Question

5 moles of liquid benzene, 8 moles of liquid toluene and 7 moles of liquid xylene are mixed at 25$^\circ$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 \(\underline{\hspace{2cm}}\) J K$^{-1}$ (rounded off to one decimal place).

Hint:

Entropy of mixing is always positive, as disorder increases when solutions form.

Answer 1

Correct Answer: 178.7 - 180.7

Total moles present:
$n = 5 + 8 + 7 = 20$
Mole fractions:
$x_1 = 0.25,\; x_2 = 0.40,\; x_3 = 0.35$
Entropy of mixing for an ideal liquid solution:
$\Delta S = -R \sum n_i \ln x_i$
Calculate each contribution:
$5 \ln(0.25) = -6.93$
$8 \ln(0.40) = -7.33$
$7 \ln(0.35) = -7.35$
Sum:
$\sum n_i \ln x_i = -21.61$
Thus:
$\Delta S = -8.314(-21.61) = 179.6 \text{ J/K}$
Rounded to one decimal place: $179.6$ J K$^{-1}$.