pH Scale, Auto-ionization, and Degree of Dissociation

The pH Scale

  • Introduced in 1909 by Danish biochemist Soren Sorensen.
  • Used to measure the concentration of hydrogen ions.
  • Defined as the negative logarithm to the base 10 of the concentration of H+(aq)H^+(aq) or H3O+(aq)H_3O^+(aq) in mol dm−3\text{mol dm}^{-3}.
  • For a neutral solution: [H+]=10−7 mol dm−3[H^+] = 10^{-7} \text{ mol dm}^{-3} and pH=7pH = 7.
  • For an acidic solution: [H^+] > 10^{-7} \text{ mol dm}^{-3} and pH < 7.
  • For a basic solution: [H+]<10−7 mol dm−3[H^+] < 10^{-7} \text{ mol dm}^{-3} and pH>7pH > 7.

pH, pOH, and Kw Relationship

  • The relationship between pOH and pH is related to the dissociation constant for water (ionic product) Kw\text{Kw}.
  • pH+pOH=14pH + pOH = 14
  • pOH=−log⁡[OH−]pOH = -\log[OH^-]
  • pH=−log⁡[H+]pH = -\log[H^+]
  • Kw=[H+][OH−]K_w = [H^+][OH^-]

Auto-ionization of Water

  • Auto-ionization equation:
    H<em>2O(l)+H</em>2O(l)⇌H3O+(aq)+OH−(aq)H<em>2O(l) + H</em>2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)
  • Dissociation constant for water (ionic product) Kw\text{Kw}.
  • At 298 K: Kw=1.0×10−14 mol2dm−6=[H+][OH−]K_w = 1.0 \times 10^{-14} \text{ mol}^2 \text{dm}^{-6} = [H^+][OH^-].
  • −log⁡(10−14)=−log⁡[H+]−log⁡[OH−]- \log(10^{-14}) = -\log[H^+] - \log[OH^-]
  • 14=pH+pOH14 = pH + pOH
  • The ionization of water is an endothermic process.
  • The ionic product of water increases rapidly with increasing temperature.
Temperature (°C)Kw(mol2dm−6)K_w (\text{mol}^2 \text{dm}^{-6})
01.1×10−151.1 \times 10^{-15}
206.8×10−156.8 \times 10^{-15}
505.5×10−145.5 \times 10^{-14}
1005.1×10−135.1 \times 10^{-13}

Degree of Dissociation ($\alpha$)

  • Ratio of the molarity of H+H^+ or H3O+H_3O^+ ions to that of the acid before dissociation.
  • For weak acids, \alpha < 1 or \text{%}\alpha < 100\text{%}.
  • In weak acid, the degree of dissociation is affected by the concentration of acids.
  • Ratio of the molarity of OH−OH^- ion to that of the base before dissociation.
  • For strong base, α=1\alpha = 1 or \text{%}\alpha = 100\text{%}.
  • For weak base, \alpha < 1 or \text{%}\alpha < 100\text{%}.
  • In weak base, the degree of dissociation is affected by the concentration of bases.
  • α=[HA]<em>diss[HA]</em>o\alpha = \frac{[HA]<em>{\text{diss}}}{[HA]</em>o}
  • α=[HB+]<em>diss[B]</em>o\alpha = \frac{[HB^+]<em>{\text{diss}}}{[B]</em>o}

Relationship between α\alpha, Ka\text{Ka} and Kb\text{Kb}

  • The degree of dissociation ($\alpha$) of a weak acid or a weak base can be calculated from the following equations.

  • The degree of dissociation or ionization for weak acids or weak bases is inversely proportional to its molarity/concentration.

  • For Weak acids: α=Ka[HA]o\alpha = \sqrt{\frac{Ka}{[HA]_o}}

  • For Weak bases: α=Kb[B]o\alpha = \sqrt{\frac{Kb}{[B]_o}}

  • These formulas are only valid when \text{%} \alpha < 10\text{%}