Write solubility product expressions, calculate Ksp and solubility, and predict precipitation.

The solubility product Ksp, relating Ksp to molar solubility, the common ion effect, and predicting whether a precipitate forms.

Generated by Claude Opus 4.77 min answerUpdated 2026-05-30

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You must write $K_{sp}$ expressions, link $K_{sp}$ to molar solubility, and predict precipitation.

The dissolution equilibrium

When an ionic solid is only slightly soluble, a saturated solution reaches equilibrium with the undissolved solid:

\text{AgCl}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{Cl}^-(aq)

The solid is left out of the expression, so the equilibrium constant is the product of the dissolved ion concentrations.

A larger $K_{sp}$ means a more soluble salt. The value depends on temperature.

Relating Ksp to solubility

Molar solubility $s$ is the moles of salt that dissolve per litre to give a saturated solution. From the dissolution equation, the ion concentrations are written in terms of $s$ , then substituted into the $K_{sp}$ expression.

example

Solubility from Ksp

The $K_{sp}$ of silver chloride is $1.8 \times 10^{-10}$ at 25 degrees Celsius. Find its molar solubility.

Step 1: $\text{AgCl}(s) \rightleftharpoons \text{Ag}^+ + \text{Cl}^-$ , so if $s$ moles dissolve, $[\text{Ag}^+] = s$ and $[\text{Cl}^-] = s$ .

Step 2: $K_{sp} = [\text{Ag}^+][\text{Cl}^-] = s \times s = s^2$ .

Step 3: $s = \sqrt{K_{sp}} = \sqrt{1.8 \times 10^{-10}} = 1.3 \times 10^{-5}\ \text{mol L}^{-1}$ .

So only about $1.3 \times 10^{-5}$ mol dissolves per litre, confirming silver chloride is sparingly soluble.

Predicting precipitation

When two solutions are mixed, calculate the ionic product $Q$ using the actual mixed concentrations (remember dilution on mixing). Compare with $K_{sp}$ .

If $Q > K_{sp}$ , the solution is supersaturated and a precipitate forms.
If $Q = K_{sp}$ , the solution is exactly saturated.
If $Q < K_{sp}$ , no precipitate forms.

In the exam, write the dissolution equation, build $K_{sp}$ with the correct powers, use $s$ carefully when a coefficient is not 1, and compare $Q$ with $K_{sp}$ after accounting for dilution.

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