For the reaction taking place at certain temperature $\mathrm{NH}_{2} \mathrm{COONH}_{4}(\mathrm{~s})…

For the reaction taking place at certain temperature $\mathrm{NH}_{2} \mathrm{COONH}_{4}(\mathrm{~s}) ightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g})$
if equilibrium pressure is $3 \mathrm{X}$ bar then $\Delta_{\mathrm{r}} \mathrm{G}^{\circ}$ would be
  1. $-\mathrm{RT} \ln 9-3 \mathrm{RT} \ln \mathrm{X}$
  2. $\mathrm{RT} \ln 4-3 \mathrm{RT} \ln \mathrm{X}$
  3. $-3 \mathrm{RT} \ln \mathrm{X}$
  4. None of these

Solution

$\Delta \mathrm{G}^{\circ}=-\mathrm{RT} \ln \mathrm{K}_{\mathrm{p}} ; \mathrm{K}_{\mathrm{P}}=(2 \mathrm{x})^{2} \mathrm{X}=4 \mathrm{x}^{3}$
$\Delta \mathrm{G}^{\circ}=-\mathrm{RT} \ln \left(4 \mathrm{X}^{3}ight)$
$\Delta \mathrm{G}^{\circ}=-\mathrm{RT} \ln 4-3 \mathrm{RT} \ln \mathrm{X}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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