### Acid-Base Equilibria (pH, Buffers, $K_a$) Acid-base equilibria govern reactions where protons (H⁺) transfer between molecules. Under the **Brønsted-Lowry definition**, acids donate H⁺, and bases accept H⁺. Every acid (HA) has a conjugate base (A⁻), forming conjugate pairs (e.g., CH₃COOH/CH₃COO⁻). #### Acid Strength and $K_a$ The **acid dissociation constant ($K_a$)** quantifies acid strength in water: $$\ce{HA <=> H+ + A-} \quad K_a = \ce{\frac{[H+][A-]}{[HA]}}$$ Higher $K_a$ values indicate stronger acids (more dissociation). $K_a$ is often expressed as **$pK_a = -\log K_a$**, where lower $pK_a$ values denote stronger acids. For weak acids, $K_a$ ranges from $10^{-2}$ to $10^{-12}$; strong acids (e.g., HCl) have $K_a \gg 1$. #### pH and [H⁺] Calculations **pH** measures acidity: $$\text{pH} = -\log[\ce{H+}]$$ - **Strong acids**: $pH = -\log[\ce{HA}]$ (complete dissociation). - **Weak acids**: Use $K_a$ equilibrium. For a weak acid HA at concentration $C$, solve: $$K_a = \frac{x^2}{C - x} \approx \frac{x^2}{C} \quad (\text{if } x \ll C),$$ where $x = [\ce{H+}]$. Thus, $[\ce{H+}] \approx \sqrt{K_a \cdot C}$. #### Buffer Systems **Buffers** resist pH changes when small amounts of acid/base are added. They consist of a weak acid and its conjugate base (e.g., CH₃COOH/CH₃COO⁻). Buffering occurs via Le Chatelier’s principle: - Adding H⁺ shifts equilibrium toward HA. - Adding OH⁻ consumes H⁺, shifting equilibrium toward A⁻. The **Henderson-Hasselbalch equation** calculates buffer pH: $$\text{pH} = \text{p}K_a + \log\left(\frac{[\ce{A-}]}{[\ce{HA}]}\right)$$ - **Optimal buffering** occurs when $pH \approx pK_a$ (i.e., $[\ce{A-}]/[\ce{HA}] = 1$). - **Buffer capacity** (resistance to pH change) is highest when [HA] and [A⁻] are large and equal. #### Key Applications 1. **Weak acid pH**: Calculate [H⁺] from $K_a$ and initial concentration. 2. **Buffer preparation**: Select an acid with $pK_a$ near the target pH; adjust $[\ce{A-}]/[\ce{HA}]$. 3. **Common-ion effect**: Adding a salt (e.g., NaA) to a weak acid suppresses dissociation, lowering [H⁺] compared to the acid alone.

1: Definition and scope of analytical chemistry

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