Problem 24 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Which of the following \(0.1 \mathrm{M}\) aqueous solutions will have the lowest freezing point? (a) Potassium sulphate (b) Sodium chloride (c) Urea (d) Glucose

Step-by-Step Solution

Answer

Potassium sulphate has the lowest freezing point as it has the highest van 't Hoff factor \( i = 3 \).

Step 1: Identify the Freezing Point Depression Formula

The freezing point depression is calculated by the formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the change in freezing point, \( i \) is the van 't Hoff factor, \( K_f \) is the freezing point depression constant, and \( m \) is the molality.

Step 2: Determine van 't Hoff Factor for Each Compound

- Potassium sulphate \( (K_2SO_4) \) dissociates into 3 ions: 2 \( K^+ \) and 1 \( SO_4^{2-} \). Thus, \( i = 3 \). - Sodium chloride \( (NaCl) \) dissociates into 2 ions: \( Na^+ \) and \( Cl^- \). Thus, \( i = 2 \). - Urea and Glucose do not dissociate into ions in solution, so \( i = 1 \) for both.

Step 3: Analyze the Freezing Point Changes

The freezing point depression depends directly on the van 't Hoff factor \( i \). The higher the \( i \), the greater the freezing point depression. So, compare the \( i \) values: - Potassium sulphate: \( i = 3 \) - Sodium chloride: \( i = 2 \) - Urea and Glucose: \( i = 1 \)

Step 4: Determine the Solution with Lowest Freezing Point

Since the solution with the highest van 't Hoff factor will have the lowest freezing point, Potassium sulphate, with \( i = 3 \), has the lowest freezing point compared to the others.

Key Concepts

van 't Hoff Factor

The van 't Hoff factor, often denoted as \( i \), is a crucial concept in understanding how solutes affect the colligative properties of a solution, such as freezing point depression. It represents the number of particles that a compound dissociates into when dissolved in a solvent.
For ionic compounds, this dissociation process significantly increases the effective concentration of dissolved particles, influencing the solution's properties.
Let's examine the van 't Hoff factor with some examples:

• Potassium sulfate \((K_2SO_4)\): This salt dissociates into three ions in an aqueous solution, specifically two potassium ions \((K^+)\) and one sulfate ion \((SO_4^{2-})\). As a result, its van 't Hoff factor \( i \) equals 3.
• Sodium chloride \((NaCl)\): Dissociates into two ions, sodium \((Na^+)\) and chloride \((Cl^-)\), leading to a factor of 2.
• Non-electrolytes like urea and glucose do not dissociate, hence have a van 't Hoff factor of 1.

A higher van 't Hoff factor means more dissociation into particles, which amplifies the effect on colligative properties.

Colligative Properties

Colligative properties are determined by the number of solute particles in a solution rather than the identity of the particles. This makes them unique and measurable properties.
The four primary colligative properties are:

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

These properties are vital because they help us understand how adding solute to a solvent affects the solution's physical behavior.
Freezing point depression, specifically, is a colligative property where the addition of solute particles lowers the temperature at which the liquid becomes solid. The effect of solutes on these properties ties directly to the van 't Hoff factor. For instance, solutions with higher \( i \) values, like potassium sulfate, exhibit a more significant freezing point depression because more particles disrupt the structure needed for freezing to occur.

Solution Chemistry

Solution chemistry explores how substances dissolve and interact in a solvent to form homogeneous mixtures. It delves deep into understanding solute-solvent interactions and how they influence solution behavior.
Two fundamental types of substances dissolve in solutions:

• Electrolytes, which dissociate into ions and conduct electricity, leading to higher van 't Hoff factors.
• Non-electrolytes, which do not dissociate, maintaining a factor of 1.

The properties of solutions, such as boiling point, freezing point, and osmotic pressure, rely heavily on these interactions.
For instance, when evaluating which solution has the lowest freezing point, one must consider how many particles the solute releases into the solution. This is predicted using the dissociative properties of the solute, often quantified by the van 't Hoff factor.
In the given example, solutions like potassium sulfate exhibit significant effects on these properties due to their dissociation into multiple particles.