# 7.11.3 Ionization Constants of Weak Acids

Consider a weak acid HX that is partially ionized in the aqueous solution. The equilibrium can be expressed by:

HX(aq) +  H2O(l)    ⇔   H3O+(aq) +  X-(aq)

Initial concentration (M)

c                                     0                     0

Let α be the extent of ionization

Change (M)

-cα                                  +cα                +cα

Equilibrium concentration (M)

c-cα                                  cα                  cα

Here, c = initial concentration of the undissociated acid, HX at time, t = 0. = extent up to which HX is ionized into ions. Using these notations, we can derive the equilibrium constant for the above discussed acid dissociation equilibrium:

Ka = c2α2/c(1- α) = cα2/1- α

Ka is called the dissociation or ionization constant of acid HX. It can be represented alternatively in terms of molar concentration as follows,

Ka = [H+][X-]/[HX]

At a given temperature T, Ka is a measure of the strength of the acid HX i.e., larger the value of Ka, the stronger is the acid. Ka is a dimensionless quantity with the understanding that the standard state concentration of all species is 1M.

The pH scale for the hydrogen ion concentration has been so useful that besides pKw, it has been extended to other species and quantities. Thus, we have

pKa = -log(Ka)

Knowing the ionization constant, Ka of an acid and its initial concentration, c, it is possible to calculate the equilibrium concentration of all species and also the degree of ionization of the acid and the pH of the solution.

A general step-wise approach can be adopted to evaluate the pH of the weak electrolyte as follows:

Step 1. The species present before dissociation are identified as Brönsted-Lowry acids / bases.

Step 2. Balanced equations for all possible reactions i.e., with a species acting both as acid as well as base are written.

Step 4. Enlist in a tabular form the following values for each of the species in the primary reaction

(a) Initial concentration, c.

(b) Change in concentration on proceeding to equilibrium in terms of , degree of ionization.

(c) Equilibrium concentration

Step 5. Substitute equilibrium concentrations into equilibrium constant equation for principal reaction and solve for α

Step 6. Calculate the concentration of species in principal reaction.

Step 7. Calculate pH = -log[H3O+]