Which one of the following statements is false?

Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression

The correct answer is option 1. Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression.

Let us delve into the reasoning behind each statement to clearly understand why the first statement is false:

1. Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression

Freezing Point Depression (\(\Delta T_f\)): The freezing point depression is a colligative property that depends on the molal concentration of the solute and the nature of the solvent. The equation for freezing point depression is:

\(\Delta T_f = i \cdot K_f \cdot m\)

where:

\( \Delta T_f \) is the freezing point depression.

\( i \) is the van't Hoff factor (for sucrose, \( i = 1 \) since it does not dissociate).

\( K_f \) is the cryoscopic constant of the solvent.

\( m \) is the molality of the solution.

\( K_f \) is a property specific to each solvent and represents how much the freezing point is lowered per molal concentration of a solute.

Since \( K_f \) varies from one solvent to another, two sucrose solutions of the same molality in different solvents will not have the same freezing point depression because the \( K_f \) values will be different.

2. The osmotic pressure (\(\pi\)) of a solution is given by the equation \(\pi = MRT\), where M is the molarity of the solution

This statement is correct. The formula for osmotic pressure (\(\pi\)) is derived from the van't Hoff equation for dilute solutions:

\(\pi = MRT \)

where:

\( \pi \) is the osmotic pressure.

\( M \) is the molarity of the solution.

\( R \) is the universal gas constant.

\( T \) is the absolute temperature (in Kelvin).

3. Raoult’s law states that the vapor pressure of a component over a solution is proportional to its mole fraction

This statement is correct. Raoult's law for an ideal solution states that the partial vapor pressure of each component in the solution is directly proportional to its mole fraction in the solution:

\(P_A = P_A^\circ x_A \)

where:

\( P_A \) is the partial vapor pressure of component A in the solution.

\( P_A^\circ \) is the vapor pressure of pure component A.

\( x_A \) is the mole fraction of component A in the solution.

4. The correct order of osmotic pressure for 0.01 M aqueous solution of each compound is BaCl2 > KCl > CH3COOH > Sucrose

This statement is correct because osmotic pressure (\(\pi\)) is a colligative property that depends on the number of solute particles in the solution. The more particles present, the higher the osmotic pressure:

\(BaCl_2\) dissociates into 3 ions (Ba\(^{2+}\) and 2 Cl\(^-\)): \(i = 3\)

\(KCl\) dissociates into 2 ions (K\(^+\) and Cl\(^-\)): \(i = 2\)

\(CH_3COOH\) (acetic acid) partially dissociates into CH3COO\(^-\) and H\(^+\), so \(i\) is slightly greater than 1 but much less than 2.

Sucrose does not dissociate: \(i = 1\)

So, the osmotic pressures follow the order:
\(\pi(\text{BaCl}_2) > \pi(\text{KCl}) > \pi(\text{CH}_3\text{COOH}) > \pi(\text{Sucrose}) \)

Conclusion:

The false statement is: "Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression." This is because the freezing point depression depends on the cryoscopic constant (\( K_f \)) of the solvent, which varies between different solvents. Therefore, even with the same molality, different solvents will result in different freezing point depressions.