Solubility Equilibria, Buffers and Titration

When a slightly soluble ionic solid is in contact with its saturated solution, dissolving and precipitating happen at equal rates. The solid is left out of the expression, so the equilibrium constant is just the product of the ion concentrations, each raised to its coefficient. It is called the solubility product constant, $K_{sp}$. The molar solubility, $s$, is the number of moles of the solid that dissolve per litre of saturated solution.

When two solutions are mixed, calculate the ion product $Q$ using the concentrations after mixing (remember that mixing equal volumes halves each concentration). If $Q>K_{sp}$, the solution holds more ions than it can at equilibrium, so a precipitate forms until $Q=K_{sp}$. If $Q<K_{sp}$, no precipitate forms. If $Q=K_{sp}$, the solution is exactly saturated. The common ion effect is Le Chatelier's principle applied to solubility. Dissolving AgCl in a solution that already contains ${\text{Cl}}^{-}$ (for example, from NaCl) pushes $\text{AgCl}(s)\rightleftharpoons {\text{Ag}}^{+}+{\text{Cl}}^{-}$ to the left, so less AgCl dissolves. The same idea explains how many kidney stones, which are often made of calcium salts, can form when the ion concentrations in urine exceed the solubility product.

A buffer is a solution that resists changes in pH when small amounts of acid or base are added. It contains a weak acid and its conjugate base in similar amounts, such as acetic acid and sodium acetate. The weak acid neutralizes added base, ${\text{CH}}_3\text{COOH}+{\text{OH}}^{-}\to {\text{CH}}_3{\text{COO}}^{-}+{\text{H}}_2\text{O}\text{,}$ and the conjugate base neutralizes added acid, ${\text{CH}}_3{\text{COO}}^{-}+{\text{H}}_3{\text{O}}^{+}\to {\text{CH}}_3\text{COOH}+{\text{H}}_2\text{O}\text{.}$ The pH changes only slightly because the ratio of the two components changes only slightly. A weak base with its conjugate acid (such as ${\text{NH}}_3$ with ${\text{NH}}_4\text{Cl}$) works the same way.

In a titration, a solution of known concentration (the titrant, delivered from a burette) is added to a measured volume of the unknown until the equivalence point, where the moles of acid and base match the mole ratio in the balanced equation. The endpoint is where an indicator changes colour; a well-chosen indicator makes the endpoint land on or very near the equivalence point. Plotting pH against volume of titrant gives a titration curve with a steep jump near equivalence.

• In a weak acid-strong base curve, the region before equivalence is a buffer: both HA and ${\text{A}}^{-}$ are present, so the pH rises slowly.
• At the half-equivalence point, $[\text{HA}]=[{\text{A}}^{-}]$, so $\text{pH}=\text{p}{K}_a$. This is how Ka for acetic acid can be measured from a titration curve.
• Phenolphthalein, which changes from colourless to pink at roughly pH 8 to 10, suits a weak acid-strong base titration. Methyl orange, which changes at roughly pH 3 to 4.5, suits a strong acid-weak base titration.