Problem 37 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following solution has least vapour pressure? (a) \(0.01 \mathrm{M} \mathrm{CaCl}_{2}\) (b) \(0.01 \mathrm{M}\) glucose (c) \(0.01 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\) (d) \(0.01 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4}\)

Step-by-Step Solution

Answer

The solution with Na₃PO₄ has the least vapor pressure due to the highest particle concentration.

Step 1: Understand Molality Influence

Vapor pressure lowering is a colligative property. It depends on the number of solute particles in the solution rather than the type of solute. This means we need to find which solution has the highest number of particles in solution.

Step 2: Determine Ion Count for Each Compound

To determine the number of dissolved particles, we will calculate ions produced from 1 mole of each solute: - **CaCl₂**: Dissociates into 3 ions (1 Ca²⁺ and 2 Cl⁻) - **Glucose**: Does not dissociate in solution, so 1 particle - **Na₂SO₄**: Dissociates into 3 ions (2 Na⁺ and 1 SO₄²⁻) - **Na₃PO₄**: Dissociates into 4 ions (3 Na⁺ and 1 PO₄³⁻)

Step 3: Calculate Effective Particle Concentration

Each solution has a concentration of 0.01M. The concentration of particles will be: - **CaCl₂**: 0.01 M x 3 particles = 0.03 M particles - **Glucose**: 0.01 M x 1 particle = 0.01 M particles - **Na₂SO₄**: 0.01 M x 3 particles = 0.03 M particles - **Na₃PO₄**: 0.01 M x 4 particles = 0.04 M particles

Step 4: Identify Least Vapor Pressure

Higher the concentration of particles, the lower the vapor pressure of the solution. Comparing concentrations: - Glucose has the fewest particles and thus the highest vapor pressure. - Na₃PO₄ has the highest concentration of particles at 0.04 M, hence provides the lowest vapor pressure.

Key Concepts

Vapor Pressure

Vapor pressure is an essential concept in chemistry that describes the pressure exerted by the vapor in equilibrium with its liquid at a given temperature. In simpler terms, it is a measure of how easily molecules can escape from a liquid to form a gas above the liquid's surface.

When a solute is dissolved in a solvent, the vapor pressure of the solvent typically decreases, a phenomenon governed by colligative properties.

• These properties depend solely on the number of solute particles, not their identity.
• This means any solute, whether it is ionic or molecular, will affect vapor pressure based on how many particles it contributes to the solution.
• As the particle count in a solution increases, the vapor pressure decreases because fewer solvent molecules are able to escape into the gas phase.

Understanding vapor pressure is crucial for predicting boiling and freezing points of solutions.

Solution Chemistry

Solution chemistry focuses on the study of solutes and solvents forming solutions, which can be gases, liquids, or solids. It is important to understand how solutes dissolve, interact with solvents, and affect properties like vapor pressure.

• In a solution, a solute is the substance that is dissolved, while the solvent is the substance doing the dissolving.
• Dissolving a solute in a solvent involves breaking the solute's bonds and forming new interactions between solute and solvent molecules.
• In this context, colligative properties are vital, as they depend on the number of particles the solute releases into the solution rather than the solute's identity.

These properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure. They can provide insights into molecular weights and ionization properties of substances.

Ionic Dissociation

Ionic dissociation occurs when ionic compounds dissolve in water, releasing ions into the solution. Understanding this process is fundamental to predicting many solution behaviors, including changes to vapor pressure.

• When an ionic compound like NaCl dissolves, it separates into its constituent ions, \({ Na^+ }\) and \({ Cl^- }\).
• This action increases the number of particles in the solution, significantly impacting colligative properties like vapor pressure.
• The degree of dissociation depends on the solute, affecting how many ions are produced per formula unit.

In the original exercise, among the options, \({ CaCl_2 }\), \({ Na_2SO_4 }\), and \({ Na_3PO_4 }\) all dissociate into multiple ions, whereas glucose does not, illustrating the direct impact of ionic dissociation on the overall particle count in solution.