Hydrolysis of sucrose is given by the following reaction: $ ext{Sucrose} + ext{H}_2 ext{O} ightleftharpo

Question

Hydrolysis of sucrose is given by the following reaction: $	ext{Sucrose} + 	ext{H}_2	ext{O} ightleftharpoons 	ext{Glucose} + 	ext{Fructose}$. If the equilibrium constant ($K_c$) is $2 	imes 10^{13}$ at $300 	ext{ K}$, the value of $\Delta_r G^\ominus$ at the same temperature will be:

Accepted Answer

The relationship between standard Gibbs free energy change ($\Delta_r G^\ominus$) and the equilibrium constant ($K_c$) is given by the equation:
$\Delta_r G^\ominus = -RT \ln K_c$

Given the values:
Universal gas constant, $R = 8.314 	ext{ J mol}^{-1} 	ext{ K}^{-1}$
Temperature, $T = 300 	ext{ K}$
Equilibrium constant, $K_c = 2 	imes 10^{13}$

Substituting these values into the equation, we get:
$\Delta_r G^\ominus = -8.314 	ext{ J mol}^{-1} 	ext{ K}^{-1} 	imes 300 	ext{ K} 	imes \ln (2 	imes 10^{13})$

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