Question
For the reaction taking place at certain temperature $$N{H_2}COON{H_4}\left( s \right) \rightleftharpoons $$ $$2N{H_3}\left( g \right) + C{O_2}\left( g \right),$$ if equilibrium pressure is $$3X$$ $$bar$$ then $${\Delta _r}{G^ \circ }$$ would be
A.
$$ - RT\,\,{\text{ln}}\,\,9 - 3RT\,\,{\text{ln}}\,\,X$$
B.
$$RT\,\,{\text{ln}}\,\,4 - 3RT\,\,{\text{ln}}\,\,X$$
C.
$$ - 3RT\,\,{\text{ln}}\,\,X$$
D.
$${\text{None of these}}$$
Answer :
$${\text{None of these}}$$
Solution :
$$\eqalign{
& \Delta {{\text{G}}^ \circ } = - RT\,\,{\text{ln}}\,\,{K_p};{K_p} = {\left( {2x} \right)^2}X = 4{x^3} \cr
& \Delta {G^ \circ } = - RT\,\,{\text{ln}}\,\,\left( {4{X^3}} \right) \cr
& \Delta {G^ \circ } = - RT\,\,{\text{ln}}\,\,4 - 3RT\,\,{\text{ln}}\,\,X \cr} $$