%3Cp%3Ea%20solution%26nbsp%3Bcontaine%26nbsp%3B2.69%26nbsp%3Bgrams%26nbsp%3Bof%2

Question

%3Cp%3Ea%20solution%26nbsp%3Bcontaine%26nbsp%3B2.69%26nbsp%3Bgrams%26nbsp%3Bof%26nbsp%3Bsurose%26nbsp%3B(C12%26nbsp%3BH22%26nbsp%3BO11)in%26nbsp%3B56.9%26nbsp%3Bgrams%26nbsp%3Bof%26nbsp%3Bmethyl%26nbsp%3Balcohol.%26nbsp%3B(CH3%26nbsp%3BOH).%26nbsp%3Bthe%26nbsp%3Bvapor%26nbsp%3Bpressure%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Balcohol%26nbsp%3Bin%26nbsp%3Bthis%26nbsp%3Bmixture%26nbsp%3Bat%26nbsp%3B50.0%26nbsp%3Bc%26nbsp%3Bis%26nbsp%3B73.9%26nbsp%3Btorr%26nbsp%3B.%26nbsp%3Bcalculate%26nbsp%3Bthe%26nbsp%3Bvapor%26nbsp%3Bpressure%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3BPURE%26nbsp%3B%26nbsp%3Balcohol%26nbsp%3Bat%26nbsp%3Bthis%26nbsp%3Btemperature%26nbsp%3B%3C%2Fp%3E

Explanation / Answer

In a solution, the vapor pressure of each component is equal to the vapor pressure of the component multiplied by its mole fraction in the solution.

So, for a), you first have to calculate the mole fraction of methanol and ethanol in the solution:

30 g methanol / 32.0 g/mol = 0.9375 mol methanol
45 g ethanol / 46.1 g/mol = 0.976 mol ethanol

mole fraction methanol = 0.9375 / (0.9375 + 0.976) = 0.490
mole fraction ethanol = 1 - 0.490 = 0.510

Vapor pressure methanol = 94 mm Hg X 0.490 = 46.1 mm Hg
Vapor pressure ethanol = 44 mm Hg X 0.510 = 22.4 mm Hg

Vapor pressure of solution = 46.1 + 22.4 = 68.5 mm Hg

b) The partial pressure of each component should be directly related to the mole fraction in the vapor. So for methanol, in the vapor,

mole fraction methanol in vapor = 46.1 / 68.5 = 0.673
mole fraction ethanol in vapor = 22.4 / 68.5 = 0.327

c) Fractional distillation should allow you to separate methanol from ethanol.

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