The heats of combustion of carbon and carbon monoxide are $-393.5$ and $-283.5\mathrm{kJ}{\mathrm{mol}}^{-1}$, respectively. The heat of formation (in $\mathrm{kJ}{\mathrm{mol}}^{-1}$) of carbon monoxide is

The given informations are:

(i) $\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{CO}}_2\left(\mathrm{g}\right) {\mathrm{\Delta }}_{\mathrm{c}}H=-393.5\mathrm{kJ}{\mathrm{mol}}^{-1}$

(ii) $\mathrm{CO}\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to \mathrm{CO}\left(\mathrm{g}\right);{\mathrm{\Delta }}_{\mathrm{c}}H=-283.5\mathrm{kJ}{\mathrm{mol}}^{-1}$

(iii)$\mathrm{C}\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to \mathrm{CO}\left(\mathrm{g}\right);{\mathrm{\Delta }}_{\mathrm{f}}H=?$

Equation (iii) is obtained by carrying out the manipulation Eq. (i) - Eq. (ii). Hence,

$\begin{array}{l}{\mathrm{\Delta }}_{\mathrm{f}}{H}_{\left(\mathrm{iii}\right)}={\mathrm{\Delta }}_{\mathrm{c}}{H}_{\left(\mathrm{i}\right)}-{\mathrm{\Delta }}_{\mathrm{c}}{H}_{\text{(ii) }}=\{-393.5-(-283.5\left)\right\}\mathrm{kJ}{\mathrm{mol}}^{-1}\\ =-110.0\mathrm{kJ}{\mathrm{mol}}^{-1}\end{array}$