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Hydrolysis of sucrose is given by the following reaction. Sucrose + $H_2O\rightleftharpoons$ Glucose + Fructose. If the equilibrium constant ($K_c$) is $2\times10^{13}$ at 300 K, the value of $\Delta_rG^\circ$ at the same temperature will be:
A
$8.314\ J\,mol^{-1}K^{-1}\times300\ K\times\ln(2\times10^{13})$
B
$8.314\ J\,mol^{-1}K^{-1}\times300\ K\times\ln(3\times10^{13})$
C
$-8.314\ J\,mol^{-1}K^{-1}\times300\ K\times\ln(4\times10^{13})$
D
$-8.314\ J\,mol^{-1}K^{-1}\times300\ K\times\ln(2\times10^{13})$
Detailed Solution
$\Delta G = \Delta G^\circ + RT\ln Q$; at equilibrium, $\Delta G = 0$ and $Q = K_{eq}$
$\Delta_rG^\circ = -RT\ln K_{eq}$
$\Delta_rG^\circ = -8.314\ J\,mol^{-1}K^{-1} \times 300\ K \times \ln(2 \times 10^{13})$