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Buffer range and capacity

A buffer's usefulness has two distinct limits: range, which describes the pH interval over which both members of the conjugate pair are present in useful proportions, and capacity, which describes how much strong acid or base the buffer can absorb before its pH changes substantially.

For an acid buffer,

$$\mathrm{pH}=pK_a+\log\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}.$$

If the ratio $[\mathrm{A^-}]/[\mathrm{HA}]$ lies between about $0.1$ and $10$, then

$$pK_a-1\lesssim\mathrm{pH}\lesssim pK_a+1.$$

This approximate interval is the buffer's most effective pH range. Outside it, one member of the pair is becoming scarce, so the solution loses the ability to neutralize additions in one direction.

Buffer capacity depends mainly on the absolute amounts of the two components, not just their ratio. Two buffers can have the same pH because they have the same base-to-acid ratio, yet the more concentrated buffer can absorb more added strong acid or base.

For example, buffers containing

$$0.010,\mathrm M\ \mathrm{HA}+0.010,\mathrm M\ \mathrm{A^-}$$

and

$$0.50,\mathrm M\ \mathrm{HA}+0.50,\mathrm M\ \mathrm{A^-}$$

have approximately the same pH, $pK_a$, but the second has far greater capacity because much more material is available to consume added $\mathrm{H_3O^+}$ or $\mathrm{OH^-}$.

For a fixed total buffer concentration, capacity is most balanced when acid and conjugate base are present in comparable amounts. If almost all buffer material is in one form, the solution can resist perturbation well in one direction but poorly in the other.

Buffer design therefore involves two choices: select a conjugate pair whose $pK_a$ lies near the desired pH, and provide enough total buffer concentration to withstand the expected acid or base load. Range is controlled mainly by the ratio and $pK_a$; capacity is controlled mainly by how much buffer material is present.