Which among the following statements is false?

Options

A. The correct order of osmotic pressure for 0.01 M aqueous solution of each compound is
`BaCl_(2) gt KCl gt CH_(3)COOH gt "Sucrose."`
B. The osmotic pressure `(pi)` of a solution is given by the equation (`i MRT,` where M is the molarity of the solution).
C. Raoult's law states that the vapour pressure of a component over a solution is proportional to it's mole fraction.
D. Two sucrose solutions of the same molality prepared in different solvents will have the same freezing point depression.

Answer

To determine which statement is false among the given options, we will analyze each statement step by step.

### Step 1: Analyze the first statement regarding osmotic pressure
The first statement claims that the correct order of osmotic pressure (π) of a 0.01 molar aqueous solution of each compound is based on the van 't Hoff factor (i). The osmotic pressure (π) is given by the formula:
\[ \pi = i \cdot M \cdot R \cdot T \]
Where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor (number of particles after dissociation)
- \( M \) = molarity
- \( R \) = gas constant
- \( T \) = temperature in Kelvin

**Calculation of i values:**
- For **BaCl₂**: It dissociates into 1 Ba²⁺ and 2 Cl⁻ ions, so \( i = 3 \).
- For **KCl**: It dissociates into 1 K⁺ and 1 Cl⁻ ion, so \( i = 2 \).
- For **CH₃COOH**: It partially dissociates into CH₃COO⁻ and H⁺ ions, so \( i \approx 2 \) (weak electrolyte).
- For **Sucrose**: It does not dissociate, so \( i = 1 \).

**Order of osmotic pressure based on i values:**
1. BaCl₂ (i = 3)
2. KCl (i = 2)
3. CH₃COOH (i ≈ 2)
4. Sucrose (i = 1)

### Step 2: Analyze the second statement regarding osmotic pressure formula
The second statement asserts that the formula for osmotic pressure is \( \pi = i \cdot M \cdot R \cdot T \), where M is the molality. This is incorrect because M should represent molarity, not molality. Therefore, this statement is false.

### Step 3: Analyze the third statement regarding Raoult's Law
The third statement relates to Raoult's Law, which states that the vapor pressure of a component in a solution is proportional to its mole fraction. This is a correct statement, as Raoult's Law is given by:
\[ P_a = P^0_a \cdot X_a \]
Where \( P_a \) is the vapor pressure of the component, \( P^0_a \) is the vapor pressure of the pure component, and \( X_a \) is the mole fraction of the component in the solution.

### Step 4: Analyze the fourth statement regarding freezing point depression
The fourth statement claims that two sucrose solutions with the same molality prepared in different solvents will have the same freezing point depression. This is false because the freezing point depression (\( \Delta T_f \)) depends on the solvent's cryoscopic constant (\( K_f \)), which varies between different solvents. Therefore, even if the molality is the same, the freezing point depression can differ.

### Conclusion
The false statements are:
1. The second statement about osmotic pressure formula (M should be molarity, not molality).
2. The fourth statement about freezing point depression (it depends on the solvent).

### Final Answer
The false statement is the second one regarding the osmotic pressure formula, where M is incorrectly stated as molality instead of molarity.