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On the basis of thermochemical equations (a), (b) and (c), find out which of the algebric relationships given in options (A) to (D) is correct.
\( \mathrm{P} \)
(a) \( \mathrm{C} \) (graphite) \( +\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g}) ; \quad \Delta_{\mathrm{r}} \mathrm{H}=\mathrm{x} \mathrm{kJ} \mathrm{mol}^{-1} \)
(b) \( \mathrm{C} \) (graphite) \( +\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g}) ; \quad \underset{\mathrm{r}}{\Delta} \mathrm{H}=\mathrm{y} \mathrm{kJ} \mathrm{mol}^{-1} \)
(c) \( \mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g}) ; \quad \Delta \underset{\mathrm{r}}{\mathrm{H}}=\mathrm{z} \mathrm{kJ} \mathrm{mol}^{-1} \)
(A) \( z=x+y \)
(B) \( x=y-z \)
(C) \( x=y+z \)
(D) \( y=2 z-x \)
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