Given: (i) C (graphite) + O_2( g ) → CO_2( g ); Δ rH^ =x kJ mol^-1 (ii) C (graphite) +1/2 O_2( g ) → CO_2( g ); Δ rH^ =y kJ mol^-1 (iii) CO ( g )+1/2…

Given :

$$\begin{aligned} & \mathrm{C} \text { (graphite) }+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) ; & \Delta \mathrm{rH}^{\ominus}=x \mathrm{~kJ} \mathrm{~mol}^{-$\displaystyle 1$} \end{aligned}

$$(ii) $$ \begin{aligned} & \mathrm{C} \text { (graphite) }+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) ; & \Delta \mathrm{rH}^{\ominus}=y \mathrm{~kJ} \mathrm{~mol}^{-$\displaystyle 1$} \end{aligned}

$$(iii)

$$\begin{aligned} & \mathrm{CO}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) ; & \Delta \mathrm{rH}^{\ominus}=z \mathrm{~kJ} \mathrm{~mol}^{-$\displaystyle 1$} \end{aligned}

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