The Henderson-Hasselbalch Equation

Learning Objective 8.9.A Identify the pH of a buffer solution based on the identity and concentrations of the conjugate acid-base pair used to create the buffer.

Quick Notes

The Henderson–Hasselbalch equation is used to calculate the pH of a buffer solution.

It links pH, pK_a, and the concentration ratio of conjugate base to acid.

Small additions of acid or base do not significantly change the pH of a well-prepared buffer.

Full Notes

What is the Henderson–Hasselbalch Equation?

The Henderson–Hasselbalch equation links the pH of a buffer solution to the concentration of the weak acid (HA) and its conjugate base (A⁻).

AP Chemistry graphic of the Henderson–Hasselbalch equation showing pH = pKa + log([A−]/[HA]).

Where:

pH is the acidity of the solution
pK_a is the negative logarithm of the acid dissociation constant (K_a)
[A⁻] is the concentration of the conjugate base
[HA] is the concentration of the weak acid

How It Works

When [A⁻] = [HA], then pH = pK_a (optimal buffering point).
When [A⁻] > [HA], the pH is above the pK_a (the solution is more basic).
When [A⁻] < [HA], the pH is below the pK_a (the solution is more acidic).

Buffering Action

When small amounts of acid or base are added to a buffered solution the ratio [A⁻]/[HA] changes only slightly and therefore, the pH changes very little. This is why buffers are effective at resisting pH changes.

Worked Example

Q: What is the pH of a buffer solution that is 0.20 M acetic acid (CH₃COOH) and 0.10 M sodium acetate (CH₃COONa)? The pK_a of acetic acid is 4.76.

Identify HA = CH₃COOH, A⁻ = CH₃COO⁻; [HA] = 0.20 M, [A⁻] = 0.10 M, pK_a = 4.76.
Apply Henderson–Hasselbalch
pH = pK_a + log\([A⁻]/[HA]\) = 4.76 + log(0.10 / 0.20).
Evaluate ratio
0.10 / 0.20 = 0.50 → log(0.50) ≈ −0.30.
Calculate pH
pH = 4.76 + (−0.30) = 4.46.

Answer: The buffer’s pH is 4.46. Because [A⁻] < [HA], pH is below pK_a, consistent with the rule above.

Summary

The Henderson–Hasselbalch equation lets you calculate the pH of a buffer using pK_a and the ratio of base to acid.
Buffers are most effective when pH ≈ pK_a, i.e., when [A⁻] ≈ [HA].
Adding acid/base to a buffer causes only a small shift in pH.