Q17 / 120 · JEE Main 2007 · Chemistry

Assuming that water vapour is an ideal gas, the internal energy $(\Delta \mathrm{U})$ when $1\mathrm{~mol}$ of water is vapourised at $1 \mathrm{~bar}$ pressure and $100^{\circ} \mathrm{C}$, (Given: Molar enthalpy of vapourization of water at $1 \mathrm{~bar}$ and $373 \mathrm{~K}=41 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ ) will be

  • A
    $4.100 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  • B
    $3.7904 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  • Correct answer
    C
    $37.904 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  • D
    $41.00 \mathrm{~kJ} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & \mathrm{H}_2 \mathrm{O}(\ell) \stackrel{\text { vaporisation }}{\longrightarrow} \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \\ & \Delta \mathrm{n}_{\mathrm{g}}=1-0=1 \\ & \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT} \\ & \Delta \mathrm{U}=\Delta \mathrm{H}-\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT} \\ & =41-8.3 \times 10^{-3} \times 373 \\ & =37.9 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$ Hence, (C) is correct.

Hence, the correct answer is option: 'C'.

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