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 ( C H O H ) 3 is 94 torr at 2 0 C . The vapor pressure of ethanol ( C H O H ) 2 5 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 2 0 C ?

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 4 5 C . The vapor pressure of water at 4 5 C is 0.095 atm and the density of water at 4 5 C 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 . 5 7 2 k P a , and the vapor pressure of pure liquid benzene at 300 K is 𝑃 = 9 . 6 5 7 k P a . 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 ) 𝑇 and the mole fraction of toluene in the vapor 𝑋 t o l u e n e .

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

Q4:

Consider a 0.01 M aqueous solution of K C l . 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 higher.
  • CThere is not enough information provided to answer this question.
  • DIt will be lower.

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 . 2 1 4 t o l u e n e k P a and 𝑃 = 6 . 6 7 7 b e n z e n e k P a , respectively. At 300 K, the vapor pressure of pure liquid toluene is 𝑃 = 3 . 5 7 2 k P a and the vapor pressure of pure liquid benzene is 𝑃 = 9 . 6 5 7 k P a . What are the activities ( 𝑎 ) and activity coefficients ( 𝛾 ) of toluene and benzene in this solution?

  • A 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
  • B 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
  • CThere is not enough information provided to answer this question.
  • D 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

Q6:

Consider a dilute liquid solution comprised of solvent A and solute B . For this system, which of the following statements is incorrect?

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

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