Question

Hydrolysis of sucrose is given by the following reaction. $\text{Sucrose}+H_{2}O\rightleftharpoons \text{Glucose+Fructose}$
If the equilibrium constant $\left(K_c\right)$ is $2\times {10}^{13}$ at $300K$, the value of ${\Delta }_r{G}^0$ at the same temperature will be :

• A. $-8.314Jmo{l}^{-1}{K}^{-1}\times 300K\times \ln (2\times {10}^{13})$
• B. $8.314Jmo{l}^{-1}{K}^{-1}\times 300K\times \ln (2\times {10}^{13})$
• C. $-8.314Jmo{l}^{-1}\times 300K\times \ln (3\times {10}^{13})$
• D. $-8.314Jmo{l}^{-1}{K}^{-1}\times 300K\times \ln (4\times {10}^{13})$

Answer 1

The correct option is A $-8.314Jmo{l}^{-1}{K}^{-1}\times 300K\times \ln (2\times {10}^{13})$

The relation between gibbs free energy and equilibrium constat is given by:
${\Delta }_r{G}^0=-RT\ln K_c{\Delta }_r{G}^0=-8.314\times 300\times \ln (2\times {10}^{13})$
${\Delta }_r{G}^0=-8.314Jmo{l}^{-1}{K}^{-1}\times 300K\times \ln (2\times {10}^{13})$
Option (a) is correct