Mixtures of benzene and cyclohexane exhibit ideal behavior. A solution was created containing 1.5 moles of liquid benzene and 2.5 moles of liquid cyclohexane, and at 50°C the total vapor pressure of the solution was measured to be 340 torr. Another solution was created containing 1.5 moles of liquid benzene and 3.5 moles of liquid cyclohexane, and at 50°C the measured total vapor pressure was 370 torr.
(A) Calculate the vapor pressures of pure benzene and pure cyclohexane at 50°C.

Using Raoult's law, pressure of a solution is defined by the sum of the product sbetween mole fraction of both solvents and pressure of pure solvents.

[tex]P_{solution} = X_{A}P^0_{A}+X_{B}P^0_{B}[/tex]

In the first solution:

[tex]X_{cyclohexane}=\frac{2.5mol}{2.5mol+1.5mol} =0.625[/tex]

[tex]X_{benzene}=\frac{1.5mol}{2.5mol+1.5mol} =0.375[/tex]

[tex]340torr = 0.625P^0_{A}+0.375P^0_{B}[/tex] (1)

For the second equation:

[tex]X_{cyclohexane}=\frac{3.5mol}{3.5mol+1.5mol} =0.700[/tex]

[tex]X_{benzene}=\frac{1.5mol}{3.5mol+1.5mol} =0.300[/tex]

[tex]370torr = 0.700P^0_{A}+0.300P^0_{B}[/tex](2)

Replacing (2) in (1):

[tex]340torr = 0.625P^0_{A}+0.375(1233.3-2.333P^0_{A})[/tex]

[tex]340torr = 0.625P^0_{A}+462.5-0.875P^0_{A}[/tex]

-122.5torr = -0.250P°A

[tex]P^0_{A} = 490 torr[/tex]

Vapour pressure of cyclohexane at 50°C is 490torr

And for benzene:

[tex]370torr = 0.700*490torr+0.300P^0_{B}[/tex]

[tex]P^0_{B}=90torr[/tex]

Vapour pressure of benzene at 50°C is 90torr