Calculating the composition of vapor in mass percent

[rzinn]

Homework Statement

Here's the question form the text. (I have the answer, but don't know how to do part c.
"A solution contains 50.0g of heptane (C7H16) and 50.0g of octane (C8H18) at 25 C. the vapor pressures of pure heptane and pure octane at 25 C are 45.8 torr and 10.9 torr, respectively. assuming ideal behavior, calculate each of the following:
a) vapor pressure of each of the solution components in the mixture
b) the total pressure above the solution
c)the composition of the vapor in mass percent.

the answer to a is: Pressure of C7H16: 24.4 torr
Pressure of C8H18: 5.09 torr

b) total pressure is: 29.49 torr.

I have no idea how to go about part c. Any help is appreciated.

Homework Equations

The Attempt at a Solution

 

[littlefranco]

Remember that the partial pressure of a gas is directly proportional to the concentration of the gas. You know the fraction of the total pressure that the partial pressure of each substance comprises, which is equal to the mole fraction of each gas. You can then convert this into the mass percent of each gas.

 

[Blueshift5]

To calculate the composition of the vapor in mass percent, we need to first calculate the moles of each component in the solution. This can be done using the given masses and the molar masses of heptane and octane.

Molar mass of heptane (C7H16) = 100.2 g/mol
Molar mass of octane (C8H18) = 114.2 g/mol

Using the given masses, we can calculate the moles of each component:

Moles of heptane = 50.0 g / 100.2 g/mol = 0.499 mol
Moles of octane = 50.0 g / 114.2 g/mol = 0.438 mol

Next, we can calculate the total moles of the solution by adding the moles of each component:

Total moles of solution = 0.499 mol + 0.438 mol = 0.937 mol

To calculate the mass percent of each component in the vapor, we need to first calculate the partial pressures of each component. This can be done using Dalton's law of partial pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each component.

Partial pressure of heptane = 0.499 mol / 0.937 mol x 29.49 torr = 15.63 torr
Partial pressure of octane = 0.438 mol / 0.937 mol x 29.49 torr = 13.86 torr

Now, we can calculate the mass percent of each component in the vapor using the following formula:

Mass percent = (partial pressure of component / total pressure) x 100%

Mass percent of heptane = (15.63 torr / 29.49 torr) x 100% = 53.06%
Mass percent of octane = (13.86 torr / 29.49 torr) x 100% = 46.94%

Therefore, the composition of the vapor in mass percent is 53.06% heptane and 46.94% octane.