Which one of the following statements is FALSE ?

Options

A. Raoult's law states that the vapour pressure of a component over a solution is proportional to its mole fraction in solution
B. The osmotic pressure `( pi ) ` of a solution is given by the equation `pi = iCR T` where C is the molarity of the solution.
C. The correct order of osmotic pressure for 0.01 M aqueous solution of each compound is `BaCl_2` `gt` `KCl` `gt` `CH_(3)COOH` `gt` sucrose
D. none of these

Answer

To determine which statement is FALSE among the given 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 the component over a solution is proportional to its mole fraction.

**Analysis:**
- Raoult's law states that the vapor pressure (P) of a solvent in a solution is directly proportional to the mole fraction (X) of the solvent in the solution.
- Mathematically, it can be expressed as:
\[ P = P^0 \cdot X \]
where \( P^0 \) is the vapor pressure of the pure solvent.
- This statement is TRUE.

### Step 2: Analyze the Second Statement
**Statement:** The osmotic pressure of a solution is given by the equation \( \pi = ICRT \), where C is the molarity of the solution.

**Analysis:**
- The equation for osmotic pressure (\( \pi \)) is indeed given by:
\[ \pi = ICRT \]
where:
- \( \pi \) = osmotic pressure,
- \( I \) = van 't Hoff factor (number of particles the solute dissociates into),
- \( C \) = molarity of the solution,
- \( R \) = ideal gas constant,
- \( T \) = temperature in Kelvin.
- This statement is also TRUE.

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

**Analysis:**
- For 0.01 M solutions:
- **BaCl2** dissociates into 3 ions: \( Ba^{2+} + 2Cl^{-} \) → \( I = 3 \)
- **KCl** dissociates into 2 ions: \( K^{+} + Cl^{-} \) → \( I = 2 \)
- **CH3COOH** (acetic acid) is a weak acid and does not fully dissociate, so \( I < 2 \).
- **Sucrose** does not dissociate at all, so \( I = 1 \).

- Therefore, the order of osmotic pressure based on the van 't Hoff factor \( I \) would be:
- BaCl2 (I = 3) > KCl (I = 2) > CH3COOH (I < 2) > Sucrose (I = 1).

- The statement claims the order is BaCl2, KCl, and CH3COOH, which is misleading because it does not include sucrose and does not accurately reflect the dissociation of acetic acid. Thus, this statement is FALSE.

### Conclusion
The FALSE statement is the third one regarding the order of osmotic pressure.

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