Acids, Bases and Aqueous Equilibria

Strong acids: $[\text{H}^+] = [\text{acid}]$; pH = $-\log[\text{H}^+]$

Strong bases: $[\text{OH}^-] = [\text{base}]$ (×2 for Ba(OH)₂); pOH = $-\log[\text{OH}^-]$; pH = 14 − pOH

Weak acids: $K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$; if $K_a \ll c$: $[\text{H}^+] \approx \sqrt{K_a \cdot c}$

Weak bases: $K_b = \frac{[\text{OH}^-][\text{BH}^+]}{[\text{B}]}$

$K_a \times K_b = K_w = 1.0 \times 10^{-14}$

Weak acid + conjugate base (or weak base + conjugate acid)

Henderson-Hasselbalch: $\text{pH} = pK_a + \log\frac{[\text{A}^-]}{[\text{HA}]}$

Buffer capacity: larger amounts of weak acid and conjugate base → better buffering.

Effective buffer range: $pK_a \pm 1$

Key Points

• Initial point: pH of acid/base alone
• Buffer region: gradual pH change
• Half-equivalence: pH = $pK_a$ (for weak acid)
• Equivalence point: moles acid = moles base; pH depends on salt hydrolysis
• Post-equivalence: pH determined by excess titrant

$\text{AB}(s) \rightleftharpoons \text{A}^+(aq) + \text{B}^-(aq)$ $K_{sp} = [\text{A}^+][\text{B}^-]$

• $Q < K_{sp}$: unsaturated (no precipitate)
• $Q = K_{sp}$: saturated
• $Q > K_{sp}$: precipitate forms

Common ion effect: adding a common ion decreases solubility.

• Strong acids/bases: direct [H⁺] or [OH⁻]
• Weak acids: use $K_a$ and ICE table
• Buffers: $\text{pH} = pK_a + \log([\text{A}^-]/[\text{HA}])$
• Titrations: identify key points (initial, half-equiv, equiv, post-equiv)
• $K_{sp}$: compare Q to predict precipitation