Problem 72 - A Complete Resource Book in Chemistry for JEE Main

Question

The aqueous solution that has the lowest vapour pressure at a given temperature is (a) \(0.1\) molal sodium phosphate (b) \(0.1\) molal barium chloride (c) \(0.1\) molal sodium chloride (d) \(0.1\) molal glucose

Step-by-Step Solution

Answer

(a) 0.1 molal sodium phosphate

Step 1: Understanding vapour pressure

Vapour pressure of a solution is influenced by the number of solute particles in the solution. The more the number of solute particles, the lower the vapour pressure.

Step 2: Defining the colligative properties

Colligative properties depend on the number of solute particles but not on the type of particle. These properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

Step 3: Dissociation of electrolytes

When ionic compounds dissolve in water, they dissociate into ions. For example, sodium chloride, when dissolved, produces two ions: Na⁺ and Cl⁻.

Step 4: Calculating the number of particles for each option

- **Sodium phosphate (Na₃PO₄):** Dissociates into 4 ions (3 Na⁺ and 1 PO₄³⁻) - **Barium chloride (BaCl₂):** Dissociates into 3 ions (1 Ba²⁺ and 2 Cl⁻) - **Sodium chloride (NaCl):** Dissociates into 2 ions (Na⁺ and Cl⁻) - **Glucose (C₆H₁₂O₆):** Does not dissociate, remains 1 particle.

Step 5: Comparing number of particles

Determine which solution has the most solute particles: - Sodium phosphate (4 particles) - Barium chloride (3 particles) - Sodium chloride (2 particles) - Glucose (1 particle) Sodium phosphate has the most particles, leading to the most significant lowering of vapor pressure.

Step 6: Conclusion

The aqueous solution with the lowest vapor pressure is the one with the highest number of dissociated particles. Thus, the 0.1 molal sodium phosphate solution has the lowest vapor pressure.

Key Concepts

Vapor Pressure Lowering

When you dissolve a solute in a solvent, the resulting solution typically exhibits a lower vapor pressure compared to the pure solvent. This is known as vapor pressure lowering, a primary colligative property. It occurs because the solute particles disrupt the solvent molecules' ability to evaporate at the surface.
In simpler terms, adding a solute essentially "dilutes" the surface with non-volatile particles, making fewer solvent molecules available to escape into the vapor phase.

• The magnitude of vapor pressure lowering depends on the number of solute particles, not their identity.
• This relationship results in solutions with higher solute concentrations exhibiting more significant vapor pressure lowering.

For example, among the substances listed, sodium phosphate (Na₃PO₄) lowers vapor pressure the most. It dissociates into multiple ions, increasing the particle count in the solution.

Dissociation of Electrolytes

Certain compounds, known as electrolytes, dissociate into ions when dissolved in water. This dissociation increases the number of solute particles, significantly affecting the colligative properties of the solution.
For instance, when sodium chloride (NaCl) dissolves, it separates into two ions: Na⁺ and Cl⁻. However, other electrolytes can produce more ions upon dissociation.

• Sodium phosphate (Na₃PO₄) produces 4 ions: 3 Na⁺ and 1 PO₄³⁻.
• Barium chloride (BaCl₂) yields 3 ions: 1 Ba²⁺ and 2 Cl⁻.
• Sodium chloride (NaCl) yields 2 ions.

The more ions produced, the larger the effect on colligative properties like vapor pressure lowering. Thus, understanding dissociation is crucial in predicting and explaining these properties in solutions.

Number of Solute Particles

The concept of the number of solute particles is central to colligative properties. These properties only depend on how many particles there are, not what type they are. This is why glucose, which doesn't dissociate into ions, has less impact compared to ionic compounds.
To determine the number of solute particles, you consider both the original solute amount and how much it splits into ions. More dissociation means more particles—and a greater change in colligative properties.
In the given examples:

• Sodium phosphate produces 4 particles, strongly lowering the vapor pressure.
• Barium chloride results in 3 particles.
• Sodium chloride yields 2 particles.
• Glucose stays as a single particle.

By knowing the number of particles, you can predict which solution will experience more significant colligative effects, such as the lowest vapor pressure in the sodium phosphate solution.