Question

A solution contains 43.0 g of heptane (C7H16) and 46.0 g 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.

The vapor pressure of heptane in the mixture.
The vapor pressure of octane in the mixture.
The total pressure above the solution.
What is the concentration of heptane in mass percent?
What is the concentration of octane in mass percent?

Why is the composition of the vapor different from the composition of the solution?

Answer 1

A solution contains 43.0 g of heptane (C7H16) and 46.0 g 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.

Solution :- Calculating mole fraction of heptanes and octane

Moles of heptane = 43.0 g / 100.21 g per mol =0.4291 mol

Moles of octane = 46.0 g / 114.23 g per mol =0.4027 mol

Mole fraction of heptanes = 0.4291 mol / (0.4291 mol + 0.4027 mol ) = 0.516

Mole fraction of octane = 1 – 0.5116 = 0.484

The vapor pressure of heptane in the mixture.

Solution :- Vapor pressure of heptane = mole fraction * pure vapor pressure

                                                               = 0.516 *45.8 torr

                                                               =23.6 torr

The vapor pressure of octane in the mixture.

Solution :- vapor pressure of octane = 0.484 mol * 10.9 torr = 5.28 torr

The total pressure above the solution.
Total vapor pressure = 23.6 torr + 5.28 torr = 28.9 torr

What is the concentration of heptane in mass percent?

% heptanes = (mass of heptanes / total mass )*100%

                    = 43.0 g / (43 g + 45 g)*100%

                    = 48.8 %

What is the concentration of octane in mass percent?

Solution :-

Mass percent of the octane = 100.0 % -48.8% = 51.2%

So the percent of the octane = 51.2%

Why is the composition of the vapor different from the composition of the solution?

Since the boiling point of the compounds are difference therefore the vapor pressure of the each compounds are different. This means that at the same concentration of the military model.