Buffer Calculations (Edexcel International A Level (IAL) Chemistry): Revision Note

Buffer Calculations

• The pH of a buffer solution can be calculated using:

  • The K_a of the weak acid

  • The equilibrium concentration of the weak acid and its conjugate base (salt)

• To determine the pH, the concentration of hydrogen ions is needed which can be found using the equilibrium expression

• To simplify the calculations, logarithms are used such that the expression becomes:

• Since -log₁₀ [H⁺] = pH, the expression can also be rewritten as:

• This is known as the Hendersen-Hasselbalch equation

How to make a buffer solution with a required pH

• To make a buffer solution with a pH of less than 7, you need to use a mixture of a weak acid and its conjugate base

  • Conversely, you can make a buffer solution with a pH greater than 7 by using a mixture of a weak base and its conjugate acid

• Imagine we want to make a buffer solution with a pH of 5.00 at a temperature of 298K

• This would require a hydrogen ion concentration of:

[H+(aq)] = 1.00 x 10^-5 mol dm^-3 

• The hydrogen ion concentration of a buffer solution of a weak acid and its conjugate base is calculated using the formula:

[H⁺ (aq)] = K_a x $\frac{\left[\mathrm{acid}\right]}{\left[\mathrm{base}\right]}$

• We will use ethanoic acid as our weak acid of choice, with a K_a value of 1.74 x 10^-5 mol dm^-3 

• Substituting our known values into the equation we get:

1.00 x 10^-5 = 1.74 x 10^-5 x $\frac{\left[\mathrm{acid}\right]}{\left[\mathrm{base}\right]}$

• This gives a value for the ratio of the concentrations of acid and base needed in our buffer solution:

$\frac{\left[\mathrm{acid}\right]}{\left[\mathrm{base}\right]}$= 0.575

• Mixing an equal volume of ethanoic acid with a concentration of 0.575 mol dm^-3 and a sodium ethanoate solution of 1.00 mol dm^-3 would allow us to make this buffer solution

• This would give a solution with an acid concentration of 0.2875 mol dm^-3 and a salt concentration of 0.500 mol dm^-3

$\frac{0.2875}{0.500}$= 0.575