A solution containing `10 g per dm^(3)` of urea (mol.wt. `= 60 g mol^(-1)`) is isotonic with a `5%` ( mass//vol.) of a non-volatile solute. The molecular mass of non-volatile solute is:

Options

A. `250 g mol^(-1)`
B. `300 g mol^(-1)`
C. `350g mol^(-1)`
D. `200 g mol^(-1)`

Explanation

To solve the problem, we need to find the molecular mass of a non-volatile solute that is isotonic with a solution containing 10 g of urea per dm³. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the molarity of the urea solution
Given:
- Mass of urea = 10 g
- Molecular weight of urea = 60 g/mol

Molarity (M) is calculated using the formula:
\[ \text{Molarity} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)} \times \text{volume (L)}} \]
Since we have 10 g of urea in 1 dm³ (1 L):
\[ \text{Molarity of urea} = \frac{10 \, \text{g}}{60 \, \text{g/mol} \times 1 \, \text{L}} = \frac{10}{60} = \frac{1}{6} \, \text{mol/L} \]

### Step 2: Understand the isotonic condition
The problem states that the urea solution is isotonic with a 5% (mass/volume) solution of a non-volatile solute. This means that both solutions have the same molarity.

### Step 3: Calculate the mass of the non-volatile solute in the 5% solution
A 5% (mass/volume) solution means there are 5 g of solute in 100 mL of solution. To find the concentration in g/dm³:
\[ \text{Mass of non-volatile solute in 1 dm}^3 = 5 \, \text{g} \times 10 = 50 \, \text{g} \]

### Step 4: Set up the equation for molarity of the non-volatile solute
Let the molecular mass of the non-volatile solute be \( M \) g/mol. The molarity of the non-volatile solute can be calculated as:
\[ \text{Molarity of non-volatile solute} = \frac{50 \, \text{g}}{M \, \text{g/mol} \times 1 \, \text{L}} = \frac{50}{M} \, \text{mol/L} \]

### Step 5: Set the molarities equal to each other
Since the solutions are isotonic:
\[ \frac{1}{6} = \frac{50}{M} \]

### Step 6: Solve for \( M \)
Cross-multiplying gives:
\[ 1 \cdot M = 6 \cdot 50 \]
\[ M = 300 \, \text{g/mol} \]

### Conclusion
The molecular mass of the non-volatile solute is **300 g/mol**.