# GATE2020: 31

Consider the gas phase reaction $N_2O_4 \rightleftarrows 2NO_2$ occuring in an isothermal and isobaric reactor maintained at $298 K$ and $1.0$ bar. The standard Gibbs energy change of the reaction at $298 K$ is $\Delta G^\circ_{298}=5253 \; J\;mol^{-1}.$ The standard states are those of pure ideal gases at $1.0$ bar. The equilibrium mixture in the reactor behaves as an ideal gas. The value of the universal gas constant is $8.314\;J\;mol^{-1}\;K^{-1}.$ If one mole of pure $N_2O_4$ is initially charged to the reactor, the fraction of $N_2O_4$ that decomposes into $NO_2$ at equilibrium is
1. $0$
2. $0.17$
3. $0.38$
4. $1$