Consider the following data

Heat of combustion of $\mathrm{H}_{2}(\mathrm{g})\quad\quad=-241.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$

Heat of combustion of $\mathrm{C}(\mathrm{s})\quad\quad=-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$

Heat of combustion of $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})\quad=-1234.7 \mathrm{~kJ}~{\mathrm{mol}}^{-1}$$

The heat of formation of $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})$ is $(-)$ ___________ $\mathrm{kJ} ~\mathrm{mol}^{-1}$ (Nearest integer).

The reaction for the formation of $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})$ is given by: <br/><br/> $$2\mathrm{C}(\mathrm{s}) + 6\mathrm{H}_{2}(\mathrm{g}) + \frac{1}{2}\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l}) + 3\mathrm{H}_{2}\mathrm{O}(\mathrm{l})$$ <br/><br/> The heat of combustion for $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})$ is: <br/><br/> $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l}) + 3\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2\mathrm{CO}_{2}(\mathrm{g}) + 3\mathrm{H}_{2}\mathrm{O}(\mathrm{l})$$ <br/><br/> By adding the formation reaction with the combustion reaction times -1, we get: <br/><br/> $$2\mathrm{C}(\mathrm{s}) + 3\mathrm{H}_{2}(\mathrm{g}) + \frac{3}{2}\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2\mathrm{CO}_{2}(\mathrm{g}) + 3\mathrm{H}_{2}\mathrm{O}(\mathrm{l})$$ <br/><br/> This reaction has a heat equal to the heat of formation of ethanol times -1. <br/><br/> Therefore, the heat of formation of ethanol is equal to: <br/><br/> $$-1234.7 \mathrm{~kJ/mol} + 2*(-393.5 \mathrm{~kJ/mol}) + 3*(-241.8 \mathrm{~kJ/mol})$$ <br/><br/> Calculating this gives: <br/><br/> $$\Delta H_f(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})) = -277.7 \approx -278 \mathrm{~kJ/mol}$$ (rounded to the nearest integer)