Which one of the following statement is Flase?

Options

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

Explanation

To determine which statement is false among the provided options, let's analyze each statement step by step.

### Step 1: Analyze the First Statement
**Statement:** Raoult's law states that the vapor pressure of a component over a solution is proportional to its mole fraction.

**Analysis:** This statement is true. Raoult's law indeed states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in the solution. Therefore, this statement is not false.

### Step 2: Analyze the Second Statement
**Statement:** The osmotic pressure (π) of a solution is given by the equation π = mRT, where m is the molarity.

**Analysis:** This statement is also true. The osmotic pressure can be expressed as π = iCRT, where C is the molarity, R is the universal gas constant, and T is the temperature in Kelvin. Since molarity (m) and concentration (C) can be used interchangeably in this context, this statement is not false.

### Step 3: Analyze the Third Statement
**Statement:** The correct order of osmotic pressure for 0.01 molar aqueous solution of each compound is: BaCl2 > KCl > CH3COOH > sucrose.

**Analysis:** This statement is true. The osmotic pressure depends on the number of particles in solution. BaCl2 dissociates into 3 ions (Ba²⁺ and 2 Cl⁻), KCl dissociates into 2 ions (K⁺ and Cl⁻), CH3COOH is a weak electrolyte and partially dissociates, and sucrose does not dissociate at all. Therefore, the order of osmotic pressure is indeed BaCl2 > KCl > CH3COOH > sucrose. This statement is not false.

### Step 4: Analyze the Fourth Statement
**Statement:** A sucrose solution of the same molarity prepared in different solvents will have the same freezing point.

**Analysis:** This statement is false. The freezing point depression depends on the solvent's cryoscopic constant (Kf). Different solvents have different Kf values, which means that the freezing point depression will vary with the solvent, even if the molarity of the sucrose solution is the same. Therefore, this statement is indeed false.

### Conclusion
The false statement among the options is:
**Option 4:** A sucrose solution of the same molarity prepared in different solvents will have the same freezing point.

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