CHM-09

Henderson–Hasselbalch

pH = pKa + log10([A−]/[HA]). Buffer equation.

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Acid–baseHenderson 1908Hasselbalch

Governing equation

\mathrm{pH}=\mathrm{p}K_a+\log_{10}\dfrac{[A^-]}{[HA]}

where

\mathrm{p}K_a: pKa (—)
[A^-]: Conjugate base (mol/L)
[HA]: Acid (mol/L)
pH: pH (—)

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-09 — Henderson–Hasselbalch) is the form associated with Henderson 1908 · Hasselbalch. Working symbols: $\mathrm{p}K_a$ , $[A^-]$ , $[HA]$ $\rightarrow$ $pH$ . From Ka = [H+][A−]/[HA] one takes −log10. Best buffering when [A−] ≈ [HA].

Purpose

Purpose: compute

pH

from

\mathrm{p}K_a

[A^-]

[HA]

in Physical chemistry via

\mathrm{pH}=\mathrm{p}K_a+\log_{10}\dfrac{[A^-]}{[HA]}

pH = pKa + log10([A−]/[HA]). Buffer equation. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mathrm{p}K_a = 4.760\,\mathrm{—}

[A^-] = 0.100\,\mathrm{mol/L}

[HA] = 0.100\,\mathrm{mol/L}

, the governing relation

\mathrm{pH}=\mathrm{p}K_a+\log_{10}\dfrac{[A^-]}{[HA]}

yields

pH = 4.760\,\mathrm{—}

. Dilute aqueous monoprotic buffer, activity ≈ concentration. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

pKa \mathrm{p}K_a4.76 —Conjugate base [A^-]0.1 mol/LAcid [HA]0.1 mol/L

Outputs

pH pH4.760 —

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Narration of this film

Dilute aqueous monoprotic buffer, activity ≈ concentration.

From Ka = [H+][A−]/[HA] one takes −log10. Best buffering when [A−] ≈ [HA].

Reading speed

Watch on YouTube