Which one of 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 `pi` = 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 its mole fraction
D. Two sucrose solutions of 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 need to analyze each statement based on the principles of osmotic pressure, Raoult's law, and freezing point depression.

### Step-by-Step Solution:

1. **Understanding Osmotic Pressure:**
The osmotic pressure (π) of a solution is given by the formula:
\[ \pi = i \cdot C \cdot R \cdot T \]
where:
- \(i\) = van 't Hoff factor (number of particles the solute dissociates into)
- \(C\) = molar concentration (molarity)
- \(R\) = gas constant
- \(T\) = temperature

2. **Analyzing the Given Compounds:**
- For **BaCl₂**, it dissociates into 3 ions (1 Ba²⁺ and 2 Cl⁻), so \(i = 3\).
- For **KCl**, it dissociates into 2 ions (1 K⁺ and 1 Cl⁻), so \(i = 2\).
- For **Acetic Acid (CH₃COOH)**, it partially dissociates, so \(1 < i < 2\).
- For **Sucrose**, it does not dissociate, so \(i = 1\).

The order of osmotic pressure based on \(i\) values is:
\[ \text{BaCl}_2 (i=3) > \text{KCl} (i=2) > \text{Acetic Acid} (1 < i < 2) > \text{Sucrose} (i=1) \]
This statement is **true**.

3. **Checking the Formula for Osmotic Pressure:**
The statement that "Osmotic pressure of a solution is given by π = mRT" is misleading because it does not include the van 't Hoff factor \(i\). The correct formula should be:
\[ \pi = i \cdot C \cdot R \cdot T \]
Therefore, this statement is **false**.

4. **Raoult's Law:**
Raoult's law states that the vapor pressure of a component in a solution is proportional to its mole fraction. This is a correct statement and aligns with the principles of vapor pressure in solutions.

5. **Freezing Point Depression:**
The freezing point depression formula is:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where \(K_f\) is the cryoscopic constant, which varies for different solvents. Therefore, two sucrose solutions of the same molality in different solvents will not have the same freezing point depression due to different \(K_f\) values. This statement is **true**.

### Conclusion:
The false statement among the options is the one that claims "Osmotic pressure of a solution is given by π = mRT" because it omits the van 't Hoff factor \(i\).