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The vapor pressure of carbon disulfide is 355.6 torr at 25°C. What is the vapor pressure of a solution prepared by dissolving 10.60 g naphthalene (C10H8, Molar Mass = 128.2 g/mol) in 155 mL CS2 liquid (Molar Mass = 76.14 g/mol, density = 1.261 g/mL)? Assume the solution obeys Raoult's law, and treat naphthalene as a nonvolatile solute.

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Answer:

344.5764 torr

Explanation:

Molar mass of naphthalene = 128.2g/mol

Mass of naphthalene = 10.60 g

Carbon disulfide:

Molar mass= 76.14g/mol ;

volume = 155mL ;

density = 1.261 g/mL

Vapour pressure = 355.6 torr

Number of moles = mass / molar mass

CS2:

Mass = density × volume

Number of moles = (density × volume) / molar mass

Number of moles = (1.261 * 155) / 76.14 = (195.455 / 76.14) = 2.567 moles of CS2

Number of moles of C8H10:

Number of moles = 10.60 / 128.2 = 0.083 C8H10

Total number of moles :

2.567 + 0.083 = 2.65 moles

Mole fraction of each compound in solution :

CS2 :

2.567 / 2.65 = 0.969

C8H10:

0.083 / 2.65 = 0.031

According to Raoult's:

Psolution = Xsolvent × Posolvent

CS2 = solvent

Xsolvent = Mole fraction of solvent

Posolvent = Vapour pressure of pure solvent

Psolution = 0.969 × 355.6 torr = 344.5764 torr

The vapor pressure of the solution would be as follows:

[tex]344.5764[/tex] torr

Given that,

Vapor pressure of Carbon Disulfide [tex]= 355.6[/tex] torr

[tex]volume = 155mL ;[/tex]

[tex]density = 1.261 g/mL[/tex]

Naphthalene's mass [tex]= 10.60 g[/tex]

Naphthalene's molar mass [tex]= 128.2g/mol[/tex]

Now,

We know that

Number of moles [tex]= mass/molar mass[/tex]

Mass [tex]= density[/tex] × [tex]volume[/tex]

[tex]Number of moles =[/tex] [tex](density[/tex] × [tex]volume) / molar mass[/tex]

So,

Number of moles of Carbon Disulfide [tex]= (1.261[/tex] × [tex]155) / 76.14[/tex]

[tex]= (195.455 / 76.14)[/tex]

[tex]= 2.567[/tex] moles of Carbon Disulfide

Number of moles of Naphthalene:

Number of moles [tex]= 10.60 / 128.2[/tex]

[tex]= 0.083[/tex]

Now,

Total number of moles :

[tex]2.567 + 0.083[/tex]

[tex]= 2.65[/tex] moles

Mole fraction of each compound in solution :

Carbon Disulfide:

2.567 / 2.65

[tex]= 0.969[/tex]

Naphthalene

0.083 / 2.65

[tex]= 0.031[/tex]

According to Raoult's:

P[tex]solution = Xsolvent[/tex] × [tex]Posolvent[/tex]

Carbon Sulfide = Solvent

[tex]Xsolvent =[/tex] Mole fraction of solvent

[tex]Posolvent =[/tex] Vapour  pressure of the pure solvent

[tex]Psolution[/tex] [tex]= 0.969[/tex] × [tex]355.6 torr[/tex]

[tex]= 344.5764[/tex] torr

Thus, "[tex]344.5764[/tex] torr" is the correct answer.

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