A solution containing 8.6 g urea in one litre was found to be isotonic with 0.5% (mass/vol) solution of an organic, non volatile solute. The molecular mass of organic non volatile solute is:

Options

A. 348.9 g/mole
B. 34/89 g/mole
C. 3489 g/mole
D. 3.489 g/mole

Answer

To find the molecular mass of the organic non-volatile solute that is isotonic with a solution of urea, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Isotonic Solutions**:
- Two solutions are isotonic if they have the same osmotic pressure. This means that the molarity of the two solutions will be equal: \( C_1 = C_2 \).

2. **Identify Given Data**:
- Weight of urea (\( W_1 \)) = 8.6 g
- Volume of the urea solution = 1 L
- Concentration of the organic solute = 0.5% (mass/volume)

3. **Calculate Molarity of Urea**:
- The molarity (\( C_1 \)) of urea can be calculated using the formula:
\[ C_1 = \frac{\text{number of moles of solute}}{\text{volume of solution in liters}} \]
- First, we need to find the number of moles of urea:
\[ \text{Moles of urea} = \frac{W_1}{\text{Molecular weight of urea}} = \frac{8.6 \text{ g}}{60 \text{ g/mol}} \approx 0.1433 \text{ moles} \]
- Now, calculate the molarity:
\[ C_1 = \frac{0.1433 \text{ moles}}{1 \text{ L}} = 0.1433 \text{ M} \]

4. **Calculate Weight of Organic Solute**:
- A 0.5% (mass/volume) solution means there are 0.5 g of solute in 100 mL of solution.
- Therefore, in 1 L (1000 mL), the weight of the organic solute (\( W_2 \)) will be:
\[ W_2 = 0.5 \text{ g} \times 10 = 5 \text{ g} \]

5. **Set Up the Equation for Molarity of Organic Solute**:
- Let the molecular weight of the organic solute be \( M_2 \).
- The molarity (\( C_2 \)) of the organic solute can be expressed as:
\[ C_2 = \frac{W_2}{M_2 \times \text{Volume in L}} \]
- Since we are considering 1 L, we have:
\[ C_2 = \frac{5 \text{ g}}{M_2 \times 1 \text{ L}} = \frac{5}{M_2} \]

6. **Equate Molarities**:
- Since \( C_1 = C_2 \):
\[ 0.1433 = \frac{5}{M_2} \]

7. **Solve for Molecular Weight of Organic Solute**:
- Rearranging the equation gives:
\[ M_2 = \frac{5}{0.1433} \approx 34.88 \text{ g/mol} \]

### Final Answer:
The molecular mass of the organic non-volatile solute is approximately **34.89 g/mol**.