Ka, Kb, pKa and the pH of weak acids (HL)

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The **acid-dissociation constant** — the equilibrium constant for HA ⇌ H⁺ + A⁻: $K_a = \dfrac{[H^+][A^-]}{[HA]}$.

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A **stronger** weak acid — the dissociation equilibrium lies further to the right (more H⁺).

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The **base-dissociation constant** for B + H_{2}O ⇌ BH⁺ + OH⁻; a larger K_{b} = a stronger weak base.

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$\text{p}K_a = -\log_{10} K_a$ — the negative logarithm of the acid-dissociation constant.

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A **stronger** acid — the minus sign flips the scale, so the lowest pK_{a} is the strongest acid.

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Line up their **pK_{a}** values; the **lowest pK_{a}** is the strongest (largest K_{a}).

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For a conjugate pair, $K_a \times K_b = K_w$ (= 1.0 × 10⁻¹⁴ at 298 K).

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For a conjugate pair, $\text{p}K_a + \text{p}K_b = 14$ at 298 K.

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$K_b = \dfrac{K_w}{K_a}$ — divide K_{w} by the acid's K_{a}.

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$[H^+] = \sqrt{K_a\,c}$, then $\text{pH} = -\log_{10}[H^+]$.

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**1.** [H⁺] = [A⁻] (acid is the only source of H⁺). **2.** [HA] ≈ c (dissociation is negligible).

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$[OH^-] = \sqrt{K_b\,c}$ → pOH = −log[OH⁻], then **pH = 14 − pOH** (298 K).

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**No** — like K_{c}, you write the expressions yourself; only K_{w} = 1.0 × 10⁻¹⁴ is a booklet constant.