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For the reaction NH4HS(s) ⇌ NH3(g) + H2S(g) occurring at a certain temperature, the total equilibrium pressure is X bar. Express the standard Gibbs free energy change (delta_r G°) in terms of X and R, T.

1. -2RT ln X
2. -RT (ln X - ln 2)
3. -2RT (ln X - ln 2)
4. -0.5 RT (ln X - ln 2)

Correct answer: -2RT (ln X - ln 2)

Solution

Since NH4HS(s) produces equal moles of NH3(g) and H2S(g), each gas has partial pressure X/2 bar (total = X bar). Kp = (X/2) * (X/2) = X²/4 (in bar², referenced to 1 bar standard state). delta_r G° = -RT ln Kp = -RT ln(X²/4) = -RT [2 ln X - ln 4] = -RT [2 ln X - 2 ln 2] = -2RT(ln X - ln 2).

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