Consider the following reaction approaching equilibrium at and 1 atm pressure The standard Gibbs energy change at is (–) ____kJ (Nearest integer). [2023]

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Solution

Q.
Consider the following reaction approaching equilibrium at $27 ° C$ and 1 atm pressure

$A + B$ $⇌_{k_{r} = 10^{2}}^{k_{f} = 10^{3}}$ $C + D$

The standard Gibbs energy change $(Δ_{r} G^{θ})$ at $27 ° C$ is (–) ____kJ ${mol}^{- 1}$ (Nearest integer).

$(Given: R = {8.3 J K}^{- 1} {mol}^{- 1} and \ln 10 = 2.3)$ [2023]

Ans.
(6)

$K_{e q} = \frac{K_{f}}{K_{b}} = \frac{10^{3}}{10^{2}} = 10$

$Δ G ° = - RT ln K_{e q}$

$= - 8.3 \times 300 ln (10)$

$= - 8.3 \times 300 \times 2.3$

$= - 5.72 \times 10^{3} {J mol}^{- 1}$

$= - 5.72 {kJ mol}^{- 1}$

$\approx {6 kJ mol}^{- 1}$

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