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.

determine pH of weak acid question

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

determine pH of weak acid 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 Ka and substitute in the concentrations to get a expression between Ka and x.

determine pH of weak acid Ka expression before approximation

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 Ka 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.

determine pH of weak acid calculate H concentration from Ka

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

determine pH of weak acid calculate pH

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 Ka and concentration of a weak acid:

determine pH of weak acid weak acid formula

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

determine pH of weak acid weak base formula

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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