The Problem:
We are given a solution of Urea with a concentration of 10 g/dm³. We are also told that this Urea solution is isotonic with a 5% solution of a nonvolatile solute. We need to determine the molecular mass of this nonvolatile solute.

Understanding the Problem:
To solve this problem, we need to understand a few key concepts:

1. Isotonic Solution: An isotonic solution is a solution that has the same osmotic pressure as another solution. In other words, it has the same concentration of solutes as the other solution.

2. Nonvolatile Solute: A nonvolatile solute is a solute that does not easily evaporate at normal temperatures.

3. Molecular Mass: Molecular mass, also known as molar mass, is the mass of one mole of a substance. It is expressed in grams per mole (g/mol).

Solution:
To find the molecular mass of the nonvolatile solute, we can use the concept of isotonicity and compare the concentrations of the two solutions.

1. Urea Solution Concentration:
- Urea concentration = 10 g/dm³
- Urea molecular mass = 60 g/mol

2. Nonvolatile Solute Solution Concentration:
- Nonvolatile solute concentration = 5%
- Assume the molecular mass of the nonvolatile solute = x g/mol

3. Comparing Concentrations:
Since the Urea solution is isotonic with the nonvolatile solute solution, the concentrations of both solutions must be equal.

- Urea concentration = Nonvolatile solute concentration
- 10 g/dm³ = 5%

4. Converting Nonvolatile Solute Concentration:
To compare the concentrations, we need to convert the nonvolatile solute concentration from a percentage to g/dm³.

- Nonvolatile solute concentration = (5/100) x 1000 g/dm³
(We multiply by 1000 to convert from percentage to g/dm³)
- Nonvolatile solute concentration = 50 g/dm³

5. Setting up the Equation:
Now that we have the concentrations of both solutions, we can set up an equation to solve for the molecular mass of the nonvolatile solute.

- Urea concentration = Nonvolatile solute concentration
- Urea concentration = (Mass of Urea / Molar mass of Urea) = 10 g/dm³
- Nonvolatile solute concentration = (Mass of nonvolatile solute / Molar mass of nonvolatile solute) = 50 g/dm³

- 10 g/dm³ = (Mass of Urea / 60 g/mol)
- 50 g/dm³ = (Mass of nonvolatile solute / x g/mol)

6. Solving for Molecular Mass:
By rearranging the equation, we can solve for the molecular mass of the nonvolatile solute.

- x = (50 g/dm³ * 60 g/mol) / 10 g/dm³
- x = 300 g/mol

Answer:
The molecular mass of the nonvolatile solute is 300 g/mol.

300