Henderson–Hasselbalch Equation

\[pH=pK_a+\log\left(\frac{[A^-]}{[HA]}\right)\]

Variables

pHsolution pH

pKanegative logarithm of acid dissociation constant

A[A⁻]conjugate base concentration (mol/L)

HAweak acid concentration (mol/L)

AHAconcentration ratio [A⁻]/[HA]

Description

What is this formula?

The Henderson–Hasselbalch equation relates the pH of a buffer solution to the acid dissociation constant (pKa) and the ratio of conjugate base concentration to weak acid concentration.

When to use it

Use this equation to estimate the pH of buffer solutions, determine the required acid-to-base ratio for a target pH, or analyze acid–base equilibria involving weak acids.

Example

Given:

pKa = 4.76

[A−] = 0.20 mol/L

[HA] = 0.10 mol/L

Formula:

pH = pKa + log([A−]/[HA])

Substitution:

pH = 4.76 + log(0.20/0.10)

pH = 4.76 + log(2)

pH = 4.76 + 0.301

Result:

pH = 5.06

Applications

Buffer preparation

Analytical chemistry

Biochemistry

Pharmaceutical formulations

Environmental chemistry

Note

This equation is an approximation derived from the acid dissociation equilibrium expression. It is most accurate for dilute buffer solutions where activity coefficients are close to unity. At high ionic strengths or very concentrated solutions, activity corrections may be required.