Calculate buffer pH and component concentrations
Use Ka, pKa and the weak-acid/conjugate-base ratio to calculate buffer pH and composition.
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 25. Use the equilibrium expressions and data stated in the question; written practice is self-checked and human subject-teacher review remains pending.
Before you begin
- Use AS equilibrium expressions, mole calculations, logarithms, and Brønsted–Lowry acid–base ideas.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which ratio appears in pH = pKa + log₁₀(...)?
What you will learn
- Rearrange Ka for a buffer's hydrogen-ion concentration
- Use pH = pKa + log₁₀([A⁻]/[HA])
- Use neutralisation stoichiometry before applying the buffer ratio
The buffer equation follows from Ka
For HA ⇌ H⁺ + A⁻, Ka = [H⁺][A⁻]/[HA]. Rearranging and taking negative base-10 logarithms gives pH = pKa + log₁₀([A⁻]/[HA]). Use this relation for a weak acid and its conjugate base in the same solution.
Because both species share the same solution volume, their concentration ratio is also their amount ratio. If a strong acid or alkali is added first, use the neutralisation equation to find the amounts remaining before calculating the ratio.
Calculate concentration and pH from the relevant data
A question may give Ka, pKa, amounts, volumes or target pH. Rearrange the buffer equation to solve for the unknown ratio, then combine it with total amount or dilution information if required.
The buffer equation assumes the acid equilibrium can be treated with the supplied buffer concentrations. Do not use it when one component is absent or effectively exhausted.
Pause and explain
After adding a small amount of NaOH to HA/A⁻, what should be done before a buffer calculation?
Worked example
A buffer contains [HA] = 0.20 mol dm⁻³ and [A⁻] = 0.10 mol dm⁻³. If pKa = 4.74, calculate pH.
Show the worked solution
- Use pH = pKa + log₁₀([A⁻]/[HA]).
- Substitute the ratio 0.10/0.20 = 0.50.
- Evaluate the logarithm and add pKa.
Answer pH = 4.74 + log₁₀(0.50) = 4.44.
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Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Calculate the pH of a buffer with pKa = 3.75, [HA] = 0.12 mol dm⁻³ and [A⁻] = 0.30 mol dm⁻³.
Give me a hint
Use pH = pKa + log₁₀([A⁻]/[HA]).
Compare my reasoning
- Find the ratio 0.30/0.12.
- Take its base-10 logarithm.
- Add 3.75.
pH = 3.75 + log₁₀(2.50) = 4.15.
Look for these in your work
- Correct ratio selected
- Logarithm evaluated
- pH calculated
A buffer has pKa = 4.20 and pH = 4.50. Find [A⁻]/[HA].
Give me a hint
Rearrange the buffer equation and take the antilogarithm.
Compare my reasoning
- log₁₀([A⁻]/[HA]) = 4.50 − 4.20.
- Raise 10 to the power 0.30.
- State the dimensionless ratio.
[A⁻]/[HA] = 10⁰·³⁰ ≈ 2.0.
Look for these in your work
- Equation rearranged
- Antilogarithm used
- Ratio stated
A mixture starts with 0.20 mol HA and 0.10 mol A⁻. It receives 0.02 mol OH⁻. Find the new amount ratio [A⁻]/[HA].
Give me a hint
OH⁻ converts HA into A⁻ in a 1:1 reaction.
Compare my reasoning
- HA remaining = 0.20 − 0.02 = 0.18 mol.
- A⁻ formed total = 0.10 + 0.02 = 0.12 mol.
- Divide conjugate-base amount by acid amount.
The updated ratio is 0.12/0.18 = 0.667. Since both are in the same final volume, this is also the concentration ratio.
Look for these in your work
- Reaction stoichiometry applied
- Both amounts updated
- Ratio direction correct
Common mistakes
- Inverting [A⁻]/[HA]
- Using starting amounts after neutralisation without updating them
- Using pKa with a strong acid
- Claiming the buffer equation works after one component is exhausted
What can you explain now?
Which ratio appears in pH = pKa + log₁₀(...)?
Compare with the explanation
[A⁻]/[HA]
The conjugate-base concentration is divided by the weak-acid concentration.
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Make it stick
How do Ka and the component ratio determine buffer pH, especially after neutralisation?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.