What is the value of $\Delta \mathrm{H}-\Delta \mathrm{U}$ for the following reaction? $2…

What is the value of $\Delta \mathrm{H}-\Delta \mathrm{U}$ for the following reaction? $2 \mathrm{C}_{(\mathrm{s})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightarrow \mathrm{C}_2 \mathrm{H}_{6(\mathrm{~g})}$
  1. $4 \mathrm{RT}$
  2. $-5 \mathrm{RT}$
  3. $\mathrm{RT}$
  4. $-2 \mathrm{RT}$

Solution

$\begin{aligned} & \Delta \mathrm{n}_{\mathrm{g}}=\text { (moles of product gases) } \\ & \Delta \mathrm{n}_{\mathrm{g}}=1-3=-2 \mathrm{~mol} \\ & \text { Now, using formula, } \\ & \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT} \\ \therefore \quad & \Delta \mathrm{H}=\Delta \mathrm{U}-2 \mathrm{RT} \\ \therefore \quad & \Delta \mathrm{H}-\Delta \mathrm{U}=-2 \mathrm{RT}\end{aligned}$

Asked in: MHT CET 2023 (09 May Shift 2)

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