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_(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 solve the question of which statement is false regarding solutions, we will analyze each option provided.

### Step-by-Step Solution:

1. **Understanding the First Statement:**
- The first statement claims that "two different solutions of sucrose of the same molality prepared in different solvents will have the same depression in freezing point."
- The depression in freezing point (ΔTf) is calculated using the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where \(i\) is the van't Hoff factor, \(K_f\) is the freezing point depression constant of the solvent, and \(m\) is the molality of the solution.
- Since both solutions have the same molality and the same solute (sucrose), the van't Hoff factor \(i\) will be the same (i.e., 1 for sucrose).
- However, \(K_f\) is dependent on the solvent used. Therefore, if different solvents are used, \(K_f\) will differ, leading to different values of ΔTf.
- **Conclusion:** This statement is false.

2. **Understanding the Second Statement:**
- The second statement states that "the osmotic pressure of the solution is given by the equation \(\pi = CRT\)."
- This is a correct representation of osmotic pressure, where \(C\) is the molarity of the solution, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin.
- **Conclusion:** This statement is true.

3. **Understanding the Third Statement:**
- The third statement discusses the decreasing order of osmotic pressure for 0.01 molar aqueous solutions of barium chloride (BaCl2), potassium chloride (KCl), acetic acid (CH3COOH), and sucrose.
- The osmotic pressure is influenced by the van't Hoff factor:
- For BaCl2: \(i = 3\) (Ba²⁺ + 2 Cl⁻)
- For KCl: \(i = 2\) (K⁺ + Cl⁻)
- For acetic acid (weak electrolyte): \(i\) is slightly greater than 1.
- For sucrose (non-electrolyte): \(i = 1\).
- Therefore, the order of osmotic pressure is:
\[ \text{BaCl2} > \text{KCl} > \text{CH3COOH} > \text{sucrose} \]
- **Conclusion:** This statement is true.

4. **Understanding the Fourth Statement:**
- The fourth statement refers to Raoult's law, which states that "the vapor pressure exerted by a volatile component of a solution is directly proportional to its mole fraction in the solution."
- This is indeed the essence of Raoult's law.
- **Conclusion:** This statement is true.

### Final Answer:
Based on the analysis, the false statement is the **first statement**.