 or 3M KClO4. Note, however, that all published dissociation constant values refer to the specific ionic strength and chemical composition of the dissolved salt used in their determination and that different values are obtained with different conditions.

Monoprotic acids

An acid with a single dissociative proton is called a monoprotic acid and will be denoted as HA. The dissociation reaction can be written as

H A +H_2O \rightleftharpoons A^- + H_3O^+

For such an acid, the acid dissociation constant is the ratio of the product of the concentration of the products over the product of the concentration of the reactants (this implies that the activity quotient is constant). Chemicals with constant concentration (solids, liquids, spectator ions) are neglected.

K_a = \frac{[H_3O^+][A^-]}{[HA][H_2O]}

In all but the most concentrated solutions it can be assumed that the concentration of water, H2O, is constant, approximately 55 mol dm-3, and can therefore be left out. Moreover, the hydration of the proton can also be assumed to be constant. With these assumptions the expression for the dissociation constant simplifies to

K_a = \frac{[H^+][A^-]}{[HA]}.

This is the expression in common use.

pKa is defined as -log10 Ka.

Water

Water has both acidic and basic properies. The equilibrium constant for the equilibrium

H_2O+H_2O\leftrightharpoons OH^- + H_3O^+

is given by

K_a=\frac{[H^+][OH^-]}{[H_2O]^2}

Since the concentration of water can be assumed to be constant, this expression simplifies to

K_w=[H^+][OH^-]\,

The self-ionization constant of water, Kw, can thus be seen as a special case of an acid dissociation constant.

Polyprotic acids

Polyprotic acids are acids which can loose more than one proton. The constant for dissociation of the first proton may be denoted as Ka1 and the constants for dissociation of successive protons as Ka2, etc.

It is generally true that successive pK values increase (Pauling's first rule).[2] For example, for a diprotic acid, H2A, the two equilibria are

H_2 A \rightleftharpoons HA^- +H^+
HA^{-} \rightleftharpoons A^{2-}+H^+

it can be seen that the second proton is removed from a negatively charged species. Since the proton carries a positive charge extra work is needed to remove it; that the cause of the trend noted above. There are a few exceptions to this rule which occur when there is a major structural change such as in the sequence

VO_2^{+}(aq) \rightleftharpoons H_3 VO_4 + H^+ pKa1 = 4.2
H_3 VO_4 \rightleftharpoons H_2 VO_4^{-} + H^{+} pKa2 = 2.60
H_2 VO_4^{-} \rightleftharpoons HVO_4^{2-} + H^{+} pKa3 = 7.92
HVO_4^{2-} \rightleftharpoons VO_4^{3-} + H^{+} pKa4 = 13.27

The pKas of vanadic acid, H3VO4, follow Pauling's rule just like phosphoric acid, H3PO4, (values below). All species in this series are tetrahedral, but VO_2 \left( H_2 O \right)_4 ^{+} is octahedral and pKa2 < pKa1. [3]

Bases

Historically the equilibrium constant Kb for a base was defined as the dissociation constant of HB, the acid conjugate to the base, B − . While not all bases have charges, the charge is used here to indicate that the base is any Lewis base, and is not strictly necessary as in the case of ammonia or ethanoate. It is also being used to annotate how many protons the base is capable of accepting.

B^- + H_2 O \rightleftharpoons HB + OH^{-}

Using similar reasoning to that used before

K_b = \frac{[\mbox{HB}][\mbox{OH}^-]} {[\mbox{B-}]}
\operatorname{p}K_b = -\log_{10} K_b\,

The concentration of the hydroxide ion is related to the concentration of the hydronium (assuming the solvent is water) by K_w = \left[ H^{+} \right]\left[ OH^{-} \right], therefore

[\mbox{OH}^-] = \frac{K_w}{[\mbox{H}^+]};

Kw is the constant for the self-ionization of water. Substituting the expression for \left[ OH^{-} \right] into the expression for Kb

K_b = K_w \frac{ \left[ \mbox{HB} \right] }{ \left[ \mbox{B}^- \right] \left[ \mbox{H}^{+} \right] } = \frac{K_w}{K_a}

It follows that

pKb = pKw − pKa

In water at 25 °C pKw is 14 so then pKb = 14 − pKa.

In effect there is no need to define pKb separately from pKa, but it is done because pKb values can be found in literature.

Temperature dependence

All equilibrium constants vary with temperature according the van 't Hoff equation

\frac {d\ln K} {dT} = \frac{{\Delta H_m}^{\Theta}} {RT^2}.

Thus, for exothermic reactions, (ΔH is negative) K decreases with temperature, but for endothermic reactions (ΔH is positive) K increases with temperature.

Usage

As the difference between the pH and the pKa changes, the concentration of the acid (HA) and its conjugate base (A-) also change as dictated by the Henderson-Hasselbach equation.
As the difference between the pH and the pKa changes, the concentration of the acid (HA) and its conjugate base (A-) also change as dictated by the Henderson-Hasselbach equation.

The pH of a solution of weak acid can be expressed in terms of the extent of dissociation. After rearranging the expression defining the dissociation constant, and putting pH = -log10[H+, one obtains

\mbox{pH} = \mbox{pK}_a - \log \frac{[HA]}{[A^-]}

This is a form of the Henderson-Hasselbalch equation. It can be deduced from this expression that

  • when the acid is 1% dissociated, that is, when \frac{[HA]}{[A^-]} = 100, pH = pKa − 2
  • when the acid is 50% dissociated, that is, when \frac{[HA]}{[A^-]} = 1, pH = pKa
  • when the acid is 99% dissociated, that is, when \frac{[HA]}{[A^-]} = 0.01, pH = pKa + 2

It follows that the range of pH within which there is partial dissociation of the acid is about pKa \pm 2.This is shown graphically at the right.

A weak acid may be defined as an acid with pKa greater than about -2. An acid with pKa = -2 would be 99% dissociated at pH 0, that is, in a 1M HCl solution. Any acid with a pKa less than about -2 is said to be a strong acid. Strong acids are said to be fully dissociated. There is no precise pKa value that distinguishes between strong and weak acids because strong acids, such as sulfuric acid, are associated in very concentrated solution.

On the pKa scale of acid strength, a large value indicates a very weak acid, and a small value indicates a not so weak one.

The pH of a solution of a weak acid can be easily calculated when the analytical concentration of the acid is known. See ICE table for details.

Some polyprotic acids can be treated as a set of individual acids. This is possible when successive pK values differ by 4 or more. For example with phosphoric acid

H3PO4 \rightleftharpoons H2PO4- +H+, pKa1 = 2.15
H2PO4- \rightleftharpoons HPO42- +H+, pKa2 = 7.20
HPO42- \rightleftharpoons PO43- +H+, pKa3 = 12.37

Both the hydrogenphosphate and dihydrogenphosphate ions can be treated as acids in their own right. On the other hand, the two pKs for malonic acid are 2.51 and 5.05, so there are pH values at which both malonic acid and the hydrogenmalonate ion co-exist. More elaborate calculations are needed to calculate the composition of solutions of malonic acid.

Factors that determine the relative strengths of acids

Being an equilibrium constant, the acid dissociation constant Ka is determined by the standard free energy difference ΔGo between the reactants and products, specifically, between the protonated (HA) and deprotonated (A−) forms of the substance.

Pauling's second rule[2] states that the value of the first pK for acids of the formula XOm(OH) n is approximately independent of n and X and is approximately 8 for m=0, 2 for m=1, -3 for m=2 and <-10 for m=3. This correlates with the oxidation state of the central atom, X: the higher the oxidation state the stronger the oxyacid. For example, pKa for HClO is 7.2, for HClO2 is 2.0, for HClO3 is -1 and HClO4 is a strong acid.

fumaric acid
fumaric acid
maleic acid
maleic acid

With organic acids inductive effects and mesomeric effects affect the pKs. The effects are summarised in the Hammett equation and subsequent extensions.

Structural effects can also be important. The difference between fumaric acid and maleic acid is a classic example. Fumaric acid is (E)-1,4-but-2-enedioic acid, a trans isomer, whereas maleic acid is the corresponding cis isomer, i.e. (Z)-1,4-but-2-enedioic acid (see cis-trans isomerism). Fumaric acid has pKas of approximately 3.5 and 4.5. By contrast, maleic acid has pKas of approximately 1.5 and 6.5. The reason for this large difference is that when one proton is removed from the cis- isomer (maleic acid) a strong intramolecular hydrogen bond is formed with the nearby remaining carboxyl group. This favors the formation of the maleate H+, and it opposes the removal of the second proton from that species. In the trans isomer, the two carboxyl groups are always far apart, so hydrogen bonding is not observed.

Importance of pKa values

The pKa value(s) of a compound influence many characteristics of the compound such as its reactivity, and spectral properties (colour). In biochemistry the pKa values of proteins and amino acid side chains are of major importance for the activity of enzymes and the stability of proteins. This property is of general importance in chemistry because ionization of a compound alters its physical behavior and macro properties such as solubility and lipophilicity. For example ionization of any compound will increase the solubility in water, but decrease the lipophilicity. This can be exploited in drug development to increase the concentration of a compound in the blood by adjusting the pKa of an ionizable group. This must be done with caution, however, since an ionized compound will pass less easily through cell membranes.

Further information: Protein pKa calculations

Acidity in nonaqueous solutions

Solvents will be more likely to promote ionisation of a dissolved acidic molecule if:[4]

  1. It is a Protic solvent, capable of forming hydrogen bonds
  2. It has a high donor number, making it a strong Lewis base.
  3. it has a high dielectric constant (Relative permittivity).

Solvents can be polar, protic, donor or none of the above. None of the above, indicated by a blank entry, means neutral or noninteracting behavior. Data taken at or near 25°C.[5]

Compound Solvent Class Dielectric constant
1,4-dioxane Donor 2.2
Hexane 1.9
Carbon tetrachloride 2.2
Benzene 2.3
Diethyl ether Donor 4.3
Acetic acid Protic donor 6.1
Tetrahydrofuran Donor 7.6
Acetone Polar donor 21
Dimethylsulfoxide Polar donor 47
Water Polar protic donor 78
Formamide Polar protic donor 111

An acidic solvent will also suppress dissociation of an acid. For example, hydrogen chloride is a weak acid when dissolved in the acidic solvent acetic acid, characterized by having a greater pKa than when in water. This is because, as per Le Chatelier's Principle, the release of protons by hydrogen chloride would increase the concentration in the solution. This would increase the reverse reaction rate, resulting in the reprotonation of some of the chloride ions. The extent of the reprotonation in the case of the disrupted equilibrium is determined by the acid dissociation constant. See ICE table for a quantitative explanation of how to calculate these changes in equilibrium position.

Acidity scales have been developed for solvents aside from water, notably for dimethyl sulfoxide (abbrev. 'DMSO') and acetonitrile.[6] Because water is a protic solvent it is more basic than DMSO, and its dielectric constant is greater, this means that acids will deprotonate to a lesser extent than in water (see the above paragraph). For this reason, DMSO is widely used as an alternative to water in evaluating acids and bases.

There are some drawbacks to using alternative solvents, due to a process called homoconjugation. In solvents of low dielectric constant, ions tend to associate which complicates the interpretation of pKas. In particular, aprotic solvents will encourage acids (typically polar molecules) to hydrogen bond with their conjugate base. Because the formation of the bond is exothermic and therefore stabilizing, this has the effect of increasing the amount of deprotonation. When water is used, however, because it is both protic and polar it is capable of both accepting and donating hydrogen bonds. This allows it to prevent 'clumping' of ions.

In acetonitrile solution, para-toluenesulfonic acid has a homoconjugation constant pKf, of -2.9.[7] This indicates that the toluenesulfonate anion has a strong tendency to form a hydrogen bond with the parent acid. Homoconjugation has the effect of enhancing the acidity of acids, lowering their effective pKas, by stabilizing the conjugate base. Due to homoconjugation, the proton-donating power of toluenesulfonic acid in acetonitrile solution is enhanced by a factor of nearly 800.

pKa of some common substances

There are multiple techniques to determine the pKa of a chemical causing some discrepancy between different sources. Well measured values are typically are within 0.1 units of each other. Data presented here was taken at 25 °C in water.

Chemical Name pKa1 pKa2 pKa3
Acetic acid [8] 4.756
Adenine[8] 4.17
Aniline [9] 27
Arsenic acid [9] 2.22 6.98 11.53
Benzoic acid[8] 4.204
Boric acid [9] 9.21
Butanoic acid [9] 4.82
Chromic acid [9] 0.98 6.5
Codeine [9] 8.17
Cresol [9] 10.29
Diethylene glycol [9] 14.18
Formic acid[8] 3.751
Glycerol [9] 13.99
Hydrofluoric acid [9] 3.17
Hydrocyanic acid [9] 9.21
Hydrogen selenide [9] 3.89
Hydrogen peroxide (90%) [9] 11.7
Lactic acid [9] 3.86
Maleic acid [9] 1.92 6.23
Propanoic acid [9] 4.87
Phenol[8] 9.99
Phosphoric acid[10] 2.12 7.21 12.38
L-(+)-Ascorbic Acid[8] 4.17 11.57

Note: Values for amines and associated compounds are for the protonated ammonium form.

See also

References

  1. ^ a b c F.J,C. Rossotti and H. Rossotti, The Determination of Stability Constants, McGraw-Hill, 1961.
  2. ^ a b Greenwood, N. N.; Earnshaw, A. (1997). Chemistry of the Elements, 2nd Edition, Oxford:Butterworth-Heinemann. ISBN 0-7506-3365-4.  p. 50
  3. ^ Greenwood, N. N.; Earnshaw, A. (1997). Chemistry of the Elements, 2nd Edition, Oxford:Butterworth-Heinemann. ISBN 0-7506-3365-4.  Chapter 22
  4. ^ Loudon, G. Marc (2005). Organic Chemistry, 4th Edition, New York: Oxford University Press. ISBN 0-19-511999-1.  p. 317
  5. ^ Loudon, G. Marc (2005). Organic Chemistry, 4th Edition, New York: Oxford University Press. ISBN 0-19-511999-1.  p. 318
  6. ^ March, J.; Smith, M. (2007). Advanced Organic Chemistry, 6th edition, New York: J. Wiley and Sons. ISBN 978-0-471-72091-1. 
  7. ^ Coetzee, J. F. and Padmanabhan, G. R., "Proton Acceptor Power and Homoconjugation of Mono- and Diamines", J. Amer. Chem. Soc.,1965, 87, 5005-5010.
  8. ^ a b c d e f Speight, James G. Lange's Handbook of Chemistry (16th Edition). McGraw-Hill.
  9. ^ a b c d e f g h i j k l m n o p Knovel Critical Tables (2nd Edition). (2003). Knovel.
  10. ^ Brown, T.E.; Lemay, H.E.; Bursten, B.E. (2006). Chemistry The Central Science, 10th Edition, Pearson Publications, A27. ISBN 0131096869. 

Further reading

  • Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight. 3rd ed. New York: W. H. Freeman and Company, 2005
  • Housecroft, Catherine and Sharpe, Alan, Inorganic Chemistry, Prentice Hall, 2nd. edition, 2004. (Non-aqueous solvents)
  • Hulanicki, A. (1987). Reactions of acids and bases in analytical chemistry. Horwood. ISBN 0853123306.  (translation editor: Mary R. Masson)
  • Perrin, D. D.; Dempsey, B. and Serjeant, E.P. (1981). pKa prediction for organic acids and bases. Chapman and Hall. ISBN 041222190x. 
  • Albert, A.; Serjeant, E.P. (1971). The determination of ionization constants : a laboratory manual. Chapman and Hall. ISBN 0412103001.  (Previous edition published as Ionization constants of acids and bases. London: Methuen, 1962)

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