at 298K,the vapour of pure water is 23.76mmHg and that of dilute aqueous ultimate urea is 22.9mmHg. Estimate the molarity of the solution

Give ans.

To estimate the molarity of the solution using the vapor pressure, we can apply Raoult's law. According to Raoult's law, the vapor pressure of a solvent above a solution is equal to the mole fraction of the solvent, multiplied by the vapor pressure of the pure solvent.

In this case, the solvent is water, and the solute is urea. Let's denote the vapor pressure of pure water as Pₒ and the vapor pressure of the solution as P. The mole fraction of water in the solution can be calculated using the following equation:

Xₒ = Pₒ / P

Where:
Xₒ = mole fraction of water (solvent)
Pₒ = vapor pressure of pure water
P = vapor pressure of the solution

Using the given values, Pₒ = 23.76 mmHg and P = 22.9 mmHg. Plugging these values into the equation, we can calculate Xₒ.

Xₒ = 23.76 mmHg / 22.9 mmHg
Xₒ ≈ 1.036

Since the mole fraction of water cannot be greater than 1, we can conclude that the given solution is not an ideal solution. However, to estimate the molarity of the solution, we can assume an ideal solution.

In an ideal solution, the mole fraction of solute (urea) can be calculated as:

Xᵩ = 1 - Xₒ

Where:
Xᵩ = mole fraction of solute (urea)

Xᵩ = 1 - 1.036
Xᵩ ≈ -0.036

Since the calculated value -0.036 implies an unphysical negative mole fraction, it can be concluded that the given information is not sufficient to estimate the molarity of the solution accurately.