Notes › Physical Chemistry

Ionic Equilibrium

1. Acid–Base Concepts

  • Arrhenius: acids give $H^+$, bases give $OH^-$ in water.
  • Brønsted–Lowry: acids donate protons, bases accept them. Each acid has a conjugate base; a stronger acid has a weaker conjugate base.
  • Lewis: acids accept an electron pair ($BF_3$, $AlCl_3$, $Ag^+$); bases donate one ($NH_3$, $OH^-$).

2. Ionic Product of Water and pH

$K_w = [H^+][OH^-] = 1.0 \times 10^{-14}$ at 298 K. It increases with temperature, because the ionisation of water is endothermic.

$$pH = -\log[H^+] \qquad pH + pOH = pK_w = 14\ \ (298\ K)$$

Interactive diagram: open this page in a browser to use it.

3. Weak Acids and Bases

For a weak acid HA at concentration $C$ with degree of ionisation $\alpha$ (Ostwald's dilution law):

$$K_a = \frac{C\alpha^2}{1-\alpha} \approx C\alpha^2 \qquad [H^+] = \sqrt{K_a C} \qquad pH = \tfrac{1}{2}(pK_a - \log C)$$

For a conjugate pair, $K_a \times K_b = K_w$.

4. Salt Hydrolysis

  • Strong acid + strong base (NaCl): neutral, pH 7.
  • Weak acid + strong base ($CH_3COONa$): basic. $pH = 7 + \tfrac{1}{2}(pK_a + \log C)$.
  • Strong acid + weak base ($NH_4Cl$): acidic. $pH = 7 - \tfrac{1}{2}(pK_b + \log C)$.
  • Weak acid + weak base ($CH_3COONH_4$): $pH = 7 + \tfrac{1}{2}(pK_a - pK_b)$, independent of concentration.

5. Buffer Solutions

A buffer resists change in pH when small amounts of acid or base are added. The Henderson–Hasselbalch equation:

$$pH = pK_a + \log\frac{[Salt]}{[Acid]} \qquad pOH = pK_b + \log\frac{[Salt]}{[Base]}$$

Buffer capacity is greatest when $[Salt] = [Acid]$, i.e. pH = $pK_a$. Blood is buffered near pH 7.4 by $H_2CO_3/HCO_3^-$.

6. Solubility Product

For a sparingly soluble salt $A_xB_y \rightleftharpoons xA^{y+} + yB^{x-}$ with solubility $s$:

$$K_{sp} = (xs)^x (ys)^y$$
  • AgCl: $K_{sp} = s^2$. $CaF_2$: $K_{sp} = 4s^3$. $Ca_3(PO_4)_2$: $K_{sp} = 108s^5$.
  • Precipitation occurs when the ionic product $Q_{sp} > K_{sp}$.
  • Common ion effect: adding a common ion lowers solubility (AgCl is less soluble in NaCl solution than in pure water).

⚠️ Common Pitfall

For very dilute strong acids (like $10^{-8}$ M HCl), you cannot ignore the $H^+$ from water. The pH is slightly below 7 (about 6.98), not 8.

Practice questions

  1. The pH of 0.001 M HCl is:

    1. 1
    2. 2
    3. 3
    4. 11
    Answer

    C. HCl is a strong acid: [H⁺] = 10⁻³, so pH = 3.

  2. The solubility product of CaF₂ in terms of its solubility s is:

    1. s²
    2. 2s³
    3. 4s³
    4. 27s⁴
    Answer

    C. CaF₂ ⇌ Ca²⁺ + 2F⁻; Kₛₚ = s(2s)² = 4s³.

  3. An aqueous solution of CH₃COONa is:

    1. Acidic
    2. Basic
    3. Neutral
    4. Amphoteric
    Answer

    B. It is the salt of a weak acid and a strong base; acetate hydrolyses to give OH⁻.

  4. A buffer of acetic acid (pKₐ = 4.76) and sodium acetate in equal concentrations has pH:

    1. 4.76
    2. 7.00
    3. 9.24
    4. 2.38
    Answer

    A. pH = pKₐ + 1 = 4.76.

  5. Which of these is a Lewis acid but not a Brønsted acid?

    1. HCl
    2. BF₃
    3. NH₄⁺
    4. H₂O
    Answer

    B. BF₃ accepts an electron pair but has no proton to donate.

  6. The solubility of AgCl is lowest in:

    1. Pure water
    2. 0.1 M NaCl
    3. 0.1 M NaNO₃
    4. 0.1 M NH₃
    Answer

    B. The common ion Cl⁻ suppresses dissolution. NH₃ actually increases solubility by forming [Ag(NH₃)₂]⁺.

← Chemical Equilibrium · Redox Reactions →