Hydrolysis of salts

Not every salt solution is neutral

A salt forms when an acid neutralises a base. So you might expect every salt solution to be neutral, with pH 7. Test a few with a pH meter, though, and you get a surprise.

• Sodium chloride in water: pH 7.
• Sodium acetate in water: above 7, basic.
• Ammonium chloride in water: below 7, acidic.

The reason is that some ions react with water. This reaction is called salt hydrolysis. It is just the reverse of neutralisation, and it happens only to an ion that came from a weak acid or a weak base.

Which ions react with water?

An ion from a strong acid or a strong base, such as $\text{Na}^+$, $\text{K}^+$, $\text{Cl}^-$ or $\text{NO}_3^-$, has almost no wish to grab or give a proton. It stays as it is.

An ion from a weak acid is a fairly strong conjugate base. The acetate ion takes a proton from water:

• $\text{CH}_3\text{COO}^-(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{CH}_3\text{COOH}(aq) + \text{OH}^-(aq)$

Hydroxide ions build up, so the solution turns basic.

An ion from a weak base is a fairly strong conjugate acid. The ammonium ion gives a proton to water:

• $\text{NH}_4^+(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{NH}_3(aq) + \text{H}_3\text{O}^+(aq)$

Hydronium ions build up, so the solution turns acidic.

The four kinds of salt

Sort a salt by the acid and the base it came from:

• Strong acid and strong base, such as NaCl or $\text{KNO}_3$: no hydrolysis. The solution is neutral.
• Weak acid and strong base, such as $\text{CH}_3\text{COONa}$ or $\text{Na}_2\text{CO}_3$: the anion hydrolyses. The solution is basic.
• Strong acid and weak base, such as $\text{NH}_4\text{Cl}$: the cation hydrolyses. The solution is acidic.
• Weak acid and weak base, such as $\text{CH}_3\text{COONH}_4$: both ions hydrolyse. The pH depends on which is the weaker partner.

The hydrolysis constant

For the acetate ion, the equilibrium constant of hydrolysis is $K_h$. It is linked to the acid's $K_a$ and to $K_w$:

• $K_h = \dfrac{K_w}{K_a}$

The weaker the acid, the smaller $K_a$, and the larger $K_h$. A very weak acid leaves a strongly hydrolysing anion.

For acetic acid, $K_a = 1.8 \times 10^{-5}$. So $K_h = \dfrac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.6 \times 10^{-10}$.

The degree of hydrolysis $h$ is the share of the anions that react. For a salt of concentration $C$:

• $h = \sqrt{\dfrac{K_h}{C}}$

In $0.10\ \text{mol/L}$ sodium acetate, $h = \sqrt{5.6 \times 10^{-9}} = 7.5 \times 10^{-5}$. Fewer than one acetate ion in ten thousand reacts. Yet that is enough to shift the pH.

Three formulas for the pH

Working through the equilibria gives a short formula for each kind of salt, at $298\ \text{K}$:

• Weak acid and strong base: $\text{pH} = 7 + \tfrac{1}{2}(\text{p}K_a + \log C)$
• Strong acid and weak base: $\text{pH} = 7 - \tfrac{1}{2}(\text{p}K_b + \log C)$
• Weak acid and weak base: $\text{pH} = 7 + \tfrac{1}{2}(\text{p}K_a - \text{p}K_b)$

Here $\text{p}K_a = -\log K_a$, and $C$ is the salt's concentration in mol/L.

Sodium acetate, $0.10\ \text{mol/L}$. Acetic acid has $\text{p}K_a = 4.74$.

• $\text{pH} = 7 + \tfrac{1}{2}(4.74 + \log 0.10) = 7 + \tfrac{1}{2}(4.74 - 1) = 8.87$

Ammonium chloride, $0.10\ \text{mol/L}$. Ammonia has $\text{p}K_b = 4.74$.

• $\text{pH} = 7 - \tfrac{1}{2}(4.74 - 1) = 5.13$

Ammonium acetate. Here $\text{p}K_a$ and $\text{p}K_b$ are equal, so $\text{pH} = 7.00$, whatever the concentration. The two hydrolyses cancel out.

Practise with new numbers

Try it in Python

The program works out the pH of the three salts from the formulas above.

Common mistakes

• Thinking every salt is neutral. Only a salt of a strong acid and a strong base gives pH 7.
• Mixing up the signs in the formulas. A salt of a weak acid gives a pH above 7, so its formula starts with $7 +$.
• Forgetting the concentration. For the first two kinds, $\log C$ matters. Only the third kind is independent of $C$.
• Using $K_a$ where $K_b$ belongs. For an ammonium salt, use $\text{p}K_b$ of ammonia.

Remember these

• Hydrolysis: an ion from a weak acid or a weak base reacts with water.
• Weak acid and strong base: basic. Strong acid and weak base: acidic. Strong and strong: neutral.
• $K_h = K_w / K_a$ and $h = \sqrt{K_h / C}$.
• $\text{pH} = 7 + \tfrac{1}{2}(\text{p}K_a + \log C)$ for a salt of a weak acid.

Check yourself

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

1. Is a solution of potassium nitrate acidic, basic or neutral?

2. Why is a solution of sodium carbonate basic?

3. Acid X is weaker than acid Y. Whose sodium salt gives the more basic solution, at the same concentration?

4. Why does the pH of ammonium acetate not depend on its concentration?