Animated Solution for Chemistry - Solutions: Which one of the following statements is false?

In this problem, we are tasked with identifying the false statement among four fundamental principles of solutions and colligative properties. Let's embark on a journey to evaluate each statement one by one, breaking down the physical chemistry behind them.

The first statement claims that Raoult's law states the vapour pressure of a component over a solution is proportional to its mole fraction. This is the very definition of Raoult's law for volatile liquids! Mathematically, it is expressed as:

Here, $p_A$ is the partial vapour pressure, $x_A$ is the mole fraction of the component in the solution, and $p_A^{\circ }$ is the vapour pressure of the pure component. Since the statement perfectly aligns with this definition, statement (a) is absolutely true.

The second statement provides the equation for osmotic pressure as $\pi =MRT$. Osmotic pressure is a colligative property, and its complete formula includes the van't Hoff factor ($i$):

However, for non-electrolytes (like glucose or urea) where the solute neither dissociates nor associates, the van't Hoff factor $i=1$. In general definitions, especially when not explicitly dealing with electrolytes, $\pi =MRT$ is widely accepted as the standard defining equation. Therefore, statement (b) is considered true in its general context.

The third statement gives an order of osmotic pressures for $0.01\text{ M}$ aqueous solutions: ${\text{BaCl}}_2>\text{KCl}>{\text{CH}}_3\text{COOH}>\text{sucrose}$. Since the concentration ($M$) and temperature ($T$) are constant, the osmotic pressure will depend entirely on the van't Hoff factor ($i$), because $\pi \propto i$.

Let's determine the $i$ value for each solute: 1. ${\text{BaCl}}_2$: A strong electrolyte that completely dissociates into one ${\text{Ba}}^{2+}$ and two ${\text{Cl}}^{-}$ ions. Thus, $i=3$. 2. $\text{KCl}$: A strong electrolyte that completely dissociates into one ${\text{K}}^{+}$ and one ${\text{Cl}}^{-}$ ion. Thus, $i=2$. 3. ${\text{CH}}_3\text{COOH}$: A weak acid that only partially dissociates. Its $i$ value will be greater than 1 but less than 2 ($1<i<2$). 4. $\text{Sucrose}$: A non-electrolyte that does not dissociate at all. Thus, $i=1$.

Comparing these values, we get $3>2>(1\text{ to }2)>1$. This perfectly matches the given order, making statement (c) true.

The final statement claims that two sucrose solutions of the same molality prepared in different solvents will have the same freezing point depression. Let's look at the formula for freezing point depression:

Here, $m$ is the molality, which is given as the same for both solutions. But what about $K_f$? The molal depression constant, $K_f$, is a characteristic property of the solvent, not the solute. It depends on the solvent's molar mass, freezing point, and enthalpy of fusion.

If we use different solvents, their $K_f$ values will inherently be different. Consequently, even with the same molality, the product $K_{f}m$ will yield different values for $\Delta T_f$. Therefore, the freezing point depressions will be different. This makes statement (d) the false statement we were looking for!