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 find the molecular mass of solute X, we can follow these steps:

### Step 1: Understand the concept of isotonic solutions
Isotonic solutions have the same osmotic pressure. This means that the number of solute particles in both solutions is equal when compared at the same temperature and volume.

### Step 2: Define the given solutions
- We have a 10% solution of urea.
- We have a 6% solution of a non-volatile solute X.

### Step 3: Calculate the mass of solute in each solution
- For the 10% urea solution:
- This means there are 10 grams of urea in 100 grams of solution.

- For the 6% solution of solute X:
- This means there are 6 grams of solute X in 100 grams of solution.

### Step 4: Determine the molecular mass of urea
- The molecular mass of urea (NH₂CONH₂) is 60 g/mol.

### Step 5: Set up the equation for osmotic pressure
The osmotic pressure (π) is given by the formula:
\[ \pi = \frac{n}{V}RT \]
Where:
- \( n \) = number of moles of solute
- \( V \) = volume of the solution
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

Since both solutions are isotonic, we can equate their osmotic pressures:
\[ \pi_{\text{urea}} = \pi_{X} \]

### Step 6: Express the number of moles for both solutions
The number of moles \( n \) can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]

For urea:
\[ n_{\text{urea}} = \frac{10 \text{ g}}{60 \text{ g/mol}} = \frac{1}{6} \text{ mol} \]

For solute X:
\[ n_{X} = \frac{6 \text{ g}}{M_{X}} \text{ mol} \]
Where \( M_{X} \) is the molecular mass of solute X.

### Step 7: Set the number of moles equal
Since the osmotic pressures are equal:
\[ \frac{1}{6} = \frac{6}{M_{X}} \]

### Step 8: Solve for \( M_{X} \)
Cross-multiplying gives us:
\[ M_{X} = 6 \times 6 = 36 \text{ g/mol} \]

### Conclusion
The molecular mass of solute X is 36 g/mol.

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