Chemistry - Thermochemistry Question with Solution | TestHub

Given:

$\left(\mathrm{i}\right)$$\text{C}\left(\mathrm{graphite}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{CO}}_2\left(\mathrm{g}\right);$${\mathrm{\Delta rH}}^{\mathrm{\Theta }}=\mathrm{x}\mathrm{ }\mathrm{kJ}\mathrm{ }{\mathrm{mol}}^{-1}$

$\left(\mathrm{ii}\right)$$\mathrm{C}\left(\mathrm{graphite}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to \mathrm{CO}\left(\mathrm{g}\right) ;$${\mathrm{\Delta rH}}^{\mathrm{\Theta }}=\mathrm{y}\mathrm{ }\mathrm{kJ}\mathrm{ }{\mathrm{mol}}^{-1}$

$\left(\mathrm{iii}\right)\mathrm{ }\mathrm{CO}\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{CO}}_2\left(\mathrm{g}\right);$${\mathrm{\Delta rH}}^{\mathrm{\Theta }}=\mathrm{z}\mathrm{ }\mathrm{kJ}\mathrm{ }{\mathrm{mol}}^{-1}$

Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?