Explain how a buffer maintains pH using equilibrium and calculate buffer pH.

What this dot point is asking

TASC expects you to explain buffer action through equilibrium and Le Chatelier's principle, write the neutralising equations, and calculate buffer pH.

What a buffer is

A common example is ethanoic acid mixed with sodium ethanoate: the solution contains plenty of the weak acid $\text{CH}_3\text{COOH}$ and plenty of its conjugate base $\text{CH}_3\text{COO}^-$. A buffer can be made either by mixing the weak acid with a salt of its conjugate base, or by partially neutralising a weak acid with a strong base.

How a buffer works

The buffer relies on the equilibrium $\text{CH}_3\text{COOH}(aq) \rightleftharpoons \text{H}^+(aq) + \text{CH}_3\text{COO}^-(aq)$, with a large reservoir of both partners.

• When acid (extra $\text{H}^+$) is added, it is consumed by the conjugate base: $\text{CH}_3\text{COO}^-(aq) + \text{H}^+(aq) \rightarrow \text{CH}_3\text{COOH}(aq)$. The added hydrogen ions are mopped up, so the pH barely changes.
• When base (extra $\text{OH}^-$) is added, it is neutralised by the weak acid: $\text{CH}_3\text{COOH}(aq) + \text{OH}^-(aq) \rightarrow \text{CH}_3\text{COO}^-(aq) + \text{H}_2\text{O}(l)$. The added hydroxide is removed, so the pH barely changes.

Because both partners are present in large amounts, the buffer absorbs additions of either acid or base.

Buffer capacity

Buffer capacity is the amount of acid or base a buffer can absorb before the pH changes sharply. It is greatest when the two components are present in roughly equal, high concentrations. Once one partner is largely used up, the buffer fails and the pH swings rapidly.

Choosing a buffer for a target pH

To make a buffer at a particular pH, choose a weak acid whose $pK_a$ is close to the desired pH, then adjust the ratio of acid to conjugate base. Because $\text{pH} = pK_a + \log_{10}\dfrac{[\text{base}]}{[\text{acid}]}$, equal amounts of the two give $\text{pH} = pK_a$, and shifting the ratio up or down moves the pH by at most about one unit before the buffer becomes ineffective. This is why each buffer system has a useful working range of roughly $pK_a \pm 1$.

Biological and natural buffers

Buffers are essential in living systems. Human blood is held near pH $7.4$ mainly by the carbonic acid and hydrogencarbonate system, $\text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^-$, with the lungs and kidneys removing or retaining $\text{CO}_2$ and $\text{HCO}_3^-$ to keep the ratio steady. Even small departures from this pH are dangerous, which shows how tightly biological buffers must work. Ocean water is similarly buffered by the carbonate system, which is why rising atmospheric $\text{CO}_2$ gradually lowers ocean pH as the buffer is progressively consumed.

In the exam, name both components of the buffer, write the neutralising equations for added acid and added base, link the resistance to Le Chatelier's principle, and use $K_a$ with the concentration ratio to calculate the pH.