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A solution is prepared by mixing 3.44 mol of acetone with 1.45 mol of cyclohexane at 30°C.

Calculate the [tex]\chi_{\text{acetone}}[/tex] and [tex]\chi_{\text{cyclohexane}}[/tex] in the vapor above the solution.

Given:
[tex]P^{\circ}_{\text{acetone}} = 229.5 \text{ torr}[/tex]
[tex]P^{\circ}_{\text{cyclohexane}} = 97.6 \text{ torr}[/tex]

Answer :

First calculate the mole fraction of each substance:
acetone: 3.44 mol ÷ (3.44 mol + 1.45 mol) = 0.703
cyclohexane: 1.45 ÷ (3.44 mol + 1.45 mol) = 0.297
Raoult's Law: P(total) = P(acetone) · χ(acetone) + P(cyclohexane) · χ(cyclohexane)
P(total) = 229.5 torr · 0.703 + 97.6 torr · 0.297
P(total) = 190.3 torr
χ for acetone: 229.5 torr · 0.703 ÷ 190.3 torr = .848
χ for cyclohexane: 97.6 torr · 0.297 ÷ 190.3 torr = .152

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