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Concept 03 / 08Equilibrium

Salt Hydrolysis: pH of Salt Solutions

Why salt solutions can be acidic, basic or neutral, hydrolysis constants and degree of hydrolysis for salts of weak acids, weak bases and both, pH formulas for each salt type, and applications to titration end points and indicator choice.

Figure 1
Salt hydrolysis is the reaction of a salt's cation or anion (or both) with water to produce H+\mathrm{H^{+}} or OH−\mathrm{OH^{-}}. Ions derived from strong acids or strong bases (Cl−\mathrm{Cl^{-}}, NO3−\mathrm{NO_{3}^{-}}, Na+\mathrm{Na^{+}}, K+\mathrm{K^{+}}) are too weak as conjugates to react with water; ions from weak partners do react. 1. Salt of strong acid and strong base (NaCl, KNO3\mathrm{KNO_{3}}): no hydrolysis, pH =7= 7. 2. Salt of weak acid and strong base (CH3COONa\mathrm{CH_{3}COONa}): the anion hydrolyses, CH3COO−+H2O⇌CH3COOH+OH−\mathrm{CH_{3}COO^{-} + H_{2}O \rightleftharpoons CH_{3}COOH + OH^{-}}, making the solution basic. Hydrolysis constant Kh=KwKaK_{h} = \frac{K_{w}}{K_{a}}; degree of hydrolysis h=Khch = \sqrt{\frac{K_{h}}{c}}; pH=7+12(pKa+log⁡c)\text{pH} = 7 + \frac{1}{2}(\text{p}K_{a} + \log c). 3. Salt of strong acid and weak base (NH4Cl\mathrm{NH_{4}Cl}): the cation hydrolyses, NH4++H2O⇌NH3+H3O+\mathrm{NH_{4}^{+} + H_{2}O \rightleftharpoons NH_{3} + H_{3}O^{+}}, making the solution acidic. Kh=KwKbK_{h} = \frac{K_{w}}{K_{b}}; h=Khch = \sqrt{\frac{K_{h}}{c}}; pH=7−12(pKb+log⁡c)\text{pH} = 7 - \frac{1}{2}(\text{p}K_{b} + \log c). Hydrated metal ions with high charge density also make solutions acidic: [Fe(H2O)6]3+\mathrm{[Fe(H_{2}O)_{6}]^{3+}}, Al3+\mathrm{Al^{3+}}, Cu2+\mathrm{Cu^{2+}}. 4. Salt of weak acid and weak base (CH3COONH4\mathrm{CH_{3}COONH_{4}}): both ions hydrolyse. Kh=KwKaKbK_{h} = \frac{K_{w}}{K_{a}K_{b}}; h=Khh = \sqrt{K_{h}} (independent of concentration); pH=7+12(pKa−pKb)\text{pH} = 7 + \frac{1}{2}(\text{p}K_{a} - \text{p}K_{b}). If Ka=KbK_{a} = K_{b} (ammonium acetate), the solution is neutral even though hydrolysis is extensive. Amphiprotic anions. For NaHCO3\mathrm{NaHCO_{3}}, pH≈12(pKa1+pKa2)\text{pH} \approx \frac{1}{2}(\text{p}K_{a1} + \text{p}K_{a2}), about 8.38.3, independent of concentration. Applications. At the equivalence point of a titration, the solution is just the salt, so its pH decides the indicator: weak acid with strong base (basic end point) uses phenolphthalein; strong acid with weak base (acidic end point) uses methyl orange; strong with strong can use either; weak with weak has no sharp end point. Key Takeaways: - WA + SB salt: pH=7+12(pKa+log⁡c)\text{pH} = 7 + \frac{1}{2}(\text{p}K_{a} + \log c), basic. - SA + WB salt: pH=7−12(pKb+log⁡c)\text{pH} = 7 - \frac{1}{2}(\text{p}K_{b} + \log c), acidic. - WA + WB salt: pH=7+12(pKa−pKb)\text{pH} = 7 + \frac{1}{2}(\text{p}K_{a} - \text{p}K_{b}), independent of cc. - Kh=KwKaK_{h} = \frac{K_{w}}{K_{a}}, KwKb\frac{K_{w}}{K_{b}} or KwKaKb\frac{K_{w}}{K_{a}K_{b}}. - Pitfall: a neutral pH does not mean no hydrolysis (ammonium acetate hydrolyses considerably). Brain-Teaser 1: Find the pH and degree of hydrolysis of 0.1 M0.1\,\mathrm{M} sodium acetate (pKa=4.74\text{p}K_{a} = 4.74, Ka=1.8×10−5K_{a} = 1.8 \times 10^{-5}). Solution: pH=7+12(4.74+log⁡0.1)=7+12(3.74)=8.87\text{pH} = 7 + \frac{1}{2}(4.74 + \log 0.1) = 7 + \frac{1}{2}(3.74) = 8.87. Kh=10−141.8×10−5=5.56×10−10K_{h} = \frac{10^{-14}}{1.8 \times 10^{-5}} = 5.56 \times 10^{-10}, h=5.56×10−9=7.5×10−5h = \sqrt{5.56 \times 10^{-9}} = 7.5 \times 10^{-5}, that is 0.0075%0.0075\%. Brain-Teaser 2: Find the pH of 0.1 M0.1\,\mathrm{M} NH4Cl\mathrm{NH_{4}Cl} (pKb=4.74\text{p}K_{b} = 4.74). Solution: pH=7−12(4.74+log⁡0.1)=7−1.87=5.13\text{pH} = 7 - \frac{1}{2}(4.74 + \log 0.1) = 7 - 1.87 = 5.13. Brain-Teaser 3: Arrange 0.1 M0.1\,\mathrm{M} solutions of NaCl, Na2CO3\mathrm{Na_{2}CO_{3}}, NH4Cl\mathrm{NH_{4}Cl} and CH3COONa\mathrm{CH_{3}COONa} in order of increasing pH. Solution: NH4Cl\mathrm{NH_{4}Cl} (acidic, 5.15.1) < NaCl (77) < CH3COONa\mathrm{CH_{3}COONa} (8.98.9) < Na2CO3\mathrm{Na_{2}CO_{3}} (about 11.611.6). Carbonate is the most basic because HCO3−\mathrm{HCO_{3}^{-}} is a much weaker acid (pKa2=10.3\text{p}K_{a2} = 10.3) than acetic acid, so CO32−\mathrm{CO_{3}^{2-}} is a stronger base.