Question

If a solution containing \(10\) g per \(\text{dm}^{3}\) of urea (molecular mass \(=60\text{g mol}^{-1}\)) is isotonic with \(5\%\) solution of a nonvolatile solute, find the molar mass of a nonvolatile solute.

• A. \(200\text{g mol}^{-1}\)
• B. \(250\text{g mol}^{-1}\)
• C. \(300\text{g mol}^{-1}\)
• D. \(350\text{g mol}^{-1}\)

Hint:

Isotonic solutions have equal molar concentration, so equate the molarity of urea with that of the 5 percent solution.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Isotonic solutions have the same osmotic pressure and so the same molar concentration at the same temperature.

Step 2: Urea solution
10 g per \(\text{dm}^3\) of urea, \(M=60\): molarity \(=\dfrac{10}{60}=0.1667\) mol/L.

Step 3: Other solution
A 5% solution has 5 g in 100 mL, which is 50 g per litre. Its molarity is \(\dfrac{50}{M}\).

Step 4: Calculation
Equate: \(\dfrac{50}{M}=\dfrac{10}{60}\), so \(M=300\text{ g mol}^{-1}\).

Step 5: Compare the options
This is option (C).

Final Answer:
The molar mass of the nonvolatile solute is 300 g per mol. \[ \boxed{\text{(C) }300\text{ g mol}^{-1}} \]