Equilibrium - Result Question 21
####22. Hydrolysis of sucrose is given by the following reaction.
[2020]
Sucrose $+H_2 O \rightarrow$ Glucose + Fructose
If the equilibrium constant $(K_C)$ is $2 \times 10^{13}$ at $300 K$, the value of $\Delta_r G^{\ominus}$ at the same temperature will be :
(a) $8.314 J mol^{-1} K^{-1} \times 300 K \times \ln (2 \times 10^{13})$
(b) $8.314 J mol^{-1} K^{-1} \times 300 K \times \ln (3 \times 10^{13})$
(c) $-8.314 J mol^{-1} K^{-1} \times 300 K \times \ln (4 \times 10^{13})$
(d) $-8.314 J mol^{-1} K^{-1} \times 300 K \times \ln (2 \times 10^{13})$
Show Answer
Solution:
- (d) $\Delta G=\Delta G^{\circ}+R T \ln Q$
At equilibrium $\Delta G=0, Q=K _{e q}$
So, $\Delta_r G^{\circ}=-R T \ln K _{e q}$
$\Delta_r G^{\circ}=-8.314 J mol^{-1} K^{-1} \times 300 K \times \ln (2 \times 10^{13})$
