Worksheet: Raoult's Law

In this worksheet, we will practice using Raoult's law to calculate the vapor pressures of species in mixtures or solutions from their mole fractions.

Q1:

The vapor pressure of methanol (CHOH)3 is 94 torr at 20C. The vapor pressure of ethanol (CHOH)25 is 44 torr at the same temperature. A mixture consists of 50.0 g of methanol and 50.0 g of ethanol, both of which behave ideally.

What is the mole fraction of methanol in the solution?

What is the vapor pressure of methanol above the solution at 20C?

What is the mole fraction of methanol in the vapor above the solution?

Q2:

Consider a solution made by dissolving 342 g of sucrose in 127 mL of water at 45C. The vapor pressure of water at 45C is 0.095 atm and the density of water at 45C is 0.992 g/mL. What is the vapor pressure of the sucrose/water solution? The molar mass of sucrose is 180.2 g/mol.

Q3:

The vapor pressure of pure liquid toluene at 300 K is 𝑃=3.572kPa, and the vapor pressure of pure liquid benzene at 300 K is 𝑃=9.657kPa. The mole fraction of toluene in a toluene–benzene mixture is 0.6000 and the temperature is 300 K. Assuming that mixtures of toluene and benzene behave as ideal solutions, calculate the total vapor pressure of the mixture (𝑃) and the mole fraction of toluene in the vapor 𝑋toluene.

  • AThere is not enough information provided to answer this question.
  • B 𝑃 = 6 . 0 0 6 k P a ; 𝑋 = 0 . 3 5 7 t o l u e n e k P a (in vapor)
  • C 𝑃 = 7 . 2 1 9 k P a ; 𝑋 = 0 . 6 4 3 t o l u e n e k P a (in vapor)
  • D 𝑃 = 6 . 0 0 6 k P a ; 𝑋 = 0 . 6 4 3 t o l u e n e k P a (in vapor)

Q4:

Consider a 0.01 M aqueous solution of KCl. How will the vapor pressure of this solution compare with the vapor pressure of pure liquid water?

  • AIt will be the same.
  • BIt will be lower.
  • CThere is not enough information provided to answer this question.
  • DIt will be higher.

Q5:

Consider a toluene–benzene solution in which the mole fraction of toluene is 0.3300. At a temperature of 300 K, the total vapor pressure of this solution is 7.89 kPa, and the partial pressures of the toluene and benzene constituents of the vapor are 𝑃=1.214toluenekPa and 𝑃=6.677benzenekPa respectively. At 300 K, the vapor pressure of pure liquid toluene is 𝑃=3.572kPa and the vapor pressure of pure liquid benzene is 𝑃=9.657kPa. What are the activities (𝑎) and activity coefficients (𝛾) of toluene and benzene in this solution?

  • A 𝑎 ( ) = 0 . 7 7 t o l u e n e ; 𝑎 ( ) = 0 . 2 3 b e n z e n e ; 𝛾 ( ) = 1 . 1 1 t o l u e n e ; 𝛾 ( ) = 0 . 8 9 b e n z e n e
  • B 𝑎 ( ) = 0 . 3 3 9 9 t o l u e n e ; 𝑎 ( ) = 0 . 6 9 1 4 b e n z e n e ; 𝛾 ( ) = 1 . 0 3 t o l u e n e ; 𝛾 ( ) = 1 . 0 3 b e n z e n e
  • C 𝑎 ( ) = 0 . 4 6 t o l u e n e ; 𝑎 ( ) = 0 . 5 4 b e n z e n e ; 𝛾 ( ) = 0 . 7 9 t o l u e n e ; 𝛾 ( ) = 0 . 9 3 b e n z e n e
  • DThere is not enough information provided to answer this question.

Q6:

Consider a dilute liquid solution comprised of solvent A and solute B. For this system, which of the following statements is not correct?

  • AThe chemical potential of A in solution is always less than the chemical potential of pure liquid A (at fixed values of pressure and temperature).
  • BAdditions of more solute to the solution will always lower the chemical potential of the solvent.
  • CAt any given temperature, the vapor pressure of the solution will always be less than the vapor pressure of the pure solvent.
  • DAdditions of a nonvolatile solute to the solution will always lower the vapor pressure of the solution.

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