Which one of the following statement is false?

Options

A. Raoult’s law states that the vapour pressure of a component over a binary solution of volatile liquids is directly proportional to its mole fraction
B. Two sucrose solutions of the same molality prepared in different solvents will have the same depression in freezing point
C. The correct order of osmotic pressures of 0.01 M solution of each compound is `BaCl_(2) gt KCl gt CH_(3)COOH gt` "glucose"`
D. In the equation osmotic pressure `pi` = MRT, M is the molarity of the equation

Answer

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

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

**Analysis:**
Raoult's law states that the partial vapor pressure of a solvent in an ideal solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution. The formula is given by:
\[ P_A = X_A P^0_A \]
where \( P_A \) is the partial vapor pressure, \( X_A \) is the mole fraction of the solvent, and \( P^0_A \) is the vapor pressure of the pure solvent.

Since this statement is consistent with Raoult's law, **Statement 1 is true.**

### Step 2: Analyze Statement 2
**Statement 2:** Two sucrose solutions of the same molality prepared in different solvents will have the same depression in freezing point.

**Analysis:**
The depression in freezing point (\( \Delta T_F \)) is given by the formula:
\[ \Delta T_F = K_f \cdot m \]
where \( K_f \) is the freezing point depression constant of the solvent and \( m \) is the molality of the solution. Since \( K_f \) varies with different solvents, two sucrose solutions with the same molality but in different solvents will have different \( K_f \) values, leading to different depression in freezing points.

Thus, **Statement 2 is false.**

### Step 3: Analyze Statement 3
**Statement 3:** The correct order of osmotic pressure of 0.01 molar solution of each compound is \( \text{BaCl}_2 > \text{KCl} > \text{CH}_3\text{COOH} > \text{glucose} \).

**Analysis:**
Osmotic pressure (\( \Pi \)) is given by:
\[ \Pi = i \cdot M \cdot R \cdot T \]
where \( i \) is the van 't Hoff factor (number of particles the solute dissociates into), \( M \) is the molarity, \( R \) is the gas constant, and \( T \) is the temperature.

- For \( \text{BaCl}_2 \), it dissociates into \( \text{Ba}^{2+} + 2\text{Cl}^- \) (total \( i = 3 \)).
- For \( \text{KCl} \), it dissociates into \( \text{K}^+ + \text{Cl}^- \) (total \( i = 2 \)).
- For \( \text{CH}_3\text{COOH} \), it partially dissociates into \( \text{CH}_3\text{COO}^- + \text{H}^+ \) (approximately \( i = 2 \) but weaker than KCl).
- For glucose, it does not dissociate (total \( i = 1 \)).

Thus, the order of osmotic pressure is indeed \( \text{BaCl}_2 > \text{KCl} > \text{CH}_3\text{COOH} > \text{glucose} \), making **Statement 3 true.**

### Step 4: Analyze Statement 4
**Statement 4:** In the equation for osmotic pressure \( \Pi = MRT \), \( M \) is the molarity of the solution.

**Analysis:**
The correct formula for osmotic pressure includes the van 't Hoff factor:
\[ \Pi = i \cdot M \cdot R \cdot T \]
If \( i = 1 \) (for non-electrolytes), then it simplifies to \( \Pi = M \cdot R \cdot T \). However, the statement does not mention the van 't Hoff factor, which is crucial for electrolytes.

Thus, **Statement 4 is misleading but not outright false.**

### Conclusion
The false statement among the options provided is **Statement 2.**

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