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 provided options, we will 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 binary solution of volatile liquid is directly proportional to its mole fraction.

**Analysis:**
Raoult's law is defined as:
\[ P = P^0 \cdot X \]
where \( P \) is the vapor pressure of the component in the solution, \( P^0 \) is the vapor pressure of the pure component, and \( X \) is the mole fraction of the component in the solution. This statement is true.

### Step 2: Analyze the second statement
**Statement:** 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:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where \( i \) is the van 't Hoff factor (which is 1 for sucrose), \( K_f \) is the freezing point depression constant of the solvent, and \( m \) is the molality. Since the \( K_f \) values will differ for different solvents, the depression in freezing point will not be the same for the two solutions. This statement is false.

### Step 3: Analyze the third statement
**Statement:** The correct order of osmotic pressure of 0.01 molar solution of each compound is given.

**Analysis:**
The osmotic pressure (\( \pi \)) is given by:
\[ \pi = iCRT \]
where \( i \) is the van 't Hoff factor, \( C \) is the concentration, \( R \) is the gas constant, and \( T \) is the temperature. The value of \( i \) varies for different compounds:
- For BaCl2, \( i = 3 \)
- For KCl, \( i = 2 \)
- For glucose and sucrose, \( i = 1 \)

Thus, the order of osmotic pressure based on \( i \) will be different for each compound, and this statement is true.

### Step 4: Analyze the fourth statement
**Statement:** In the equation of osmotic pressure, \( \pi = MRT \), \( m \) is the molarity of the solution.

**Analysis:**
This statement is true as \( \pi = CRT \) is indeed the equation for osmotic pressure, where \( C \) represents the molarity of the solution.

### Conclusion
After analyzing all statements, the false statement is:
**"Two sucrose solutions of the same molality prepared in different solvents will have the same depression in freezing point."**