Thermodynamics and Thermochemistry 2 Question 2
2. Given :
(i) $\mathrm{C}$ (graphite) $+\mathrm{O}{2}(g) \rightarrow \mathrm{CO}{2}(g) ; \Delta_{\mathrm{r}} H^{\ominus}=x \mathrm{~kJ} \mathrm{~mol}^{-1}$
(ii) $\mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}{2}(g) \longrightarrow \mathrm{CO}{2}(g)$;
$$ \Delta_{\mathrm{r}} H^{\ominus}=y \mathrm{~kJ} \mathrm{~mol}^{-1} $$
(iii) $\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}{2}(g) \longrightarrow \mathrm{CO}{2}(g) ; \Delta_{\mathrm{r}} H^{\ominus}=z \mathrm{~kJ} \mathrm{~mol}^{-1}$
Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?
(2019 Main, 12 Jan II)
(a) $y=2 z-x$
(b) $x=y-z$
(c) $z=x+y$
(d) $x=y+z$
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Solution:
- Second equation given in this question is wrong. Hence, No answer in correct.
If corrected second equation is given,
i.e. $\quad \mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g})$ and if we take the above reaction in consideration then $x=y+z$ will be the answer as:
(ii) $\mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}{2}(g) \longrightarrow \mathrm{CO}(g), \Delta{r} H^{\circ}=y \mathrm{~kJ} / \mathrm{mol}$
(iii) $\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}{2}(g) \longrightarrow \mathrm{CO}{2}(g), \quad \quad \Delta_{r} H^{\circ}=z \mathrm{~kJ} / \mathrm{mol}$
Summing up both the equation you will get equation (i):
$\mathrm{C}$ (graphite) $+\mathrm{O}{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}{2}(\mathrm{~g}), \quad \Delta_{r} H^{\circ}=x \mathrm{~kJ} / \mathrm{mol}$
Hence, $x, y$ and $z$ are related as:
$$ x=y+z $$
