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

1) The freezing point is a temperature at which the lowering of the freezing point is observed on the addition of solute. Depression in the freezing point is a colligative property. The depression in the freezing point is $\Delta T_f$ directly proportional to the molality of the solution. The depression in freezing point is mathematically stated as follows:

\[\Delta T_f = K_f \cdot m = K_f \cdot \frac{{w_2}}{{M_2w_1}}\]

Where $K_f$ is the cryoscopic constant or molal freezing point depression constant, $w_2$ is the mass of solute in kg, $M_2$ is the molar mass of solute, and $w_1$ is the weight of the solvent. Thus, depression in the freezing point is related to the weight of the solvent. The cryoscopic constant depends on the solvent taken. Therefore, two different solutions of the same molality in different solvents will not have the same depression in freezing point.

2) Osmotic pressure is the difference in pressure between the pure liquid and the solvent when there is equilibrium between the solute and the solvent particles across the semipermeable membrane. Osmotic pressure is a colligative property. It is proportional to the concentration of solute $C$ in the solution and is written as follows:

\[\pi = CRT\]

Where $C$ is the molarity of the solution, $R$ is the gas constant, and $T$ is the absolute temperature.

3) The osmotic pressure depends on the molar mass of the non-volatile solute and is represented as follows:

\[\pi = \frac{{w_2 M_2 VRT}}{{V}}\]

The decreasing order of the osmotic pressure for a 0.01 M aqueous solution of barium chloride, potassium chloride, acetic acid, and sucrose would be:

\[\text{BaCl}_2 > \text{KCl} > \text{CH}_3\text{COOH} > \text{Sucrose}\]

This order depends on the ease of solute or ions passing through the semipermeable membrane (SPM). Bigger solute particles are difficult to pass through the SPM, while smaller particles may pass.

4) According to Raoult's law, the partial pressure of any volatile component of a solution at any temperature is equal to the vapor pressure of the pure component multiplied by the mole fraction of that component in the solution. For an 'n' number of moles of a volatile liquid and $p$ as the partial pressure, Raoult's law for a volatile liquid is written as follows:

\[P = x \cdot p_0\]

Where $p_0$ is the vapor pressure of the liquid, $x$ is the mole fraction, and $P$ is the pressure of the liquid.

Therefore, statements (2), (3), and (4) are correct.

Hence the incorrect statement is (1).