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