For the equilibrium at `298 K, N_(2)O_(4)(g) hArr 2NO_(2)(g), G_(N_(2)O_(4))^(ɵ)=100 kJ mol^(-1)` and `G_(NO_(2))^(ɵ)=50 kJ mol^(-1)`. If `5` mol of `N_(2)O_(4)` and `2` moles of `NO_(2)` are taken initially in one litre container than which statement are correct.

Options

A. Reaction proceeds in forward direction
B. `K_c=1`
C. `DeltaG=-0.55 KJ,DeltaG^@=0`
D. At equilibrium `[N_2O_4]=4.894 M,[NO_2]=2.2`

Explanation

`DeltaG=DeltaG^@+2.303 RT log Q`
`DeltaG^@=2xxG_(NO_2)^@=G_(N_2O_4)^@=2xx50-100=0`
`therefore DeltaG=0+2.303 xx8.314 xx10^(-3)xx298log""(22)/5`
`=0-0.55kI`
`DeltaG=0.55kJ`
i.e. reaction proceeds in forward direction
Also, `DeltaG^@=0=2.303 RT log K`
`therefore K=1`
`{:(N_2O_4,hArr,2NO_2),(5,"",2),((5-x),"",(2+2x)):}`
`rArr K=((2+2x)^2)/(5-x) rArr 1=((2+2x)^2)/((5-x))`
`therefore x=0.106`
`[N_2O_4]=5-0.106=4.894M`
`[NO_2}=2+2x=2.212M`