The dissociation constant of at 27°C from the following data:
+ H+ ⇌ NH4+; ΔH° = -52.21 kJ/mol; ΔS° = +1.6 JK^-1 mol^-1
⇌ H+ + OH-; ΔH° = 54.70 kJ/mol; ΔS° = -76.3 JK^-1 mol^-1
Given: R = 8

Question

The dissociation constant of $NH_3$ at 27°C from the following data:
$NH_3$ + H+ ⇌ NH4+; ΔH° = -52.21 kJ/mol; ΔS° = +1.6 JK^-1 mol^-1
$H_2O$ ⇌ H+ + OH-; ΔH° = 54.70 kJ/mol; ΔS° = -76.3 JK^-1 mol^-1
Given: R = 8.3 J/K-mol

Prashant Kotian · Accepted Answer

Correct answer: B. Basic dissociation of : + ⇌ NH4+ + OH-.
This is the sum of the two given reactions.
ΔH° = -52.21 + 54.70 = 2.49 kJ/mol = 2490 J/mol.
ΔS° = 1.6 + (-76.3) = -74.7 J/K-mol.
At 27°C (T = 300 K):
ΔG° = ΔH° - T ΔS° = 2490 - 300 × (-74.7) = 2490 + 22410 = 24900 J/mol.
Since ΔG° = -RT ln Kb => ln Kb = -ΔG° / RT = -24900 / (8.3 × 300) = -10.
Kb = e^-10.

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