Which one of the following statement is false ?

Options

A. (a) The correct order of osmotic pressure for 0.01 M aqueous solution of each compoud `BaCl_(2) gt KCl gt CH_(3)COOH` `gt Sucrose`
B. (b) Isotonic solutions are those solutions which have the same osmotic pressure
C. (c) Raoult's law state that the vapour pressure of a component over a solution is proportional to its mole fraction in liquid state
D. (d) Two sucrose solutions of same molality prepared in different solvent will have the same freezing point depression

Answer

To determine which statement is false, we will analyze each statement one by one based on the principles of chemistry related to dilute solutions, osmotic pressure, and colligative properties.

### Step-by-Step Solution:

1. **Understanding Osmotic Pressure**:
- Osmotic pressure (π) is given by the formula:
\[ \pi = iCRT \]
where:
- \(i\) = Van't Hoff factor (number of particles the solute dissociates into),
- \(C\) = concentration of the solution,
- \(R\) = universal gas constant,
- \(T\) = temperature.
- Since \(R\) and \(T\) are constants in this scenario, the osmotic pressure will depend primarily on the Van't Hoff factor \(i\).

2. **Calculating Van't Hoff Factors**:
- For **BaCl₂**:
- Dissociates into 1 Ba²⁺ and 2 Cl⁻ ions.
- \(i = 1 + 2 = 3\).
- For **KCl**:
- Dissociates into 1 K⁺ and 1 Cl⁻ ion.
- \(i = 1 + 1 = 2\).
- For **CH₃COOH** (acetic acid):
- Partially dissociates in water, hence \(i\) is slightly greater than 1 (let's say \(i > 1\)).
- For **Sucrose**:
- A non-electrolyte that does not dissociate.
- \(i = 1\).

3. **Order of Osmotic Pressure**:
- Based on the calculated \(i\) values:
- BaCl₂ (i = 3) > KCl (i = 2) > CH₃COOH (i > 1) > Sucrose (i = 1).
- Therefore, the correct order of osmotic pressure is:
\[ \text{BaCl₂} > \text{KCl} > \text{CH₃COOH} > \text{Sucrose} \]

4. **Analyzing the Statements**:
- **Statement A**: The order of osmotic pressure is correct based on our calculations.
- **Statement B**: Isotonic solutions have the same osmotic pressure, which is true.
- **Statement C**: Raoult's law states that the vapor pressure of a component in a solution is proportional to its mole fraction, which is also true.
- **Statement D**: Two sucrose solutions having the same molality prepared in different solvents will have the same freezing point depression.
- This is false because the freezing point depression depends on the cryoscopic constant \(K_f\), which varies with different solvents. Thus, even if the molality is the same, the freezing point depression will differ due to different \(K_f\) values.

5. **Conclusion**:
- The false statement is **Statement D**.

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

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