10% solution of urea is isotonic with 6% solution of a non-volatile solute X.What is the molecular mass of solute X ?

Options

A. `"6 g mol"^(-1)`
B. `"60 g mol"^(-1)`
C. `"36 g mol"^(-1)`
D. `"32 g mol"^(-1)`

Explanation

To solve the problem, we need to find the molecular mass of the non-volatile solute X, given that a 10% solution of urea is isotonic with a 6% solution of solute X. Here's the step-by-step solution:

### Step 1: Understand Isotonic Solutions
Isotonic solutions have the same osmotic pressure. Therefore, the osmotic pressure of the urea solution must equal the osmotic pressure of the solute X solution.

### Step 2: Write the Formula for Osmotic Pressure
The osmotic pressure (π) is given by the formula:
\[ \pi = C \cdot R \cdot T \]
where:
- \(C\) is the concentration (in moles per liter),
- \(R\) is the gas constant,
- \(T\) is the temperature in Kelvin.

### Step 3: Set Up the Equation for Both Solutions
Since both solutions are isotonic:
\[ \pi_{\text{urea}} = \pi_{\text{X}} \]
This implies:
\[ C_{\text{urea}} = C_{\text{X}} \]

### Step 4: Calculate the Concentration of Urea
For a 10% solution of urea:
- If we consider 100 grams of the solution, it contains 10 grams of urea.
- The molar mass of urea (NH₂CONH₂) is 60 g/mol.

Calculating the number of moles of urea:
\[ \text{Number of moles of urea} = \frac{\text{mass of urea}}{\text{molar mass of urea}} = \frac{10 \, \text{g}}{60 \, \text{g/mol}} = \frac{1}{6} \, \text{mol} \]

### Step 5: Calculate the Concentration of Solute X
For a 6% solution of solute X:
- In 100 grams of the solution, it contains 6 grams of solute X.

Let the molar mass of solute X be \(M_X\). The number of moles of solute X is:
\[ \text{Number of moles of X} = \frac{6 \, \text{g}}{M_X} \]

### Step 6: Set the Number of Moles Equal
Since the number of moles of urea equals the number of moles of solute X:
\[ \frac{1}{6} = \frac{6}{M_X} \]

### Step 7: Solve for Molar Mass of Solute X
Cross-multiplying gives:
\[ M_X = 6 \cdot 6 = 36 \, \text{g/mol} \]

### Conclusion
The molecular mass of the non-volatile solute X is **36 g/mol**.

---