08 pH and pOH
pH = −log[H⁺] (the negative logarithm, base 10, of the hydrogen-ion concentration); pOH = −log[OH⁻]; the symbol p means −log. This is a convenient way of expressing the acidity or alkalinity of a solution. Taking −log of Kw: pH + pOH = 14 (pKw = 14).
- Neutral: pH = 7 = pOH.
- Acidic: pH < 7 (pOH > 7); e.g. pH 5 → pOH 9.
- Basic: pH > 7 (pOH < 7); e.g. pH 8 → pOH 6.
Example 14. Find the pH of (a) 0.001 M HCl, (b) 0.01 M NaOH, (c) a solution with [H⁺] = 2 × 10⁻⁴ M. (a) [H⁺] = 10⁻³ → pH = 3. (b) [OH⁻] = 10⁻² → pOH = 2 → pH = 12. (c) pH = −log(2 × 10⁻⁴) = 4 − 0.30 = 3.70.
Example 15. A solution has pH 9.4. Then pOH = 4.6, [OH⁻] = 10⁻⁴·⁶ = 2.5 × 10⁻⁵ M, and [H⁺] = 10⁻⁹·⁴ = 4.0 × 10⁻¹⁰ M. (Check: product 1.0 × 10⁻¹⁴.)
Example 16 (dilution). 10 mL of 0.1 M HCl are diluted with water to 1 L: [H⁺] = 0.1 × 10/1000 = 10⁻³ M, pH = 3. Diluting an acid 100 times raises its pH by 2 units.
Typical pH values (illustration): 1 M HCl 0; 0.1 M HCl 1; gastric juice 1.6–1.8; vinegar 2.9; orange juice 3.5; tomato juice 4.2; coffee 5; milk 6.3–6.6; pure water 7; blood 7.35–7.45; sea water 8.4; magnesia emulsion 10.5; 0.1 M ammonia 11; washing soda 12.9; 0.1 M NaOH 13; 1 M NaOH 14.