Calculate difference between $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ for following reaction at…

Calculate difference between $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ for following reaction at $25^{\circ} \mathrm{C}$ ? $\mathrm{C}_2 \mathrm{H}_{6(\mathrm{~g})}+3.50_2 \rightarrow 2 \mathrm{CO}_{2(\mathrm{~g})}+3 \mathrm{H}_2 \mathrm{O}_{(\mathrm{l})}\left(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)$
  1. $-9.3 \mathrm{~kJ}$
  2. $-3.1\mathrm{~kJ}$
  3. $-6.2 \mathrm{~kJ}$
  4. $-16.10 \mathrm{~kJ}$

Solution

$\begin{aligned} & \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT} \\ & \mathrm{C}_2 \mathrm{H}_{6(\mathrm{~g})}+3.5 \mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{CO}_{2(\mathrm{~g})}+3 \mathrm{H}_2 \mathrm{O}_{(\ell)} \\ & \Delta \mathrm{n}_{\mathrm{g}}=2-3.5-1=-2.5 \\ & \Delta \mathrm{H}-\Delta \mathrm{U}=\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT} \\ & =-2.5 \times 8.314 \times 298 \\ & =-6193.93 \mathrm{~J} \\ & =-6.19 \mathrm{~kJ} \text { or }-6.2 \mathrm{~kJ}\end{aligned}$

Asked in: MHT CET 2021 (20 Sep Shift 1)

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