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A solution is prepared by mixing 2.88 mol of acetone with 1.45 mol of cyclohexane at 30°C.

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

Given:
- [tex]P^\circ_{acetone} = 229.5 \, \text{torr}[/tex]
- [tex]P^\circ_{cyclohexane} = 97.6 \, \text{torr}[/tex]

Answer :

First calculate the mole fraction of each substance:
acetone: 2,88 mol ÷ (2,88 mol + 1,45 mol) = 0,665.
cyclohexane: 1,45 ÷ (2,88 mol + 1,45 mol) = 0,335.
Raoult's Law:
P(total) = P(acetone) · χ(acetone) + P(cyclohexane) · χ(cyclohexane).
P(total) = 229,5 torr · 0,665 + 97,6 torr · 0,335.
P(total) = 185,3 torr.
χ for acetone: 229,5 torr · 0,665 ÷ 185,3 torr = 0,823.
χ for cyclohexane: 97,6 torr · 0,335 ÷ 185,3 torr = 0,177.

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