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Hexane and heptane are completely miscible. At 25 °C, the vapor pressures of hexane and heptane are 0.198 atm and 0.06 atm, respectively. The mole fractions of hexane and heptane in the vapor phase for a solution containing 4 M hexane and 6 M heptane, respectively, are:

  • A.0.688 and 0.312
  • B.0.400 and 0.600
  • C.0.312 and 0.688
  • D.0.600 and 0.400

Answer: A

The vapour mole fractions are 0.688 hexane and 0.312 heptane.

Treat 4 and 6 as the relative amounts, so the liquid mole fractions are 0.4 and 0.6. By Raoult's law the partial pressures are

\[ \begin{aligned} p_{\mathrm{hex}} &= 0.4 \times 0.198 = 0.0792\ \mathrm{atm} \\ p_{\mathrm{hep}} &= 0.6 \times 0.06 = 0.036\ \mathrm{atm} \end{aligned} \]

\[ y_{\mathrm{hex}} = \frac{0.0792}{0.1152} = 0.688 \]

So hexane is 0.688 and heptane 0.312 of the vapour. The vapour is richer in the more volatile hexane than the liquid is. 0.400 and 0.600 are the liquid composition, and 0.312 and 0.688 swaps the two components.

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