Consider the following data :

Heat of formation of $\mathrm{CO}_2(\mathrm{g})=-393.5 \mathrm{~kJ} \mathrm{~mol}{ }^{-1}$

Heat of formation of $\mathrm{H}_2 \mathrm{O}(\mathrm{l})=-286.0 \mathrm{~kJ} \mathrm{~mol}{ }^{-1}$

Heat of combustion of benzene $=-3267.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$

The heat of formation of benzene is __________ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Nearest integer)

<p>To determine the heat of formation of benzene ($ \Delta H_f[\text{C}_6 \text{H}_6] $), we use the given data:</p> <p><p>Heat of formation of $\text{CO}_2(\text{g}) = -393.5 \text{ kJ/mol}$</p></p> <p><p>Heat of formation of $\text{H}_2 \text{O}(\text{l}) = -286.0 \text{ kJ/mol}$</p></p> <p><p>Heat of combustion of benzene = $-3267.0 \text{ kJ/mol}$</p></p> <p>The reaction for the combustion of benzene is:</p> <p>$ \text{C}_6\text{H}_6 + \frac{15}{2} \text{O}_2(\text{g}) \rightarrow 6 \text{CO}_2(\text{g}) + 3 \text{H}_2\text{O}(\text{l}) $</p> <p>Using the formula for the enthalpy change of the reaction ($ \Delta H_R $):</p> <p>$ \Delta H_R = \Delta H_C = \Sigma \Delta H_f(\text{Products}) - \Sigma \Delta H_f(\text{Reactants}) $</p> <p>Substitute values into the equation:</p> <p>$ -3267 = 6 \times (-393.5) + 3 \times (-286) - \Delta H_f[\text{C}_6\text{H}_6] $</p> <p>Solving this equation, we find:</p> <p>$ \Delta H_f[\text{C}_6\text{H}_6] = 48 \text{ kJ/mol} $</p> <p>Thus, the heat of formation of benzene is $ 48 \text{ kJ/mol} $.</p>