Question

For a solution containing a non-volatile solute in a volatile solvent, which of the following relationships is correctly represented?

• A. \(P_{1}\lt P_{1}^{0}\)
• B. \(T_{b}\lt T_{b}^{0}\)
• C. \(T_{f}>T_{f}^{0}\)
• D. \(T_{f}=T_{f}^{0}\)

Hint:

A non-volatile solute lowers the vapour pressure of the solvent, raises the boiling point and lowers the freezing point.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
By Raoult's law, \(P_1 = x_1 P_1^{0}\). Since the solvent's mole fraction is less than 1, the solvent's vapour pressure is lowered.

Step 2: Effect on the properties
The vapour pressure is lower, so the solution must be heated more to boil: \(T_b \gt T_b^{0}\).
The solution freezes at a lower temperature: \(T_f \lt T_f^{0}\).

Step 3: Compare the options
Only \(P_1 \lt P_1^{0}\), option (A), is correct. The others reverse the effect on boiling or freezing point.

Final Answer:
The correct relation is that the solvent vapour pressure is lower than that of the pure solvent. \[ \boxed{\text{(A) }P_{1}<P_{1}^{0}} \]