Which of the following statements is FALSE ?

Options

A. Two different solutions of sucrose of same molality prepared in different solvents will have the same depression in freezing point.
B. The osmotic pressure of a solution is given by the equation `prod="CRT"`( where C is the molarity of the solution).
C. Decreasing order of osmotic pressure for 0.01 M aqueous solution of barium chloride, potassium chloride, acetic acid and sucrose is `BaCl_(2)gtKClgtCH_(3)COOHgt`sucrose.
D. According to Raoult's law, the vapour pressure exerted by a volatile component of a solution is directly proportional to its mole fraction in the solution.

Answer

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

### Step 1: Analyze the first statement
**Statement:** "Two different solutions of sucrose 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:
\[ \Delta T_f = K_f \times m \]
where \( K_f \) is the cryoscopic constant of the solvent and \( m \) is the molality of the solution.
- Since \( K_f \) varies for different solvents, even if the molality (m) is the same, the depression in freezing point will differ for different solvents. Therefore, this statement is FALSE.

### Step 2: Analyze the second statement
**Statement:** "The osmotic pressure of a solution is given by the equation \( \pi = CRT \)."

**Analysis:**
- The formula for osmotic pressure (\( \pi \)) is indeed given by:
\[ \pi = CRT \]
where \( C \) is the molarity of the solution, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin. This statement is TRUE.

### Step 3: Analyze the third statement
**Statement:** "Decreasing order of osmotic pressure for 0.01 molar aqueous solutions of barium chloride, potassium chloride, acetic acid, and sucrose is in this order."

**Analysis:**
- The osmotic pressure is affected by the van 't Hoff factor (\( i \)), which indicates the number of particles the solute dissociates into:
- Barium chloride (BaCl₂) dissociates into 3 particles (\( i = 3 \)).
- Potassium chloride (KCl) dissociates into 2 particles (\( i = 2 \)).
- Acetic acid (CH₃COOH) partially dissociates, so \( i \) is between 1 and 2.
- Sucrose does not dissociate (\( i = 1 \)).
- Therefore, the order of osmotic pressure from highest to lowest will be: BaCl₂ > KCl > Acetic Acid > Sucrose. This statement is TRUE.

### Step 4: Analyze the fourth statement
**Statement:** "According to Raoult's law, the vapor pressure exerted by a volatile component in a solution is directly proportional to its mole fraction in solution."

**Analysis:**
- Raoult's law states that the vapor pressure of a volatile component in a solution is directly proportional to its mole fraction (\( X \)):
\[ P = P^0 \times X \]
where \( P^0 \) is the vapor pressure of the pure component. This statement is TRUE.

### Conclusion
The FALSE statement among the options is the first one: "Two different solutions of sucrose of the same molality prepared in different solvents will have the same depression in freezing point."

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