At 40°C,heptane has a vapor pressure of about 92.2 torr and octane has a vapor pressure of about 31.2 torr.Assuming ideal behavior,what is the vapor pressure of a solution that contains twice as many moles of heptane as octane?
A)61.5 torr
B)51.5 torr
C)71.9 torr
D)82.3 torr
E)none of these

Question

Quizplus · Accepted Answer

According to Raoult's law, the vapor pressure of a solution is equal to the mole fraction of the component multiplied by its vapor pressure in the pure state. Let x be the mole fraction of octane, then the mole fraction of heptane is 2x because there are twice as many moles of heptane. Therefore:

x(31.2 torr) + 2x(92.2 torr) = (31.2 + 184.4)x torr
= 215.6x torr

The total mole fraction of the solution is x + 2x = 3x. Therefore, the vapor pressure of the solution is:

(Vapor pressure of octane) + (Vapor pressure of heptane)
= 31.2x + 184.4x = 215.6x

Dividing both sides by 3x, we get:

Vapor pressure of the solution = 215.6/3 torr = 71.9 torr

Therefore, the answer is C.

At 40°C,heptane Has a Vapor Pressure of About 92