Weak acids and bases

A weak acid HX ionises only partly: HX ⇌ H⁺ + X⁻. Its ionisation constant is:

Ka = [H⁺][X⁻] / [HX] = cα² / (1 – α), where c is the concentration and α is the degree of ionisation (the fraction ionised; α = 0.5 means 50%). pKa = –log Ka. The larger Ka, the stronger the acid (Table 6.6 in the book lists values).

When α is small (under about 5%), 1 – α ≈ 1, and the formulas simplify:

α ≈ √(Ka/c) and [H⁺] ≈ √(Ka × c).

For example, a 0.1 M acid with Ka = 1.0 × 10⁻⁵: α = √(10⁻⁵/0.1) = √(10⁻⁴) = 0.01 (1%), [H⁺] = 0.1 × 0.01 = 10⁻³ M, so pH = 3. If α is not small, the full quadratic equation must be solved.

Weak bases work the same way: B + H₂O ⇌ BH⁺ + OH⁻, with Kb = [BH⁺][OH⁻] / [B]. Ammonia has Kb = 1.77 × 10⁻⁵; aniline, a much weaker base, 4.27 × 10⁻¹⁰ (Table 6.7).

For a conjugate acid-base pair: Ka × Kb = Kw, so pKa + pKb = 14 at 298 K. The stronger the acid, the weaker its conjugate base.

Polybasic acids, with more than one ionisable hydrogen, ionise in steps, each with its own constant: Ka₁ > Ka₂ > …. It is harder to remove a proton from an ion that is already negative. For H₂S, Ka₁ = 9.1 × 10⁻⁸ and Ka₂ = 1.2 × 10⁻¹³.

Acid strength in a group increases with the size of the atom bonded to H, because a longer bond breaks more easily: HF < HCl < HBr < HI.