3.1.12.4 - Weak Acids, Bases and Ka

Weak acids, weak bases and partial dissociation

A strong acid ionises almost completely in water, but a weak acid ionises only slightly. That means most of the acid particles stay as molecules, and only a small fraction produces ions. Weak bases behave in the same general way: they react only slightly with water, so the equilibrium lies mainly to the left.

This is why a weak acid can still have a fairly high concentration but a much lower $[\mathrm{H}^+]$ than a strong acid of the same concentration. "Weak" tells you about the extent of dissociation, not how much acid was dissolved. Do not confuse weak with dilute, or strong with concentrated.

For a generic weak acid $\mathrm{HA}$:

A particle diagram is useful here because it makes the equilibrium mixture visible: many undissociated HA molecules remain, while only a few ions are present.

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Only a small proportion of $\mathrm{HA}$ dissociates, so at equilibrium there is still much more $\mathrm{HA}$ than $\mathrm{H^+}$ or $\mathrm{A^-}$.

Constructing and interpreting Ka

Because weak acid dissociation is an equilibrium, we can describe it using an equilibrium constant. For the reaction

the acid dissociation constant is:

When you construct this expression, each concentration is an equilibrium concentration in $\mathrm{mol\,dm^{-3}}$. Water is not included because it is the solvent and its concentration is treated as constant. A larger $K_a$ means the acid dissociates more and is therefore stronger. A smaller $K_a$ means less dissociation and a weaker acid.

This helps you link the equation to real chemistry. If an acid has a relatively large $K_a$, the equilibrium lies further to the right, so more $\mathrm{H^+}$ is produced. If $K_a$ is very small, the equilibrium lies mainly to the left and most acid molecules remain undissociated.

With concentrations expressed in $\mathrm{mol\,dm^{-3}}$, the units used for $K_a$ here are $\mathrm{mol\,dm^{-3}}$: the two numerator concentrations divided by one denominator concentration leave one concentration unit. $pK_a$, like pH, has no units. Compare acid strengths at the same temperature.

One easy trap is using the equation correctly but forgetting what it means. $K_a$ is not just a formula to memorise; it is a measure of the position of equilibrium for weak-acid dissociation.

Calculating pH from Ka and concentration

To calculate the pH of a weak acid, start from the equilibrium expression and use the fact that the acid dissociates only slightly. Suppose the initial concentration of $\mathrm{HA}$ is $c\ \mathrm{mol\,dm^{-3}}$. If $x$ dissociates, then at equilibrium:

• $[\mathrm{H^+}] = x$
• $[\mathrm{A^-}] = x$
• $[\mathrm{HA}] \approx c$

The approximation $[\mathrm{HA}] \approx c$ is the key step. Use this approximation only when $x$ is small relative to $c$, with no added acid or conjugate-base salt and a negligible contribution from water. Check $x/c$ after calculating. If dissociation is appreciable, retain $[\mathrm{HA}] = c-x$ and use $K_a=x^2/(c-x)$.

The diagram below summarises the ICE table setup for a weak acid before you substitute into the expression for $K_a$.

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Substituting into the $K_a$ expression gives: