Hydrolysis of sucrose is given by the following reaction
$Sucrose + H_{2} O ⇌ Glucose + Fructose$
If the equilibrium constant $(K_{C})$ is $2 x 10^{13}$ at 300 K,
the value of $Δ_{r} G^{Θ}$ at the same temperature will be

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$8 .314 J {mol}^{- 1} K^{- 1} \times 300 K \times \ln (2 \times 10^{13})$

$8 .314 J {mol}^{- 1} K^{- 1} \times 300 K \times \ln (3 \times 10^{13})$

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

$- 8 .314 J {mol}^{- 1} K^{- 1} \times 300 K \times \ln (2 \times 10^{13})$

answer is D.

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Detailed Solution

$\begin{array}{l} Δ_{r} G^{θ} = - R T \ln K_{e q} \\ Δ_{r} G^{θ} = - 8.314 \times 300 \ln K_{e q} \\ Δ_{r} G^{θ} = - 8.314 \times 300 \ln (2 \times 10^{13}) \end{array}$

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