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Exercise · Q32

Q.Ammonium acetate, CH3COONH4\text{CH}_3\text{COONH}_4, is the salt of a weak acid and a weak base with almost equal KaK_a and KbK_b values (1.8×10−51.8 \times 10^{-5} each). Using the relation pH=7+12(pKa−pKb)\text{pH} = 7 + \tfrac{1}{2}(\text{p}K_a - \text{p}K_b), show that its aqueous solution is very nearly neutral, and explain in words why this differs from the hydrolysis of CH3COONa\text{CH}_3\text{COONa}.

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For a salt of a weak acid and a weak base, both ions hydrolyze simultaneously — the cation (here NH4+\text{NH}_4^+) tending to make the solution acidic, and the anion (here CH3COO−\text{CH}_3\text{COO}^-) tending to make it basic. The net pH, pH=7+12(pKa−pKb)\text{pH} = 7 + \tfrac{1}{2}(\text{p}K_a - \text{p}K_b), depends only on the difference between pKa\text{p}K_a (of the parent acid) and pKb\text{p}K_b (of the parent base), not on the salt's concentration at all — this is a genuinely different behaviour from the weak-acid/strong-base or strong-acid/weak-base cases, whose pH values do depend on concentration through the K⋅C\sqrt{K \cdot C} relation. Here, since both Ka(CH3COOH)K_a(\text{CH}_3\text{COOH}) and Kb(NH3)K_b(\text{NH}_3) are given as the same value, 1.8×10−51.8\times10^{-5}, both p-values are identical (pKa=pKb≈4.74\text{p}K_a = \text{p}K_b \approx 4.74), so their diff …

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