How to Determine pH of Weak Acid - Ionic Equilibria

In this video we want to learn how to determine the pH of a weak acid given its concentration and acid dissociation constant.

Let's take a look at this exercise.

The first thing we can do is to write out the dissociation of the weak acid in solution and to complete the ICE table.

The ICE table is a summary to represent the changes in concentrations of reactants and products, where:

I - initial concentration
C - change in concentration
E - equilibrium concentration

So from the ICE table we know that at equilibrium,

[HA] is (0.1 - x) mol dm^-3
[H⁺] is x mol dm^-3
[A^-] is x mol dm^-3

We can then write out the acid dissociation constant term K_a and substitute in the concentrations to get a expression between K_a and x.

Notice that this is a quadratic expression and since for A Level H2 Chemistry we are not required to solve quadratic equations, we need to impose an approximation to simplify the K_a expression.

The approximation is very simple. Since HA is a weak acid with a small degree of dissociation, x is small therefore (0.1 - x) is approximately equal to 0.1.

We can then solve for x which is the concentration of H⁺ and is calculated to be 10^-3 mol dm^-3.

Finally we can calculate pH of this weak acid to be 3 using the following expression.

Usually we can apply the ICE table and approximation in a standardised way so we can derive this outcome to quickly determine H⁺ concentration given K_a and concentration of a weak acid:

Similarly we can have an expression to determine the OH^- concentration of a weak base:

For the detailed step-by-step discussion on how to determine the weak acid's pH, check out this video!

Topic: Ionic Equilibria, Physical Chemistry, A Level Chemistry, Singapore

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