7: pKa values and trends

Section 1: $pK_a$ Values and Trends

Definition and Significance
$pK_a$ quantifies acid strength, defined as $pK_a = -\log(K_a)$, where $K_a$ is the acid dissociation constant ($K_a = \frac{[H^+][A^-]}{[HA]}$). A lower $pK_a$ indicates a stronger acid (greater dissociation), while a higher $pK_a$ denotes a weaker acid. For example, HCl ($pK_a \approx -7$) is stronger than acetic acid ($pK_a = 4.8$).

Key Trends Influencing $pK_a$

1. Element Effects

   • Electronegativity: Across a row, acidity increases with higher electronegativity of the atom bonded to H.
     Example: CH₄ ($pK_a = 50$) < NH₃ ($pK_a = 38$) < H₂O ($pK_a = 15.7$) < HF ($pK_a = 3.2$).
   • Atomic Size: Down a group, larger atoms stabilize conjugate base charge better, increasing acidity.
     Example: HF ($pK_a = 3.2$) < HCl ($pK_a = -7$) < HBr ($pK_a = -9$) < HI ($pK_a = -10$).

2. Resonance Stabilization
   Delocalization of negative charge in the conjugate base dramatically lowers $pK_a$.
   Example: Acetic acid (CH₃COOH, $pK_a = 4.8$) is stronger than ethanol (CH₃CH₂OH, $pK_a = 15.9$) because acetate ion’s charge is resonance-stabilized over two oxygen atoms.

3. Inductive Effects
   Electron-withdrawing groups (EWGs, e.g., $–\ce{NO_2}$, $–\ce{Cl}$) stabilize the conjugate base via polarization, reducing $pK_a$. Proximity amplifies this effect.
   Example: Chloroacetic acid (ClCH₂COOH, $pK_a = 2.9$) is stronger than acetic acid ($pK_a = 4.8$) due to the Cl group’s $–I$ effect.

4. Hybridization
   Higher s-character in the orbital holding the negative charge increases acidity.
   Example: Terminal alkynes (H–C≡C–R, $pK_a = 25$) are more acidic than alkenes (H₂C=CH₂, $pK_a = 44$) or alkanes (CH₄, $pK_a = 50$) due to sp-hybridization (50% s-character) vs. sp² (33%) or sp³ (25%).

Practical Applications

• Predicting Reaction Outcomes: Acid-base equilibria favor the weaker acid (higher $pK_a$). For instance, ethoxide (CH₃CH₂O⁻, conjugate base $pK_a = 15.9$) deprotonates terminal alkynes ($pK_a = 25$) because the alkyne conjugate base ($pK_a = 25$) is weaker than ethanol ($pK_a = 15.9$).
• Structure-Acidity Relationships: Identify dominant stabilizing factors (resonance > induction > hybridization) when comparing molecules.