Buffer solutions

The common ion effect

Acetic acid ionises only a little:

• $\text{CH}_3\text{COOH}(aq) \rightleftharpoons \text{H}^+(aq) + \text{CH}_3\text{COO}^-(aq)$

In $0.10\ \text{mol/L}$ acetic acid alone, $[\text{H}^+] = \sqrt{K_a C} = \sqrt{1.8 \times 10^{-6}} = 1.34 \times 10^{-3}\ \text{mol/L}$. The pH is $2.87$.

Now dissolve sodium acetate in the same solution, also $0.10\ \text{mol/L}$. It adds a lot of acetate ions, the ion that the acid and the salt have in common. By Le Chatelier's principle, the equilibrium shifts to the left. The acid ionises even less.

• $[\text{H}^+] = K_a \times \dfrac{[\text{CH}_3\text{COOH}]}{[\text{CH}_3\text{COO}^-]} = 1.8 \times 10^{-5} \times \dfrac{0.10}{0.10} = 1.8 \times 10^{-5}\ \text{mol/L}$

The pH rises from $2.87$ to $4.74$. Holding back a weak electrolyte with an ion it shares is the common ion effect.

What a buffer is

That mixture of acetic acid and sodium acetate has a useful property. Add a few drops of strong acid or strong base, and its pH hardly moves. A solution like this is a buffer.

There are two common kinds:

• Acidic buffer: a weak acid and its salt with a strong base, such as acetic acid and sodium acetate. Its pH is below 7.
• Basic buffer: a weak base and its salt with a strong acid, such as ammonia and ammonium chloride. Its pH is above 7.

How a buffer resists change

A buffer holds a large store of the weak acid and of its conjugate base. Each one mops up an intruder.

• Add $\text{H}^+$: the acetate ions take it, $\text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH}$.
• Add $\text{OH}^-$: the acetic acid neutralises it, $\text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O}$.

Either way, the strong acid or base turns into the weak partner. Only the ratio of acid to salt changes a little, so the pH changes a little.

The Henderson-Hasselbalch equation

Take the logarithm of $[\text{H}^+] = K_a \dfrac{[\text{acid}]}{[\text{salt}]}$ and change signs. For an acidic buffer:

• $\text{pH} = \text{p}K_a + \log \dfrac{[\text{salt}]}{[\text{acid}]}$

For a basic buffer, the same steps give:

• $\text{pOH} = \text{p}K_b + \log \dfrac{[\text{salt}]}{[\text{base}]}$

When the salt and the acid are equal, the log term is zero and $\text{pH} = \text{p}K_a$. A buffer works best near this point, within about one pH unit of $\text{p}K_a$.

An acidic buffer. $0.10\ \text{mol/L}$ acetic acid and $0.20\ \text{mol/L}$ sodium acetate:

• $\text{pH} = 4.74 + \log \dfrac{0.20}{0.10} = 4.74 + 0.30 = 5.04$

A basic buffer. $0.20\ \text{mol/L}$ ammonia and $0.10\ \text{mol/L}$ ammonium chloride:

• $\text{pOH} = 4.74 + \log \dfrac{0.10}{0.20} = 4.74 - 0.30 = 4.44$, so $\text{pH} = 14 - 4.44 = 9.56$.

A buffer under attack

Take $100\ \text{mL}$ of the first buffer, with $0.10\ \text{mol/L}$ of acid and of salt. It holds $10\ \text{mmol}$ of each. Add $1\ \text{mmol}$ of HCl.

• The acetate falls to $9\ \text{mmol}$ and the acid rises to $11\ \text{mmol}$.
• $\text{pH} = 4.74 + \log \dfrac{9}{11} = 4.74 - 0.087 = 4.65$

The pH falls by less than a tenth. The same acid in $100\ \text{mL}$ of pure water gives $[\text{H}^+] = 0.010\ \text{mol/L}$, so the pH crashes from 7 to $2.00$.

Buffers in your body

Blood must stay close to pH 7.4. A change of a few tenths can be fatal. The main buffer is carbonic acid with the hydrogencarbonate ion, $\text{H}_2\text{CO}_3/\text{HCO}_3^-$. Phosphate and protein buffers help inside cells.

Practise with new numbers

Try it in Python

The program adds hydrochloric acid, one millimole at a time, to a buffer and to pure water.

Common mistakes

• Turning the fraction upside down. In Henderson-Hasselbalch the salt is on top for an acidic buffer.
• Using a strong acid and its salt. HCl and NaCl make no buffer: there is no weak partner to hold the protons.
• Using concentrations after mixing, then forgetting the volume. In one solution, mole ratios and concentration ratios are the same.
• Thinking a buffer never changes. Add too much acid or base and its store runs out.

Remember these

• Common ion effect: a shared ion pushes back the ionisation of a weak electrolyte.
• Acidic buffer: weak acid and its salt. Basic buffer: weak base and its salt.
• $\text{pH} = \text{p}K_a + \log\dfrac{[\text{salt}]}{[\text{acid}]}$ and $\text{pOH} = \text{p}K_b + \log\dfrac{[\text{salt}]}{[\text{base}]}$.
• A buffer works best when its pH is within one unit of $\text{p}K_a$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Why does adding sodium acetate raise the pH of acetic acid?

2. A buffer has equal amounts of a weak acid and its salt. What is its pH?

3. Which ion in an ammonia buffer takes up added hydroxide ions?

4. Why can nitric acid and sodium nitrate not make a buffer?