GATE 2022 CH – Question 49
For a pure substance, the following data at saturated conditions are given:
| $\ln P^{sat}$ (bar) | $T$ (K) |
|---|---|
| 0.693 | 350 |
| 1.386 | 370 |
Assume that the vapor phase behaves ideally, the molar volume of the liquid is negligible, and the latent heat of vaporization is constant over the given temperature range. The universal gas constant, $R = 8.314$ J K$^{-1}$ mol$^{-1}$. From the above data, the estimated latent heat of vaporization at 360 K is ____________ kJ/mol (rounded off to one decimal place).
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Correct answer: 37.11 to 37.49
Explanation
With a constant latent heat, the Clausius-Clapeyron equation is $\ln P^{sat} = A - \frac{\Delta H}{RT}$. So $\Delta H = \frac{R(\ln P_2 - \ln P_1)}{\frac{1}{T_1} - \frac{1}{T_2}} = \frac{8.314 \times 0.693}{\frac{1}{350} - \frac{1}{370}} = \frac{5.762}{1.5444 \times 10^{-4}} = 37.3 \times 10^3$ J/mol. It is constant, so it is the same at 360 K.