A solution contains 5.25 g of urea, CO(NH2)2 (a nonvolatile solute) and 0.100 kg of water. If the vapor pressure of pure water at 25∘C is 23.7 torr, what is the vapor pressure of the solution?

The vapor pressure of the solution is 23.3 torr

Explanation:

Step 1: Data given

Mass of urea = 5.25 grams

Mass of water = 0.100 kg = 100 grams

Temperature = 25.0 °C

Vapor pressure of water = 23.7 torr

Step 2: Calculate moles of water

Moles H2O = mass H2O / molar mass H2O

Moles H2O = 100 grams / 18.02 g/mol

Moles H2O = 5.55 moles

Step 3: Calculate moles of urea

Moles urea = 5.25 grams / 60.06 g/mol

Moles urea = 0.0874 moles

Step 4: Calculate mol fraction H2O

Mol fraction H2O = 5.55 moles / (5.55 + 0.0874)moles

Mol fraction H2O = 0.984

Step 5: calculate the vapor pressure of the solution

This means that you can use the mole fraction of water and the vapor pressure of pure water at  25° C  to determine the vapor pressure of the solution.

Psol =Xwater * Pwater

⇒Psol = the vapor pressure of the solution

⇒Xwater =the mol fraction of water

⇒Pwater = the vapor pressure of pure water

Psol = 0.984 * 23.7 torr

Psol = 23.3 torr

The vapor pressure of the solution is 23.3 torr