Question

A solution containing \(0.6\text{ g}\) nonelectrolyte solute in \(30\text{ g}\) water freezes at \(-0.6\ ^{\circ }\text{C}\). Calculate the molar mass of solute if cryoscopic constant of water is \(1.8\text{ K kg mol}^{-1}\).

• A. \(54\text{ g mol}^{-1}\).
• B. \(60\text{ g mol}^{-1}\).
• C. \(66\text{ g mol}^{-1}\).
• D. \(72\text{ g mol}^{-1}\).

Hint:

Find the depression in freezing point and use the cryoscopic formula to solve for molar mass.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The depression in freezing point is \(\Delta T_f = K_f \times m\), where \(m = \dfrac{w_2 \times 1000}{M_2 \times w_1}\).

Step 2: Given Data
\(\Delta T_f = 0 - (-0.6) = 0.6\text{ K}\), \(w_2 = 0.6\text{ g}\), \(w_1 = 30\text{ g}\), \(K_f = 1.8\text{ K kg mol}^{-1}\)

Step 3: Rearrange
\(M_2 = \dfrac{K_f \times w_2 \times 1000}{\Delta T_f \times w_1}\)

Step 4: Calculate
\(M_2 = \dfrac{1.8 \times 0.6 \times 1000}{0.6 \times 30} = 60\text{ g mol}^{-1}\)

Final Answer:
The molar mass of the solute is \(60\text{ g mol}^{-1}\). \[ \boxed{\text{(B) }60\text{ g mol}^{-1}} \]