\[ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g}) ...

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\[
\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g})
\]
This reaction is carried out at \( 298 \mathrm{~K} \) and 20 bar. \( 5 \mathrm{~mol} \) each of \( \mathrm{N}_{2} \mathrm{O}_{4} \) and \( \mathrm{NO}_{2} \) are taken initially :
Given : \( \Delta \mathrm{G}_{\mathrm{N}_{2} \mathrm{O}_{4}}=100 \mathrm{~kJ} \mathrm{~mol}^{-1} ; \Delta \mathrm{G}_{\mathrm{NO}_{2}}=50 \mathrm{~kJ} \mathrm{~mol}^{-1} \)
(i) Find \( \Delta \mathrm{G} \) for reaction at \( 298 \mathrm{~K} \) under given condition.
(ii) Find the direction in which the reaction proceeds to achieve equilibrium.
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