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) or H_3O^+(aq) in \text{mol dm}^{-3}.
- For a neutral solution: [H^+] = 10^{-7} \text{ mol dm}^{-3} and pH = 7.
- For an acidic solution: [H^+] > 10^{-7} \text{ mol dm}^{-3} and pH < 7.
- For a basic solution: [H^+] < 10^{-7} \text{ mol dm}^{-3} and pH > 7.
pH, pOH, and Kw Relationship
- The relationship between pOH and pH is related to the dissociation constant for water (ionic product) \text{Kw}.
- pH + pOH = 14
- pOH = -\log[OH^-]
- pH = -\log[H^+]
- K_w = [H^+][OH^-]
Auto-ionization of Water
- Auto-ionization equation:
H2O(l) + H2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq) - Dissociation constant for water (ionic product) \text{Kw}.
- At 298 K: K_w = 1.0 \times 10^{-14} \text{ mol}^2 \text{dm}^{-6} = [H^+][OH^-].
- - \log(10^{-14}) = -\log[H^+] - \log[OH^-]
- 14 = pH + pOH
- The ionization of water is an endothermic process.
- The ionic product of water increases rapidly with increasing temperature.
| Temperature (°C) | K_w (\text{mol}^2 \text{dm}^{-6}) |
|---|---|
| 0 | 1.1 \times 10^{-15} |
| 20 | 6.8 \times 10^{-15} |
| 50 | 5.5 \times 10^{-14} |
| 100 | 5.1 \times 10^{-13} |
Degree of Dissociation ($\alpha$)
- Ratio of the molarity of H^+ or 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^- ion to that of the base before dissociation.
- For strong base, \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.
- \alpha = \frac{[HA]{\text{diss}}}{[HA]o}
- \alpha = \frac{[HB^+]{\text{diss}}}{[B]o}
Relationship between \alpha, \text{Ka} and \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: \alpha = \sqrt{\frac{Ka}{[HA]_o}}
For Weak bases: \alpha = \sqrt{\frac{Kb}{[B]_o}}
These formulas are only valid when \text{%} \alpha < 10\text{%}