Buffer Calculations
- The pH of a buffer solution can be calculated using:
- The Ka 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
Worked example
Calculate the pH of a buffer solution containing 0.305 mol dm-3 of ethanoic acid and 0.520 mol dm-3 sodium ethanoate.
The Ka of ethanoic acid = 1.74 × 10-5 mol dm-3 at 298 K
Answer
Ethanoic acid is a weak acid that ionises as follows:
CH3COOH (aq) ⇌ H+ (aq) + CH3COO- (aq)
Step 1: Write down the equilibrium expression to find Ka
Step 2: Rearrange the equation to find [H+]
Step 3: Substitute the values into the expression
= 1.02 x 10-5 mol dm-3
Step 4: Calculate the pH
pH = - log [H+]
= -log 1.02 x 10-5
= 4.99
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)] = Ka x
- We will use ethanoic acid as our weak acid of choice, with a Ka 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
- This gives a value for the ratio of the concentrations of acid and base needed in our buffer solution:
= 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
= 0.575