Which of the following statements is false ?

Options

A. Two different sollutions of sucrose of same molality prepared in different solvents will have the same depression in freezing point.
B. The osmotic pressure of a solution is given by the equation `pi=CRT` (where C is the molarity of the solution)
C. Decreasing order of osmotic pressure for 0.01 M aqueous solutions of barium chloride, potassium chloride, acetic acid and sucrose is `BaCl_(2) gt KCl gt CH_(3)COOH gt " Sucrose"`
D. According to Raoult's law, the vapour pressure exerted by a volatile component of a solution is directly proportional to its mole fraction in the solution.

Explanation

To determine which statement is false regarding the freezing point depression of solutions, we need to analyze the provided statement about sucrose solutions.

### Step-by-Step Solution:

1. **Understanding Freezing Point Depression**:
- The freezing point depression (\( \Delta T_f \)) is a colligative property that depends on the number of solute particles in a solution, not on the type of solute or solvent.
- The formula for freezing point depression is given by:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \( i \) = van 't Hoff factor (for sucrose, \( i = 1 \) since it does not ionize)
- \( K_f \) = freezing point depression constant of the solvent
- \( m \) = molality of the solution

2. **Analyzing the Statement**:
- The statement claims that two different solutions of sucrose of the same molality prepared in different solvents will have the same depression in freezing point.
- Since \( K_f \) varies for different solvents, even if the molality \( m \) is the same, the freezing point depression will not be the same because \( K_f \) is different for each solvent.

3. **Conclusion**:
- Therefore, the statement is false. Two solutions of the same molality of sucrose in different solvents will not have the same depression in freezing point due to the different \( K_f \) values of the solvents.

### Final Answer:
The false statement is: "Two different solutions of sucrose of the same molality prepared in different solvents will have the same depression in freezing point."

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