Answer:
The mole fraction of hexane is 0.67
Step-by-step explanation:
This problem can be solved using Dalton´s law and Raoult´s law.
The vapor pressure of a mixture of gases is the sum of the partial pressures of each gas (Dalton´s law).
Example:
In a mixture of gases A and B
Pt = PA + PB
where:
Pt = total pressure
PA = partial pressure of A
PB = partial pressure of B
In an ideal solution, the vapor pressure of each component is equal to the vapor pressure of the pure component times the mole fraction of the component in the solution (Raoult´s law).
Example:
In a solution containing A and B, the vapor pressure of A in the solution will be:
PA = P(pure A) * Xa
Where
PA = vapor pressure of A in the solution
P(pure A) = vapor pressure of pure A
Xa = mole fraction of A
In our problem, we have that the vapor pressure of the solution is 241 torr.
Then, using Dalton´s law:
Pt = P(hexane) + P(Pentane)
Using Raoult´s law:
P(hexane) = P(pure hexane) * X(hexane)
P(pentane) = P(pure pentane) * X(pentane)
We also know that the sum of the molar fractions of each component in a solution equals 1:
X(hexane) + X(pentane) = 1
X(pentane) = 1 - X(hexane)
Replacing in the Dalton´s law in terms of X(hexane):
Pt = P(pure hexane) * X(hexane) + P(pure pentane) * (1 - X(hexane))
Solving for X(hexane):
Pt = P(pure hex) * X(hex) + P(pure pent) - P(pure pent) * X(hex)
Replacing with the data:
241 torr = 151 torr * X(hex) + 425 torr - 425 torr*X(hex)
-184 torr = -274 torr * X(hex)
-184torr/-274 torr = X(hex)
X(hex) = 0.67