Acid Dissociation Constant Definition: Ka

The acid dissociation constant is the equilibrium constant of the dissociation reaction of an acid and is denoted by K_a. This equilibrium constant is a quantitative measure of the strength of an acid in a solution. K_a is commonly expressed in units of mol/L. There are tables of acid dissociation constants, for easy reference. For an aqueous solution, the general form of the equilibrium reaction is:

HA + H₂O ⇆ A^- + H₃O⁺

where HA is an acid which dissociates in the conjugate base of the acid A^- and a hydrogen ion that combines with water to form the hydronium ion H₃O⁺. When the concentrations of HA, A^-, and H₃O⁺ no longer change over time, the reaction is at equilibrium and the dissociation constant may be calculated:

K_a = [A^-][H₃O⁺] / [HA][H₂O]

where the square brackets indicate concentration. Unless an acid is extremely concentrated, the equation is simplified by holding the concentration of water as a constant:

HA ⇆ A^- + H⁺
K_a = [A^-][H⁺]/[HA]

The acid dissociation constant is also known as the acidity constant or acid-ionization constant.

Relating Ka and pKa

A related value is pK_a, which is the logarithmic acid dissociation constant:

pK_a = -log₁₀K_a

Using Ka and pKa To Predict Equilibrium and Strength of Acids

K_a may be used to measure the position of equilibrium:

• If K_a is large, the formation of the products of the dissociation is favored.
• If K_a is small, the undissolved acid is favored.

K_a may be used to predict the strength of an acid:

• If K_a is large (pK_a is small) this means the acid is mostly dissociated, so the acid is strong. Acids with a pK_a less than around -2 are strong acids.
• If K_a is small (pK_a is large), little dissociation has occurred, so the acid is weak. Acids with a pK_a in the range of -2 to 12 in water are weak acids.

K_a is a better measure of the strength of an acid than pH because adding water to an acid solution doesn't change its acid equilibrium constant, but does alter the H⁺ ion concentration and pH.

Ka Example

The acid dissociation constant, K_a of the acid HB is:

HB(aq) ↔ H⁺(aq) + B^-(aq)
K_a = [H⁺][B^-] / [HB]

For the dissociation of ethanoic acid:

CH₃COOH_(aq) + H₂O_(l) = CH₃COO^-_(aq) + H₃O⁺_(aq)
K_a = [CH₃COO^-_(aq)][H₃O⁺_(aq)] / [CH₃COOH_(aq)]

Acid Dissociation Constant From pH

The acid dissociation constant may be found it the pH is known. For example:

Calculate the acid dissociation constant K_a for a 0.2 M aqueous solution of propionic acid (CH₃CH₂CO₂H) that is found to have a pH value of 4.88.

To solve the problem, first, write the chemical equation for the reaction. You should be able to recognize propionic acid is a weak acid (because it's not one of the strong acids and it contains hydrogen). It's dissociation in water is:

CH₃CH₂CO₂H + H₂ ⇆ H₃O⁺ + CH₃CH₂CO₂^-

Set up a table to keep track of the initial conditions, change in conditions, and equilibrium concentration of the species. This is sometimes called an ICE table:

x = [H₃O⁺

Now use the pH formula:

pH = -log[H₃O⁺]
-pH = log[H₃O⁺] = 4.88
[H₃O⁺ = 10^-4.88 = 1.32 x 10^-5

Plug in this value for x to solve for K_a:

K_a = [H₃O⁺][CH₃CH₂CO₂^-] / [CH₃CH₂CO₂H]
K_a = x² / (0.2 - x)
K_a = (1.32 x 10^-5)² / (0.2 - 1.32 x 10^-5)
K_a = 8.69 x 10^-10