Lesson 4 · 25 min

Buffers: resisting pH change

One drop of hydrochloric acid drops pure water from pH 7 to 3 but barely moves a buffer. See how a conjugate pair soaks up added acid and base, and design a buffer for a target pH.

In this lesson

Explain how a conjugate pair neutralizes added acid and base
Use the Henderson–Hasselbalch equation and know when it fails
Understand buffer range ( $\mathrm{p}K_\mathrm{a} \pm 1$ ) and buffer capacity
Design and prepare a buffer of a chosen pH

Add one drop (about 0.05 mL) of 1 M hydrochloric acid to 100 mL of pure water and the pH crashes from 7.0 to 3.3 — thousands of times more $\ce{H3O+}$ . Add the same drop to an acetic acid–sodium acetate solution and the pH hardly moves. A solution that swallows added acid or base with little change in pH is a buffer. Blood, cytoplasm, seawater, and nearly every biochemistry experiment depend on one.

Predict first

To a buffer of 0.10 M acetic acid + 0.10 M sodium acetate, add strong acid to 0.010 M (ignore the volume change). By roughly how much does the pH change?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Falls by about 3 Falls by about 1 Falls by about 0.09 Not at all

Each partner has a job

A buffer contains a weak acid and its conjugate base in comparable amounts:

added acid is converted by the conjugate base into the weak acid: $\ce{A-} + \ce{H3O+} \mathrel{\ce{->}} \ce{HA} + \ce{H2O}$ ;
added base is converted by the weak acid into water: $\ce{HA} + \ce{OH-} \mathrel{\ce{->}} \ce{A-} + \ce{H2O}$ .

Strong acid or base is traded for its weak counterpart, so the pH drifts only as the ratio of the pair changes slowly. Taking the logarithm of the equilibrium expression gives the working formula:

\mathrm{pH} = \mathrm{p}K_\mathrm{a} + \lg\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}

Henderson–Hasselbalch: it uses the made-up concentrations in place of equilibrium ones — that is its approximation.

$[\mathrm{A^-}]$: concentration of the conjugate base (e.g. sodium acetate)
$[\mathrm{HA}]$: concentration of the weak acid

The same additions to a buffer and to pure water

Buffer bench

Buffer pair Total buffer concentration · 0.100 M Base : acid ratio · 1 : 1 Strong acid added (−) / strong base added (+) · 0 mmol/L

$\ce{H2PO4- + H2O <=> HPO4^2- + H3O+}$

Buffer pH 7.20

Pure water pH 7.00

Exact pH (0): 7.20
Henderson–Hasselbalch: 7.20
pH change · Buffer: 0.00
pH change · Pure water: 0.00
Buffer capacity β: 0.0576 M

Buffer
Pure water

Change the base : acid ratio: at 1 : 1 the pH equals p

K_\mathrm{a}

and the capacity peaks. Then lower the total to 0.01 M and see why the same addition now overwhelms the buffer.

A buffer does not lock the pH; it slows its change. The larger the buffer capacity, the more acid or base it takes to move the pH by one unit. Capacity grows with the total buffer concentration and peaks at pH = p $K_\mathrm{a}$ ; beyond $\mathrm{p}K_\mathrm{a} \pm 1$ it falls away quickly. So step one in making a buffer is to choose a conjugate pair whose $\mathrm{p}K_\mathrm{a}$ is close to the target pH.

Worked example

Make an acetate buffer at pH 5.00

Make 1.00 L of acetate buffer, 0.20 M total, at pH 5.00 ( $\mathrm{p}K_\mathrm{a} = 4.76$ ). How much sodium acetate (82.03 g/mol) and glacial acetic acid (60.05 g/mol, density 1.049 g/mL) do you need?

Concept check

Which conjugate pair suits a buffer at pH 9.2 best?

\ce{CH3COOH}

\ce{CH3COO-}

K_\mathrm{a}

4.76)

\ce{H2PO4-}

\ce{HPO4^2-}

K_\mathrm{a}

7.20)

\ce{NH4+}

\ce{NH3}

K_\mathrm{a}

9.25)

\ce{HCO3-}

\ce{CO3^2-}

K_\mathrm{a}

10.33)

Try the calculation

What is the pH of a buffer of 0.30 M $\ce{NH3}$ and 0.20 M $\ce{NH4Cl}$ ? ( $\mathrm{p}K_\mathrm{a}$ of $\ce{NH4+}$ = 9.25)

Key takeaways

A buffer pairs a weak acid with its conjugate base: the base catches added acid, the acid neutralizes added base.
pH = p $K_\mathrm{a}$ + lg([A⁻]/[HA]); at a 1 : 1 ratio pH = p $K_\mathrm{a}$ and capacity is highest.
The useful range is about $\mathrm{p}K_\mathrm{a} \pm 1$ ; capacity grows with total concentration.
Dilution barely changes a buffer’s pH but lowers its capacity proportionally.

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Data and references

D. C. Harris, Quantitative Chemical Analysis, 9th ed. (2016), Ch. 9 (buffers) and Ch. 10.
J. N. Butler, Ionic Equilibrium: Solubility and pH Calculations, Wiley (1998), Ch. 4 (buffer capacity).
A. C. Guyton, J. E. Hall, Textbook of Medical Physiology, 13th ed. (2016), Ch. 31 (acid–base regulation).