Question

The solution containing 6 g urea (molar mass 60) per $\text{dm}^3$ of water and another solution containing 9 g of solute A per $\text{dm}^3$ water freezes at same temperature. What is molar mass of A?

• A. 90
• B. 180
• C. 54
• D. 120

Hint:

When two solutions with the same solvent share a colligative property value, you can equate their mole fractions directly using a simple ratio: $\frac{W_1}{M_1} = \frac{W_2}{M_2}$. Plunking numbers in gives $\frac{6}{60} = \frac{9}{M_2}$, which immediately yields $M_2 = 90$ with minimal calculation!

Answer 1

The Correct Option is A

Step 1: Read the condition.
Both solutions freeze at the same temperature, so they have equal freezing-point depression $\Delta T_f$.
Step 2: Recall the law.
$\Delta T_f = K_f \, m$, and since both use the same solvent in the same $1\ \text{dm}^3$ volume, equal $\Delta T_f$ means equal moles of solute.
Step 3: Find moles of urea.
Urea mass is 6 g and molar mass 60, so moles $= \frac{6}{60} = 0.1$ mol.
Step 4: Set moles of A equal.
Therefore solute A also provides $0.1$ mol in its litre of water.
Step 5: Write the mole equation for A.
$\text{moles} = \frac{\text{mass}}{\text{molar mass}}$, so $0.1 = \frac{9}{M_A}$.
Step 6: Solve for the molar mass.
$M_A = \frac{9}{0.1} = 90$ g mol$^{-1}$.
Step 7: State the answer.
The molar mass of A is 90, which is option (1).
\[ \boxed{M_A = \dfrac{9}{0.1} = 90} \]