Question

At 298 K, the standard enthalpies of formation for${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{2}}\left(g\right)$ and ${\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{6}}\left(g\right)$are$\mathbf{277}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$ and $\mathbf{49}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$, respectively.

1. Calculate$\mathbf{∆}{\mathbf{H}}^{\mathbf{o}}$for${\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{6}}\left(l\right)\mathbf{\to }\mathbf{3}{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{2}}\left(g\right)$
2. Both acetylene $\left(C_2{H}_2\right)$and benzene$\left(C_6{H}_6\right)$ can be used as fuels. Which compound would liberate more energy per gram when combusted in air?

Short answer

The enthalpy of reaction is $632\mathrm{kJ}/\mathrm{mol}$. Acetylene will release more energy per gram when burned in the air.

Step-by-step solution

Step 1: Calculation of standard enthalpy of reaction.

$\mathbf{∆}{\mathbf{H}}_{\mathbf{r}}^{\mathbf{o}}\mathbf{=}\mathbf{\sum }\mathbf{∆}{\mathbf{H}}_{\mathbf{P}}^{\mathbf{o}}\mathbf{-}\mathbf{\sum }\mathbf{∆}{\mathbf{H}}_{\mathbf{R}}^{\mathbf{o}}$

Substitute the values of enthalpies of reactant and product.

$\begin{array}{rcl}\mathbf{∆}{\mathbf{H}}_{\mathbf{r}}^{\mathbf{o}}& \mathbf{=}& \left[3∆H_f^o\mathrm{for}{C}_2{H}_2\left(g\right)\right]\mathbf{-}\left[1∆H_f^o\mathrm{for}{C}_6{H}_6\left(l\right)\right]\\ \mathbf{∆}{\mathbf{H}}_{\mathbf{r}}^{\mathbf{o}}& \mathbf{=}& \left[3\times 227\mathrm{kJ}/\mathrm{mol}\right]\mathbf{-}\left[1\times 49\mathrm{kJ}/\mathrm{mol}\right]\\ & \mathbf{=}& \mathbf{632}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}\\ & & \end{array}$

Step 2: Comparison between the energy released by Acetylene and benzene when burned.

As the energy of 3 moles of acetylene is more than benzene, acetylene will release more energy when burned.

Result:

Hence, the enthalpy of the reaction is $632\mathrm{kJ}/\mathrm{mol}$. Due to the higher energy of the formation of acetylene, it will produce more heat when burned.