Question

A solution contains a mixture of pentane and hexane at room temperature. The solution has a vapor pressure of 263 torr. Pure pentane and hexane have vapor pressures of 425 torr and 151 torr, respectively, at room temperature.

Required:
What is the mole fraction of hexane?

Answer 1

Xb = 0.59

Step-by-step explanation:

Let's analyze the given data.

We have a total vapor pressure of 263 Torr for the mix of the two gases. And the individual vapour pressures for each gas is given, and it's 425 Torr for pentane and 151 Torr for hexane.

We are asked to determine the mole fraction of hexane. For practical purposes, we will label pentane as "a" while hexane would be "b". So, let's write the equations that we need to calculate this.

We know that the total pressure of a solution would be:

P = Pa + Pb (1)

And we also know that these individual pressures are:

Pa = Xa * Pa° (2)

Pb = Xb * Pb° (3)

Where Pa° and Pb° are the vapour pressures of each gases.

The mole fractions (Xa and Xb), can be expressed, one in function of the other:

Xa + Xb = 1 -----> Xa = 1 - Xb (4)

Now that we know this, we can replace (4) in (2), and then, (2) and (3) can be replaced in (1):

Pa = (1 - Xb)Pa°

P = (1 - Xb)Pa° + XbPb° (5)

Replacing the given data, we have:

263 = (1 - Xb)*425 + 151Xb

Now solving for Xb, which is the mole fraction of hexane:

263 = 425 - 425Xb + 151Xb

263 - 425 = (-425 + 151)Xb

-162 = -274Xb

Xb = -162 / -274

Xb = 0.59

Hope this helps