Thermodynamics and Thermochemistry 1 Question 13
13. For the chemical reaction, $X \rightleftharpoons Y$, the standard reaction Gibbs energy depends on temperature $T$ (in $\mathrm{K}$ ) as
$$ \Delta_{\mathrm{r}} G^{\circ}\left(\text { in } \mathrm{kJ} \mathrm{mol}^{-1}\right)=120-\frac{3}{8} T $$
The major component of the reaction mixture at $T$ is
(2019 Main, 11 Jan I)
(a) $Y$ if $T=280 \mathrm{~K}$
(b) $X$ if $T=350 \mathrm{~K}$
(c) $X$ if $T=315 \mathrm{~K}$
(d) $Y$ if $T=300 \mathrm{~K}$
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Solution:
- For a given value of $T$,
(i) If $\Delta_{r} G^{\circ}$ becomes $<0$, the forward direction will be spontaneous and then the major and minor components will be $Y$ and $X$ respectively.
(ii) If $\Delta_{r} G^{\circ}$ 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. $\Delta_{r} G^{\circ}>O$ 0, major component $=X$;
(b) $\Delta_{r} G^{\circ}=120-\frac{3}{8} \times 350=-11.25$
i.e. $\Delta_{r} G^{\circ}<0$, major component $=Y$
(c) $\Delta_{r} G^{\circ}=120-\frac{3}{8} \times 315=1.875$
i.e. $\Delta_{r} G^{\circ}>0$, major component $=X$
(d) $\Delta_{r} G^{\circ}=120-\frac{3}{8} \times 300=7.5$
i.e. $\Delta_{r} G^{\circ}>0$, major component $=X$
