Weak acids, buffers, and equilibria
Weak acids only partly ionise, and mixtures of weak acids and their conjugate bases resist pH changes. These buffers keep blood, oceans, and medicines stable.
The acid dissociation constant
For a weak acid \(\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-\), \(K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}\). A larger \(K_a\) means a stronger acid. Acetic acid has \(K_a = 1.8 \times 10^{-5}\); \(\text{p}K_a = -\log K_a \approx 4.74\).
K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}pH of a weak acid
For 0.10 M acetic acid, assume \(x = [\text{H}^+]\) is small: \(K_a \approx \frac{x^2}{0.10}\), so \(x = \sqrt{1.8 \times 10^{-6}} \approx 1.3 \times 10^{-3}\) M, and pH \(\approx 2.87\). Only about 1.3% of the acid molecules ionise, which is why vinegar is safe to eat.
Weak bases
Weak bases like ammonia accept protons partly, described by \(K_b\). For conjugate pairs, \(K_aK_b = K_w\): a weak acid's conjugate base is itself a weak base. Salts of weak acids, like sodium acetate, make solutions slightly basic.
Buffers
A buffer contains a weak acid and its conjugate base in similar amounts. Added acid is consumed by the base; added base is consumed by the acid, so pH changes very little. Blood is buffered mainly by carbonic acid and bicarbonate, keeping pH near 7.4.
The Henderson-Hasselbalch equation
For a buffer, \(\text{pH} = \text{p}K_a + \log\frac{[\text{A}^-]}{[\text{HA}]}\). When the acid and base are equal, pH \(= \text{p}K_a\). An acetate buffer with twice as much acetate as acetic acid has pH \(\approx 4.74 + \log 2 \approx 5.04\). Buffers work best within about one pH unit of the p\(K_a\).
\text{pH} = \text{p}K_a + \log\frac{[\text{A}^-]}{[\text{HA}]}Titrations
In a titration, a solution of known concentration is added until the reaction is complete (the equivalence point). Plotting pH against volume gives a titration curve. For a weak acid titrated with a strong base, the pH at the halfway point equals the p\(K_a\), a common way to measure it.
Polyprotic acids
Some acids donate more than one proton, each step with its own \(K_a\): phosphoric acid \(\text{H}_3\text{PO}_4\) has three. Each successive proton is harder to remove, so \(K_{a1} > K_{a2} > K_{a3}\). Phosphate buffers are important inside cells.
Common mistakes
Treating weak acids as fully ionised. Forgetting the square root in the weak acid approximation. Using the Henderson-Hasselbalch equation outside the buffer region. Confusing equivalence point with neutral pH; for weak acid titrations, the equivalence point is above 7.
Key takeaways
\(K_a\) measures weak acid strength; \(\text{p}K_a = -\log K_a\). For a weak acid, \([\text{H}^+] \approx \sqrt{K_aC}\). Buffers combine a weak acid and its conjugate base and follow Henderson-Hasselbalch. At half-equivalence in a titration, pH equals p\(K_a\).
Flashcard
Acid dissociation constant
Check your understanding
A buffer has equal concentrations of a weak acid (pKa = 6.4) and its conjugate base. Its pH is: