Problem 20 - A Complete Resource Book in Chemistry for JEE Main

Question

The solution which has the lowest freezing point is (a) \(0.1 \mathrm{M}\) potassium nitrate (b) \(0.1 \mathrm{M}\) aluminium sulphate (c) \(0.1 \mathrm{M}\) potassium chloride (d) \(0.1 \mathrm{M}\) potassium sulphate

Step-by-Step Solution

Answer

Aluminium sulphate (19 is greatest due to highest i).

Step 1: Understanding Freezing Point Depression

Freezing point depression (19) is a colligative property, meaning it depends on the number of solute particles, not their identity. It is given by the formula 19 = iK_f m, where 19 is the freezing point depression, i is the van't Hoff factor (number of particles the compound dissociates into), K_f is the freezing point depression constant, and m is the molality.

Step 2: Calculate the van't Hoff factor for each option

For each compound, determine how many ions it dissociates into (i.e., the van't Hoff factor, i): - Potassium nitrate (KNO3) dissociates into 2 ions: K+ and NO3- (i = 2). - Aluminium sulphate (Al2(SO4)3) dissociates into 5 ions: 2 Al3+ and 3 SO4^-2 (i = 5). - Potassium chloride (KCl) dissociates into 2 ions: K+ and Cl- (i = 2). - Potassium sulphate (K2SO4) dissociates into 3 ions: 2 K+ and SO4^-2 (i = 3).

Step 3: Determine which solution has the greatest Freezing Point Depression

Since each solution is 0.1 M, the molality is assumed to be the same (0.1 mol/kg). The solution with the highest van't Hoff factor will have the greatest freezing point depression: - Potassium nitrate has i = 2. - Aluminium sulphate has i = 5. - Potassium chloride has i = 2. - Potassium sulphate has i = 3. Thus, aluminium sulphate with i = 5 will have the greatest freezing point depression.

Key Concepts

Colligative Properties

Colligative properties are fascinating in chemistry because they depend not on what the solute particles are but rather how many there are in a solution. This set of properties includes:

• Freezing point depression
• Boiling point elevation
• Vapor pressure lowering
• Osmotic pressure

When a solute is dissolved in a solvent, the interactions among the particles change. The presence of more particles can disrupt the natural can be seen in the freezing point depression, where the freezing temperature of a solution is lower than that of the pure solvent. The key takeaway is that the more particles, the greater the effect. That's why in freezing point depression, we often check how many particles a solute releases once it dissolves.

van't Hoff Factor

The van't Hoff factor, denoted as "i", is instrumental in quantifying colligative properties. It is defined as the ratio of the number of particles in solution to the number of formula units dissolved. This factor shows how many particles a solute breaks down into when dissolved:

• For non-ionic (covalent) solutes, it is typically i = 1 because they do not dissociate.
• For ionic solutes, it can vary depending on the compound. For example, a salt like NaCl dissociates into two ions, Na+ and Cl-, so i = 2.
• More complex ionic compounds, like aluminium sulfate (Al₂(SO₄)₃), dissociate into more ions, making i larger. Here, i = 5 because it dissociates into 2 Al³⁺ and 3 SO₄²⁻ ions.

Understanding the van't Hoff factor is essential for predicting how a solution will behave in terms of freezing point depression, as seen in the fact that a solution with a higher "i" will lower the freezing point more.

Dissolution of Ionic Compounds

Ionic compounds, when dissolved in water, undergo a process known as dissociation. This involves the compound breaking into its constituent ions, which are then surrounded by water molecules. This interaction is due to the attraction between the charged ions and the polar water molecules. For example, when potassium chloride (KCl) is dissolved in water, it breaks down into K+ and Cl- ions. Similarly, aluminium sulfate (Al₂(SO₄)₃) dissociates into multiple ions, increasing the number of particles considerably in the solution.

• The extent to which these compounds dissociate directly affects properties like freezing point depression.
• This is because more ions generally translate to a more significant lowering of the freezing point, linked back to the colligative property.

Thus, understanding how ionic compounds dissolve and dissociate offers insights into predicting the physical changes that solutions undergo, such as changes in freezing points.