GATE 2022 CH – Question 29

Thermodynamics · Properties of mixtures: partial molar properties, fugacity, excess properties, activity coefficients · 1 mark · Numerical answer

5 moles of liquid benzene, 8 moles of liquid toluene and 7 moles of liquid xylene are mixed at 25 °C and 1 bar. Assuming the formation of an ideal solution and using the universal gas constant $R = 8.314$ J mol$^{-1}$ K$^{-1}$, the total entropy change is __________ J K$^{-1}$ (rounded off to one decimal place).

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Correct answer: 178.80 to 180.60

Explanation

For an ideal solution the entropy of mixing is $\Delta S = -R\sum n_i\ln x_i$ with the mole fractions 0.25, 0.40 and 0.35: $5\ln 0.25 + 8\ln 0.40 + 7\ln 0.35 = -6.931 - 7.330 - 7.349 = -21.610$. So $\Delta S = 8.314 \times 21.610 = 179.7$ J/K.