The difference between the reaction enthalpy change $\left(\Delta_{\mathrm{r}} \mathrm{H}ight)$ and reaction…

The difference between the reaction enthalpy change $\left(\Delta_{\mathrm{r}} \mathrm{H}ight)$ and reaction internal energy change $\left(\Delta_{\mathrm{r}} \mathrm{U}ight)$ for the reaction:
$2 \mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{l})+15 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 12 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$
at $300 \mathrm{~K}$ is $\left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}ight)$
  1. $0 \mathrm{~J} \mathrm{~mol}^{-1}$
  2. $2490 \mathrm{~J} \mathrm{~mol}^{-1}$
  3. $-2490 \mathrm{~J} \mathrm{~mol}^{-1}$
  4. $-7482 \mathrm{~J} \mathrm{~mol}^{-1}$

Solution

$\Delta H=\Delta U+\Delta n_{\mathrm{g}} R T$
For the reaction $\Delta n_{\mathrm{g}}=12-15=-3$ $\Delta H-\Delta U=-3 \times 8.314 \times 300$
$=-7482 \mathrm{~J} \mathrm{~mol}^{-1}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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