Vapour pressure in mm Hg of 0.1 mole of urea in 180 g of water at 25°C is (The Vapour pressure of water at 25°C is 24 mm Hg)

• A. 2.376
• B. 20.76
• C. 23.76
• D. 24.76

To find the vapor pressure of a solution containing urea in water, we can use Raoult's Law. This law states that the vapor pressure of a solvent in a solution is equal to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution.

Step 1: Calculate the moles of water

The molar mass of water (H₂O) is approximately 18 g/mol. For 180 g of water:

• Moles of water = 180 g / 18 g/mol = 10 moles

Step 2: Calculate the total moles in the solution

We have 0.1 mole of urea and 10 moles of water:

• Total moles = 0.1 + 10 = 10.1 moles

Step 3: Determine the mole fraction of water

The mole fraction of water (X_H2O) is calculated as follows:

• X_H2O = Moles of water / Total moles = 10 / 10.1 ≈ 0.9901

Step 4: Calculate the vapor pressure of the solution

Using Raoult's Law:

• Vapor pressure of solution = Vapor pressure of pure water × X_H2O
• Vapor pressure of solution = 24 mm Hg × 0.9901 ≈ 23.76 mm Hg

Final Answer

The vapor pressure of the solution is approximately 23.76 mm Hg. Therefore, the correct option is C. 23.76.