Question

A solution has a 1:4 mole ratio of pentane to hexane. The vapour pressure of the pure hydrocarbons at 20°C are 440 mm of Hg for pentane and 120 mm of Hg for hexane. The mole fraction of pentane in the vapour phase would be

• A. 0.178
• B. 0.278
• C. 0.378
• D. 0.478

Answer 1

Answer: (D)

0.478

Answer 2

Pentane solution mole fraction =$\frac{1}{1}$ + 4 = $\frac{1}{5}$
Hexane solution mole fraction = $\frac{4}{1}$ + 4 = $\frac{4}{5}$
Total pressure of the solution, Ps = Xp POp + XH PHO = $\frac{1}{5}$ $\times$ 440 mm Hg + $\frac{4}{5}$ $\times$120 mm Hg = 184 mm Hg The amount of pentane in the vapour phase is expressed as $\frac{x_pp^0_p}{p_s}$ = $\frac{88}{184}$ =0.478.

Therefore, the correct option is (D): 0.478