Question

A solution containing 7.5 g of urea (molar mass = 60 g/mol) in 1 kg of water freezes at the same temperature as another solution containing 15 g of solute X in the same amount of water. The molar mass of X (g/mol) is

• A. 60
• B. 180
• C. 120
• D. 240

Hint:

Freezing point depression is colligative property, depends on molality.

Answer 1

The Correct Option is C

Step 1: Freezing point depression depends on molality
Equal freezing point depression means equal molality.
Step 2: Calculate moles of urea
\[ n_{urea} = \frac{7.5}{60} = 0.125\, mol \] Step 3: Calculate moles of solute X
\[ n_X = \frac{15}{M_X} \] Step 4: Equate molalities
\[ 0.125 = \frac{15}{M_X} \implies M_X = \frac{15}{0.125} = 120\, g/mol \] Step 5: Conclusion
Molar mass of X is 120 g/mol.