It is the second time for me posting this question. (PLEASE IF YOU DON\'T KNOW H

Question

It is the second time for me posting this question. (PLEASE IF YOU DON'T KNOW HOW TO SOLVE IT, DON'T TRY TO)

A solution contains 44.0 g of heptane (C7H16) and 60.0 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. (Note that the mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure.)

A) The vapor pressure of heptane in the mixture.

B)The vapor pressure of octane in the mixture

C)The total pressure above the solution.

D)What is the mass percent concentration of heptane in vapour phase?

E)What is the mass percent concentration of octane in vapour phase?

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

Thank you

Explanation / Answer

Gms of heptane (C7H16) = 44.0

molar mass of heptane (C7H16) = 100.2 g/mol

moles of heptane (C7H16) = mass/ molar mass = 44.0g/100.20 g/mol = 0.439 moles

partial pressure of heptane (C7H16) = 45.8 torr

Gms of octane (C8H18) = 60.0 g

molar mass of octane (C8H18) = 114.22 g/mol

moles of octane (C8H18) = mass/ molar mass = 60.0g/114.22 g/mol = 0.525 moles

partial pressure of octane (C8H18) = 10.9 torr

A) The vapor pressure of heptane in the mixture.

= {(moles of heptane)/(moles of heptane + moles of octane)}* vapor pressure of heptane

= {0.439 moles /(0.439 moles + 0.525 moles )} * 45.8 = 20.9 torr

B) The vapor pressure of octane in the mixture.

= {(moles of octane)/(moles of heptane + moles of octane)}* vapor pressure of octane

= {0.525 moles /(0.439 moles + 0.525 moles )} * 10.9 = 5.94 torr

C)The total pressure above the solution.

Vapor pressure of solution = Vapor pressure of heptane + vapor of octane = 20.9 + 5.94 = 26.8 torr

D)What is the mass percent concentration of heptane in vapour phase?

The number of moles of each gas in the vapor phase is proportional to their partial pressures, so:
(20.9 torr C7H16) x (100.2 g C7H16/mol) = 2094.2 torr·g/mol
Mass % of heptane = (2094.2 torr·g/mol) / (678.3 torr·g/mol + 2094.2 torr·g/mol) = 0.755 = 75.5% C7H16 by mass

E) What is the mass percent concentration of octane in vapour phase?

Mass % of octane = 100% - 75.5% = 24.5% C8H18 by mass

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

This is beacause, in solution we have 2 different substances that boil at different temperatures. And the solution is enriched with the substace that is more volatile, leadind to the differnece in pressure exerted and hence the vapor pressure.

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