Which of the following statements is false ?

Options

A. Two different solutions 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_3COOH gt `surcose.
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 of the given statements is false, we will analyze each statement one by one.

### Step 1: Analyze Statement A
**Statement A**: "Two different solutions of sucrose of the same molality, prepared in different solvents, will have the same depression in freezing point."

- The formula for depression in freezing point is given by:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where \( \Delta T_f \) is the depression in freezing point, \( i \) is the van't Hoff factor, \( K_f \) is the cryoscopic constant of the solvent, and \( m \) is the molality of the solution.

- For sucrose, which is a non-electrolyte, \( i = 1 \). Thus, the equation simplifies to:
\[ \Delta T_f = K_f \cdot m \]
- Since the molality \( m \) is the same for both solutions but the solvents are different, the \( K_f \) values will differ for each solvent. Therefore, \( \Delta T_f \) will also differ.

**Conclusion**: Statement A is false.

### Step 2: Analyze Statement B
**Statement B**: "The osmotic pressure of a solution is given by the equation \( \pi = CRT \) where \( C \) is the molarity of the solution."

- The correct formula for osmotic pressure is:
\[ \pi = i \cdot C \cdot R \cdot T \]
where \( i \) is the van't Hoff factor.

- The statement omits the van't Hoff factor \( i \), which is crucial for calculating osmotic pressure.

**Conclusion**: Statement B is also false.

### Step 3: Analyze Statement C
**Statement C**: "The decreasing order of osmotic pressure of 0.01 molar aqueous solutions of barium chloride, potassium chloride, acetic acid, and sucrose is correct."

- The osmotic pressure depends on the van't Hoff factor \( i \):
- For barium chloride (BaCl₂), \( i = 3 \) (dissociates into Ba²⁺ and 2 Cl⁻).
- For potassium chloride (KCl), \( i = 2 \) (dissociates into K⁺ and Cl⁻).
- For acetic acid (CH₃COOH), \( i = 1 \) (weak electrolyte, partially dissociates).
- For sucrose, \( i = 1 \) (non-electrolyte).

- Since all solutions are 0.01 M, the osmotic pressure order based on \( i \) will be:
- BaCl₂ > KCl > Acetic Acid = Sucrose

**Conclusion**: Statement C is true.

### Step 4: Analyze Statement D
**Statement D**: "According to Raoult's law, the vapor pressure exerted by a volatile component of a solution is directly proportional to the mole fraction of the solution."

- Raoult's law states that the vapor pressure \( P \) of a component in a solution is directly proportional to its mole fraction \( X \):
\[ P = P^0 \cdot X \]
where \( P^0 \) is the vapor pressure of the pure component.

**Conclusion**: Statement D is true.

### Final Conclusion
The false statements are:
- **Statement A**: False
- **Statement B**: False