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The equilibrium concentrations of the species in the reaction A+B⇌C+DA + B \rightleftharpoons C + D are 2, 3, 10 and 6 mol L−1^{-1}, respectively at 300 K. ΔG∘\Delta G^{\circ} for the reaction is (R=2R = 2 cal/mol K)

A

1372.60 cal

B

-137.26 cal

C

-1381.80 cal

D

-13.73 cal

Step-by-Step Solution

The equilibrium constant Kc=[C][D][A][B]=10×62×3=606=10K_c = \frac{[C][D]}{[A][B]} = \frac{10 \times 6}{2 \times 3} = \frac{60}{6} = 10. The standard Gibbs free energy change is given by ΔG∘=−RTln⁡Kc\Delta G^{\circ} = -RT \ln K_c. Given R=2R = 2 cal/mol K, T=300T = 300 K, and Kc=10K_c = 10, ΔG∘=−2×300×ln⁡(10)=−600×2.303=−1381.8\Delta G^{\circ} = -2 \times 300 \times \ln(10) = -600 \times 2.303 = -1381.8 cal.

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