Brønsted-Lowry acids and bases
An acid donates a proton (H+); a base accepts one. When an acid donates a proton, what remains is its conjugate base; when a base accepts one, it becomes its conjugate acid. The conjugate base of H2PO4^- is HPO4^2-. A stronger acid has a weaker conjugate base.
Water and pH
Water self-ionizes: Kw = [H3O+][OH−] = 1.0 × 10^-14 at 25 °C. Then pH = −log[H3O+] and pOH = −log[OH−], with pH + pOH = 14.00. A pH below 7 is acidic, above 7 basic. Because pH is logarithmic, one unit is a tenfold change in concentration. The number of decimal places in a pH equals the sig figs in the concentration.
Strong and weak
Strong acids (HCl, HBr, HI, HNO3, H2SO4 first proton, HClO4) and strong bases (Group 1 hydroxides, Ba(OH)2, Ca(OH)2, Sr(OH)2) ionize completely, so concentration gives pH directly. Remember that Ba(OH)2 supplies two hydroxide ions per formula unit.
Weak acids ionize partly: HA + H2O ⇌ H3O+ + A−, with Ka = [H3O+][A−]/[HA]. A larger Ka is a stronger acid. For a weak acid of initial concentration C, when ionization is small (under about 5 percent), [H3O+] ≈ sqrt(Ka × C). For a conjugate pair, Ka × Kb = Kw. Salts of a weak acid are basic, and salts of a weak base with a strong acid are acidic.
Buffers and titration
A buffer has a weak acid and its conjugate base together, resisting changes in pH. The Henderson–Hasselbalch equation is pH = pKa + log([A−]/[HA]). In a titration, the equivalence point is reached when moles of acid equal moles of base for a 1:1 reaction, so M_a V_a = M_b V_b.
Worked example
Find the pH of 0.15 M ammonia-like weak base with Kb = 1.8 × 10^-5.
- Treat the base as B + H2O ⇌ BH+ + OH−. Use the approximation [OH−] ≈ sqrt(Kb × C) = sqrt(1.8 × 10^-5 × 0.15) = 1.64 × 10^-3 M.
- Check the approximation: 1.64 × 10^-3 / 0.15 = 1.1 percent, below 5 percent, so it is valid.
- pOH = −log(1.64 × 10^-3) = 2.78.
- pH = 14.00 − 2.78 = 11.22.
A frequent slip is to report the pOH as if it were the pH. Another is forgetting to double the hydroxide concentration for Ba(OH)2. Always state clearly which species you have found, then convert.