Biphenyl, C 12 H 10 , C12H10, is a nonvolatile, nonionizing solute that is soluble in benzene, C 6 H 6 . C6H6. At 25 ∘ C, 25 ∘C, the vapor pressure of pure benzene is 100.84 Torr. What is the vapor pressure of a solution made from dissolving 10.3 g 10.3 g of biphenyl in 27.8 g 27.8 g of benzene?

Vapor pressure of solution is 98.01 Torr

Explanation:

Colligative property. In this case, we apply the lowering vapor pressure.

ΔP = P° . Xm

P° - P' = Vapor pressure of pure solvent - Vapor pressure of solution = ΔP

Xm is the molar fraction for solute. We try to determine it:

Moles of solute / Total moles → Total moles = Solute moles + Solvent moles

10.3 g . 1mol / 154 g = 0.0669 moles of biphenyl

27.8 g . 1mol / 78 g = 2.32 moles of benzene

Total moles = 2.32 moles + 0.0669 moles = 2.3869 moles

Xm for solute = 0.0669 / 2.3869 = 0.028

Let's replace data:

100.84 Torr - P' = 100.84 Torr . 0.028

P' = - (100.84 Torr . 0.028 - 100.84Torr) = 98.01 Torr

The vapor pressure of the solution is 84.9 torr

Explanation:

Biphenyl is a nonvolatile, nonionizing solute

Temperature = 25.0 °C

Vapor pressure = 100.84 torr

Mass of biphenyl = 10.3 grams

Mass of benzene = 27.8 grams

Molar mass biphenyl = 154.21 g/mol

Molar mass benzene = 78.11 g/mol

Step 2: Calculate moles

Moles = mass / molar mass

Moles biphenyl = 10.3 grams / 154.21 g/mol

Moles biphenyl = 0.0668 moles

Moles benzene = 27.8 grams / 78.11 g/mol

Moles benzene = 0.356 moles

Step 3: Calculate total moles

Total moles = 0.0668 moles + 0.356 moles

Total moles= 0.4228 moles

Step 4: Calculate mol fraction benzene

Mol fraction benzene = moles benzene / total moles

Mol fraction benzene = 0.356 moles / 0.4228 moles

Mol fraction benzene = 0.842

Step 5: Calculate vapor pressure of the solution

Psol = Xbenzene  * P°benzene

⇒Psol = the vapor pressure of the solution

⇒Xbenzene = mol fraction of benzene

⇒P°benzene = the vapor pressure of pure benzene

Psol = 0.842 * 100.84 torr

Psol = 84.9 torr

The vapor pressure of the solution is 84.9 torr

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