For the chemical reaction $\mathrm{X} \rightleftharpoons \mathrm{Y}$, the standard reaction Gibbs energy depends on temperature T (in K) as $\Delta_{\mathrm{r}} \mathrm{G}^{0}(\mathrm{in\ kJ\ mol}^{-1})=120-\frac{3}{8} \mathrm{~T}$ The major component of the reaction mixture at T is:

(D) X if $\mathrm{T}=315 \mathrm{~K}$

(A) Y if $\mathrm{T}=300 \mathrm{~K}$

(B) Y if $\mathrm{T}=280 \mathrm{~K}$

(C) X if $\mathrm{T}=350 \mathrm{~K}$

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Chemical Thermodynamics

For the chemical reaction

X ⇌ Y

, the standard reaction Gibbs energy depends on temperature T (in K) as

Δ_{r} G^{0} (in kJ mol^{- 1}) = 120 - \frac{3}{8} T

The major component of the reaction mixture at T is:

Answer: (D)

The major component follows the sign of

Δ_{r} G^{\circ} = 120 - \frac{3}{8} T

. It vanishes when

120 = \frac{3}{8} T

, that is at

T = 320 K

. Above

320 K

the free energy is negative and the product Y dominates; below

320 K

it is positive and the reactant X dominates. Checking the offered pairings, only

T = 315 K

lies below

320 K

while being paired with X, so X is the major component at

315 K

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option