JEE MAIN - Chemistry (2022 - 26th June Evening Shift - No. 18)
A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100$$^\circ$$C, then the internal energy for vaporization in kJ mol$$-$$1 is ___________. [nearest integer]
[Assume steam to be an ideal gas. Given $$\Delta$$vapH$$^\Theta $$ for water at 373 K and 1 bar is 41.1 kJ mol$$-$$1 ; R = 8.31 J K$$-$$1 mol$$-$$1]
Answer
38
Explanation
$\underset{36 \mathrm{~g}}{\mathrm{H}_{2} \mathrm{O}}(\ell) \longrightarrow \underset{36 \mathrm{~g}}{\mathrm{H}_{2} \mathrm{O}}(\mathrm{g})$ (evaporation)
$$ \begin{aligned} \mathrm{n}_{\mathrm{H}_{2} \mathrm{O}} &=\frac{36}{18}=2 \quad \Delta \mathrm{n}_{\mathrm{g}}=1-0=1 \\\\ \Delta \mathrm{U}_{\text {vap }} &=\Delta \mathrm{H}_{\text {vap }}-\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT} \\\\ &=41.1-(1) \times 8.31 \times 10^{-3} \times 373 \\\\ &=41.1-3.099 \\\\ &=38 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$
$$ \begin{aligned} \mathrm{n}_{\mathrm{H}_{2} \mathrm{O}} &=\frac{36}{18}=2 \quad \Delta \mathrm{n}_{\mathrm{g}}=1-0=1 \\\\ \Delta \mathrm{U}_{\text {vap }} &=\Delta \mathrm{H}_{\text {vap }}-\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT} \\\\ &=41.1-(1) \times 8.31 \times 10^{-3} \times 373 \\\\ &=41.1-3.099 \\\\ &=38 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$
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