Fraction pressure

Question

liquid A has a vapor pressure of 350 mmHg and liquid B has a vapor pressure of 100 mmHg.

The molar fraction of A in steam is twice that of the molar fraction in solution

what is the molar fraction of A in solution

Answer 1

Dalton's Law of Partial Pressures and Raoult's Law:

Vapor pressure of pure liquid A = 350 mm Hg

Vapor pressure of pure liquid B = 100 mm Hg

Total vapor pressure of solution = 450 mm Hg

X_A = mol fraction A in the solution = 350 / 450 = 0.778

X_B = mol fraction B in the solution 1 - 0.778 = 0.222

Vapor pressure of A in "steam" or in the vapor phase = 0.778 x 350 mm Hg = 272 mm Hg

Vapor pressure of B in "steam" or in the vapor phase = 0.222 x 100 mm Hg = 22.2 mm Hg

Total pressure in vapor phase = 294.2 mm Hg

X_A in the vapor phase = 272 mm Hg / 294 mm Hg = 0.925

If this is 2x the mol fraction of A in the liquid, the mol fraction of A in the liquid would be 0.925/2 = 0.463