Hydrolysis of sucrose is given by the following reaction: \( \mathrm{Sucrose + H_2O \rightleftharpoons Glucose + Fructose} \)\nIf the equilibrium constant (\( K_c \)) is \( 2 \times 10^{13} \) at \( 300\text{ K} \), the value of \( \Delta_r G^\circ \) at the same temperature will be _______.

\( 8.314\text{ J mol}^{-1}\text{ K}^{-1} \times 300\text{ K} \times \ln (2 \times 10^{13}) \)
\( 8.314\text{ J mol}^{-1}\text{ K}^{-1} \times 300\text{ K} \times \ln (3 \times 10^{13}) \)
\( -8.314\text{ J mol}^{-1}\text{ K}^{-1} \times 300\text{ K} \times \ln (4 \times 10^{13}) \)
\( -8.314\text{ J mol}^{-1}\text{ K}^{-1} \times 300\text{ K} \times \ln (2 \times 10^{13}) \)

Correct answer · Option 4

\( -8.314\text{ J mol}^{-1}\text{ K}^{-1} \times 300\text{ K} \times \ln (2 \times 10^{13}) \)

\( \Delta_r G^\circ = -RT \ln K_c = -8.314 \times 300 \times \ln(2 \times 10^{13}) \).