A solution contains a mixture of pentane and hexane at room temperature. The solution has a vapor pressure of 252 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? (Assume ideal behavior.)

phex = Xhex*Pohex

ppen = Xpen*Popen

eqn1 Then Xpen = 1-Xhex
eqn2 phex + ppen = 252

Substitute and solve these two equations for Xhex and Xpen.
I worked through them and got about 0.4 for pentane and about 0.6 for hexane. Post your work if you get stuck.

To find the mole fraction of hexane in the solution, we can use Raoult's Law. According to Raoult's Law, the vapor pressure of a component in a solution is directly proportional to its mole fraction in the solution.

The formula for Raoult's Law is:
Ptotal = Xpentane * Ppentane + Xhexane * Phexane

Where:
Ptotal is the total vapor pressure of the solution
Xpentane is the mole fraction of pentane in the solution
Ppentane is the vapor pressure of pure pentane
Xhexane is the mole fraction of hexane in the solution
Phexane is the vapor pressure of pure hexane

We are given the following information:
Ptotal = 252 torr
Ppentane = 425 torr
Phexane = 151 torr

Let's plug these values into the Raoult's Law equation:

252 torr = Xpentane * 425 torr + Xhexane * 151 torr

Since the solution contains only pentane and hexane, the sum of the mole fractions of the two components should be equal to 1. Therefore, we can rearrange the equation to solve for Xhexane:

252 torr - Xpentane * 425 torr = Xhexane * 151 torr

Now, let's calculate the mole fraction of hexane:

Xhexane = (252 torr - Xpentane * 425 torr) / 151 torr

To find Xpentane, we need additional information. If we know the mole fraction of one component, we can calculate the mole fraction of the other component as 1 minus the mole fraction of the first component.