Buffers, Salt Hydrolysis and Solubility: Quick Revision

A brief note on Buffers, Salt Hydrolysis and Solubility. Read it before a test. Try each question at the end before you open its answer.

Salt hydrolysis

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

Buffers

• 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.
• $\text{pH} = \text{p}K_a + \log\dfrac{[\text{salt}]}{[\text{acid}]}$; $\text{pOH} = \text{p}K_b + \log\dfrac{[\text{salt}]}{[\text{base}]}$.
• Best within one pH unit of $\text{p}K_a$. Blood: $\text{H}_2\text{CO}_3/\text{HCO}_3^-$.

Solubility product

• $\text{A}_x\text{B}_y$: $K_{sp} = [\text{A}]^x[\text{B}]^y = x^x y^y s^{x+y}$.
• AB: $s^2$. $\text{AB}_2$: $4s^3$. $\text{A}_2\text{B}_3$: $108s^5$.
• A common ion lowers $s$: for AB in $c$ mol/L of a common ion, $s \approx K_{sp} / c$.
• $Q_{sp} > K_{sp}$: a precipitate forms.

A worked example

Silver carbonate, $\text{Ag}_2\text{CO}_3$, has $K_{sp} = 8.1 \times 10^{-12}$. How much dissolves in a litre of water?

1. Type. It is $\text{A}_2\text{B}$: $[\text{Ag}^+] = 2s$ and $[\text{CO}_3^{2-}] = s$.
2. Ksp. $K_{sp} = (2s)^2 s = 4s^3$.
3. Solve. $s^3 = \dfrac{8.1 \times 10^{-12}}{4} = 2.03 \times 10^{-12}$, so $s = 1.27 \times 10^{-4}\ \text{mol/L}$.

Practice with new numbers

A program to try

The program finds the molar solubility of three salts of different types from their $K_{sp}$.

Mistakes to avoid

• Every salt is neutral. Only a salt of a strong acid and a strong base is.
• The Henderson fraction upside down. The salt goes on top for an acidic buffer.
• $K_{sp} = s^2$ for every salt. Count the ions in the formula.
• Comparing $K_{sp}$ of different salt types. Compare their solubilities instead.
• Forgetting dilution on mixing. Equal volumes halve each concentration.

Check yourself

1. Is a solution of ammonium chloride acidic or basic?

2. A buffer has twice as much salt as acid. Is its pH above or below $\text{p}K_a$?

3. Why does AgCl dissolve less in potassium chloride solution than in water?

4. Write $K_{sp}$ of a salt of type $\text{AB}_3$ in terms of $s$.