| Hydrolysis of sucrose is given by the following reaction. [NEET 2020] |
| \[\text{Sucrose+}{{\text{H}}_{\text{2}}}\text{O}\text{Glucose+Fructose}\] |
| If the equilibrium constant \[({{K}_{C}})\] is \[2\times {{10}^{13}}\] at 300 K, the value of \[{{\Delta }_{r}}{{G}^{O-}}\] at the same temperature will be: |
A) \[8.314\text{ }J\text{ }mo{{l}^{1}}{{K}^{1}}\times 300\text{ }K\times ln\,\text{(}2\times {{10}^{13}})\]
B) \[8.314\text{ }J\text{ }mo{{l}^{1}}{{K}^{1}}\times 300\text{ }K\times ln\,(3\times {{10}^{13}})\]
C) \[8.314\text{ }J\text{ }mo{{l}^{1}}{{K}^{1}}\times 300\text{ }K\times ln\text{ (}4\times {{10}^{13}})\]
D) \[8.314\text{ }J\text{ }mo{{l}^{1}}{{K}^{1}}\times 300\text{ }K\times ln\,(2\times {{10}^{13}})\]
Correct Answer: D
Solution :
[d] \[\Delta G=\Delta G{}^\circ +RT\] In \[Q\]| At equilibrium \[\Delta G=0,\,\,Q={{K}_{eq}}\] |
| So \[{{\Delta }_{r}}G{}^\circ =-RT\,\,In\,\,{{K}_{eq}}\] |
| \[{{\Delta }_{r}}G{}^\circ =-8.314\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\times 300\,\,K\times \,\,In\,\,(2\times {{10}^{13}})\] |
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