What is the difference between $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ for reaction given below at $298…

What is the difference between $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ for reaction given below at $298 \mathrm{~K}$ ? $\left(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)$ $2 \mathrm{C}_6 \mathrm{H}_{6(\ell)}+150_{2(\mathrm{~g})} \rightarrow 12 \mathrm{CO}_{2(\mathrm{~g})}+6 \mathrm{H}_2 \mathrm{O}_{(\ell)}$
  1. $-2.72 \mathrm{~kJ}$
  2. $-7.43 \mathrm{~kJ}$
  3. $-7.8 \mathrm{~kJ}$
  4. $-3.72 \mathrm{~kJ}$

Solution

$\begin{aligned} & \Delta \mathrm{H}-\Delta \mathrm{U}=\Delta \mathrm{ngRT} \\ & \Delta \mathrm{ng}=12-15=-3 \\ & \Delta \mathrm{H}-\Delta \mathrm{U}=-3 \times 8.314 \times 298 \\ & =-7432.7 \mathrm{~J}=-7.432 \mathrm{~kJ}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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