Question

Calculate cryoscopic constant of solvent if 2 g solute having molar mass \(80 \mathrm{~g} \mathrm{~mol}^{-1}\) dissolved in 75 g solvent decreases its freezing point by 0.4 K .

• A. \(1.2\text{ }\mathrm{K}\text{ }\mathrm{kg}\text{ }\mathrm{mol}^{-1}\)
• B. \(1.6\text{ }\mathrm{K}\text{ }\mathrm{kg}\text{ }\mathrm{mol}^{-1}\)
• C. \(2.1\text{ }\mathrm{K}\text{ }\mathrm{kg}\text{ }\mathrm{mol}^{-1}\)
• D. \(2.5\text{ }\mathrm{K}\text{ }\mathrm{kg}\text{ }\mathrm{mol}^{-1}\)

Hint:

Compute the molality of the solution, then use the depression in freezing point formula.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
\(\Delta T_f = K_f\times m\), where molality is moles of solute per kilogram of solvent.

Step 2: Calculation
Moles of solute \(= \dfrac{2}{80} = 0.025\) mol
Mass of solvent \(= 0.075\) kg
Molality \(m = \dfrac{0.025}{0.075} = 0.333\text{ mol kg}^{-1}\)

Step 3: Result
\(K_f = \dfrac{\Delta T_f}{m} = \dfrac{0.4}{0.333} = 1.2\text{ K kg mol}^{-1}\).

Final Answer:
The cryoscopic constant of the solvent is 1.2 K kg per mol. \[ \boxed{\text{(A) }1.2\text{ K kg mol}^{-1}} \]