Calculating the pH of a Buffer Solution

The pH of a buffer solution can be calculated from the equilibrium constant and the initial concentration of the acid.

Learning Objective

Calculate the pH of a buffer made only from a weak acid.

Key Points

The strength of a weak acid (buffer) is usually represented as an equilibrium constant.
The acid-dissociation equilibrium constant, which measures the propensity of an acid to dissociate, is described using the equation: ${ K}_{a }=\frac { { [H }^{ + }][{ A }^{ - }] }{ [HA] }$ .
Using K_a and the equilibrium equation, you can solve for the concentration of [H⁺].
The concentration of [H⁺] can then be used to calculate the pH of a solution, as part of the equation: pH = -log([H⁺]).

Term

equilibrium
The state of a reaction in which the rates of the forward (reactant to product) and reverse (product to reactant) reactions are the same.

Full Text

What Does pH Mean in a Buffer?

In chemistry, pH is a measure of the hydrogen ion (H⁺) concentration in a solution. The pH of a buffer can be calculated from the concentrations of the various components of the reaction. The balanced equation for a buffer is:

$HA \rightleftharpoons H^+ + A^-$

The strength of a weak acid is usually represented as an equilibrium constant. The acid-dissociation equilibrium constant (K_a), which measures the propensity of an acid to dissociate, for the reaction is:

$K_{a} = \frac{\left [H^{+} \right ]\left [A^{-} \right ]}{\left [HA \right ]}$

The greater [H⁺] x [A^-] is than [HA], the greater the value of K_a, the more the formation of H⁺ is favored, and the lower the pH of the solution.

ICE Tables: A Useful Tool For Solving Equilibrium Problems

ICE (Initial, Change, Equilibrium) tables are very helpful tools for understanding equilibrium and for calculating the pH of a buffer solution. They consist of using the initial concentrations of reactants and products, the change they undergo during the reaction, and their equilibrium concentrations. Consider, for example, the following problem:

Calculate the pH of a buffer solution that initially consists of 0.0500 M NH₃ and 0.0350 M NH₄⁺. (Note: K_a for NH₄⁺ is 5.6 x 10^-10). The equation for the reaction is as follows:

$NH_4^+ \rightleftharpoons H^+ + NH_3$

We know that initially there is 0.0350 M NH₄⁺ and 0.0500 M NH₃. Before the reaction occurs, no H⁺ is present so it starts at 0.

ICE table - initial

ICE table for the buffer solution of NH4+ and NH3 with the starting concentrations.

During the reaction, the NH₄⁺ will dissociate into H⁺ and NH₃. Because the reaction has a 1:1 stoichiometry, the amount that NH₄⁺ loses is equal to the amounts that H⁺ and NH₃ will gain. This change is represented by the letter x in the following table.