How Chemists Predict Whether a Precipitate Will Form

Add a few drops of hydrochloric acid to pure water and its pH crashes; add the same drops to a buffer and the pH barely moves. A related idea decides whether a salt stays dissolved or drops out as a solid — the question behind kidney stones, hard-water scale and the purification of common salt.

This lesson covers buffer solutions and their pH, and the solubility product with its use in predicting precipitation.

A buffer is a solution of a weak acid and its salt with a strong base, or a weak base and its salt with a strong acid, and it resists pH change because one component neutralises added acid while the other neutralises added base.

Types of buffer:

- Acidic buffer — a weak acid with its conjugate base, such as acetic acid and sodium acetate; pH below 7
- Basic buffer — a weak base with its conjugate acid, such as ammonium hydroxide and ammonium chloride; pH above 7

Mechanism in an acetic acid and sodium acetate buffer:

- The buffer holds large amounts of both $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$ and $\mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}$
- Added acid is removed by acetate ions: $\mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}+{\mathrm{H}}^{+}\to \mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$
- Added base is removed by acetic acid: $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}+\mathrm{O}{\mathrm{H}}^{-}\to \mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}+{\mathrm{H}}_2\mathrm{O}$
- Each addition changes the ratio of acid to salt only slightly, so the pH hardly changes

Mechanism in an ammonium hydroxide and ammonium chloride buffer:

- Added acid reacts with the base: $\mathrm{N}{\mathrm{H}}_4\mathrm{OH}+{\mathrm{H}}^{+}\to \mathrm{N}{\mathrm{H}}_4^{+}+{\mathrm{H}}_2\mathrm{O}$
- Added base reacts with ammonium ions: $\mathrm{N}{\mathrm{H}}_4^{+}+\mathrm{O}{\mathrm{H}}^{-}\to \mathrm{N}{\mathrm{H}}_4\mathrm{OH}$

Buffer capacity. A buffer works best when acid and salt are present in similar amounts, and it fails once one component is used up.

An everyday example. Eye drops and injectable medicines are buffered close to the pH of body fluids, so they do not sting or damage tissue.

The substance. A buffer does not hold its pH under all conditions — add enough strong acid to use up the salt, and the pH falls as steeply as it would in water.

**The solubility product, $K_{sp}$, is the equilibrium constant for a sparingly soluble salt dissolving into its ions, and a precipitate forms whenever the ionic product of the solution exceeds $K_{sp}$.

Defining $K_{sp}$.** For silver chloride in a saturated solution:

$$\mathrm{AgCl}(\mathrm{s})\rightleftharpoons \mathrm{A}{\mathrm{g}}^{+}(\mathrm{aq})+\mathrm{C}{\mathrm{l}}^{-}(\mathrm{aq})K_{sp}=[\mathrm{A}{\mathrm{g}}^{+}][\mathrm{C}{\mathrm{l}}^{-}]$$

**Relating $K_{sp}$ to molar solubility s:**

- Salt of type AB, such as AgCl: $K_{sp}=s^2$
- Salt of type $\mathrm{A}{\mathrm{B}}_2$, such as $\mathrm{Ca}{\mathrm{F}}_2$: $K_{sp}=s\times (2s{)}^2=4s^3$

Worked example 1. For silver chloride, $K_{sp}=1.8\times 10^{-10}$:

$$s=\sqrt{1.8\times 10^{-10}}=1.34\times 10^{-5}{\text{ mol L}}^{-1}$$

Worked example 2. For calcium fluoride, $K_{sp}=3.2\times 10^{-11}$:

$$s=\sqrt[3]{\frac{3.2\times 10^{-11}}{4}}=\sqrt[3]{8.0\times 10^{-12}}=2.0\times 10^{-4}{\text{ mol L}}^{-1}$$

Predicting precipitation. Compare the ionic product Q with $K_{sp}$:

- $Q>K_{sp}$ — a precipitate forms
- $Q=K_{sp}$ — the solution is just saturated
- $Q<K_{sp}$ — no precipitate forms

Worked example 3. Equal volumes of $2.0\times 10^{-4}$ M silver nitrate and $2.0\times 10^{-4}$ M sodium chloride are mixed. Mixing halves each concentration:

$$Q=(1.0\times 10^{-4})(1.0\times 10^{-4})=1.0\times 10^{-8}>1.8\times 10^{-10}$$

so silver chloride precipitates.

Common ion effect. A salt is less soluble in a solution that already contains one of its ions. In 0.10 M sodium chloride, the solubility of silver chloride falls to $\frac{1.8\times 10^{-10}}{0.10}=1.8\times 10^{-9}$ mol L${}^{-1}$.

An everyday example. Common salt is purified by passing hydrogen chloride gas into saturated brine: the extra chloride ions push the ionic product of sodium chloride past its limit, and pure crystals settle out.

The substance. **A larger $K_{sp}$ does not always mean higher solubility** — silver chloride has the larger $K_{sp}$ yet is less soluble than calcium fluoride, so compare $K_{sp}$ values directly only for salts of the same formula type.