7. A solution contains a mixture of pentane and hexane at room temperature. The solution has a vapor pressure of 250 torr. Pure pentane and hexane have vapor pressures of 425 torr and 151 torr, respectively, at room temperature. What is the mole fraction of hexane?

mole fraction hexane 0.64

Explanation:

We know from Raoult's law of partial pressures that for a binary mixture, the vapor pressure above solution is the sum of the partial pressures of each gas:

P total = P (A) + P (B)

Also the partial pressure of a component is the product of its mole fraction, X, times its pure vapor pressure:

Ptotal = X (A) Pº (A) + X (B) Pº (B)

Since for solution of two components the mole fractions add to one, we now have all the information required to compute the answer.

250 torr = X (hexane) 151 torr + (1 - X (hexane)) 425 torr

250 = 151X (hexane) + 425 - 425 X (hexane)

274 X (hexane) = 175

X (hexane) = 1 - 0.6 = 0.64