Question

For the chemical reaction, ⇌ Y, the standard reaction Gibbs energy depends on temperature T (in K) as \(\;{\Delta _r}\;G^\circ \left( {\;in\;kJ\;mo{l^{ - 1}}} \right) = 120 - \frac{3}{8}\;T\). The major component of the reaction mixture at T is 
1. Y if T = 280 K
2. X if T = 350 K
3. X if T = 315 K
4. Y if T = 300 K

Answer 1

Correct Answer - Option 3 : X if T = 315 K

Concept:

For a given value of T, 

(i) If Δ_rG° becomes < 0, the forward direction will be spontaneous and then the major and minor components will be Y and X respectively. 

(ii) If Δ_rG° becomes > 0, the forward direction, will be non-spontaneous and then the major and minor components will be X and Y respectively. 

(a) \({\Delta _r}G^\circ = 120 - \frac{3}{8} \times 280 = 15\) i.e. Δ_rG° > 0, major component = X

(b) \({\Delta _r}G^\circ = 120 - \frac{3}{8} \times 350 = - 11.25\) i.e. ΔrG° < 0, major component = Y

(c) \({\Delta _r}G^\circ = 120 - \frac{3}{8} \times 315 = 1.875{\rm{\;}}\) i.e. Δ_rG° > 0, major component = X

(d) \({\Delta _r}G^\circ = 120 - \frac{3}{8} \times 300 = 7.5{\rm{\;}}\)i.e. Δ_rG° > 0, major component = X.