Acid Dissociation Constant

:HA(aq) + H₂O(l) H₃O⁺(aq) + A^–(aq)

:

} {[\mbox{HA}]}

The equilibrium is often written in terms of "H⁺(aq)", which reflects the Bronsted-Lowry Theory of acids.

:HA(aq) H⁺(aq) + A^–(aq)

Because this constant differs for each acid and varies over many degrees of magnitude, the acidity constant is often represented by the Additive Inverse of its Common Logarithm , represented by the symbol p''K''_a (using the same mathematical relationship as {Link without Title} is to PH ).

:p''K''_a = −log₁₀''K''_a'''

In general, a larger value of ''K''_a (or a smaller value of p''K''_a) indicates a stronger Acid , since the extent of dissociation is larger at the same concentration.

Using the acid dissociation constants, the concentration of acid, its conjugate base, protons and hydroxide can be easily determined. If an acid is partly neutralized, the ''K''_a can also be used to find the pH of the resulting Buffer . This same information is summarized in the Henderson-Hasselbalch Equation .

BASICITY CONSTANT OF THE CONJUGATE BASE

By analogy, one can define the basicity constant ''K''_b and the p''K''_b of the Conjugate Base A^–:

:

K_b = rac{{[\mbox{A}^-}

:p''K''_b = −log₁₀ ''K''_b'''

This is the dissociation constant for the equilibrium

:A^–(aq) + H₂O(l) HA(aq) + OH^–(aq)

Analogously to ''K''_a, an increasing value of ''K''_b indicates a stronger Base , since the number of protons accepted is larger at an identical concentration.

RELATIONSHIP BETWEEN ACIDITY AND BASICITY CONSTANTS

There exists a relationship between the value of ''K''_a for an acid HA and the value of ''K''_b for its conjugate base A^–. Since adding the ionization reaction for HA and the ionization reaction of A^– always gives the reaction for the Self-ionization Of Water , the product of the acidity and basicity constants gives the dissociation constant of water (''K''_w), which is 1.0 × 10^-14 at 25°C. In other words,

K

:p''K''_a + p''K''_b = p''K''_w

As the product of ''K''_a and ''K''_b remains constant, it follows that stronger acids have weaker conjugate bases, while weaker acids have stronger conjugate bases.

FACTORS THAT DETERMINE THE RELATIVE STRENGTHS OF ACIDS AND BASES

Being an Equilibrium Constant , the acid dissociation constant

K_{a}

is determined
by the difference in free energies

\Delta G^{\circ}

between the reactants and products,
specifically, between the protonated (AH) and de-protonated (A^–) states. Molecular
interactions that favor the deprotonated (A^–) state over the protonated (AH) state
will increase

K_{a}

(because the ratio

{Link without Title} / {Link without Title} increases) or,
equivalently, decrease p

K_{a}

. Conversely, molecular interactions that favor the protonated
(AH) state over the de-protonated (A^–) state will decrease

K_{a}

(because the ratio

{Link without Title} / {Link without Title} is lower) or, equivalently, increase p

K_{a}

.

For example, suppose that the protonated (AH) form donates a Hydrogen Bond AH

\cdots

X to
another atom X, which the de-protonated form cannot do (since it has no hydrogen left). The protonated form is favored by having a hydrogen bond, so the p

K_{a}

increases (the

K_{a}

decreases). The magnitude of the p

K_{a}

shift can even be determined from the change
in

\Delta G^{\circ}

using the equation

K_{a} = e^{-rac{\Delta G^\circ}{RT}}

.

Other molecular interactions can also shift the p

K_{a}

. Adding an electron-withdrawing
chemical group (such as Oxygen , a Halide , a Cyano group or even a Phenyl ring) to the
molecule near the titrating hydrogen will
favor the deprotonated state (by stabilizing the electron left behind when the proton dissociates) and,
thus, decrease p

K_{a}

(increase

K_{a}

). For example, successive oxidation of HClO and
Perchloric Acid HClO₄ is approximately 11 orders of magnitude (p

K_{a}

shift of ~11). Electrostatic interactions can affect the equilibrium as well. The presence of surrounding
negative charges would disfavor the formation of a negatively charged, de-protonated species and,
thus, increase p

K_{a}

. In particular, the ionization of one group on a molecule can
affect the p

K_{a}

of another.

Fumaric and Maleic Acid are classic examples of p

K_{a}

shifts. Both molecules have the same composition, being two Carboxylic Acid groups separated by two
double-bonded carbon atoms; fumaric acid is the Trans Isomer , whereas maleic acid is the
Cis Isomer By symmetry, one might imagine that the two carboxylic acids had the same
p

K_{a}

, which is typically ~4 for Carboxylic Acid s. That's almost true for
Fumaric Acid , which has p

K_{a}

's of roughly 3.5 and 4.5. By contrast, Maleic Acid
has p

K_{a}

's of roughly 1.5 and 6.5. When ''one'' of its carboxylic acids de-protonates,
the other can form a strong hydrogen bond to it; overall, the effect is to favor the de-protonated
state of the hydrogen-bond-accepting group (lowering its p

K_{a}

from ~4 to 1.5)
and to favor the protonated state of the hydrogen-bond-donating group
(raising its p

K_{a}

from ~4 to 6.5).

IMPORTANCE OF PKA VALUES

The pKa value(s) of a compound influence many characteristics of the compound such as its reactivity, solubility 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 .

See Methods For Calculating Protein PKa Values

P''K''<SUB>A</SUB> OF SOME COMMON SUBSTANCES

Measurements are at 25ºC in water: