Problem 5 - Chemistry in 30 days

Question

The van't Hoff factors \(i\) for an electrolyte which undergoes dissociation and association in solvents are respectively (a) greater than 1 and greater than 1 (b) less than 1 and greater than 1 (c) less than 1 and less than 1 (d) greater than 1 and less than I

Step-by-Step Solution

Answer

The correct answer is (d).

Step 1: Understanding Van't Hoff Factor

The van't Hoff factor (0i
7D) is a measure of the effect of a solute on the colligative properties of a solution. It quantifies how many particles an electrolyte becomes in solution.

Step 2: Dissociation

When an electrolyte dissolves and dissociates in a solvent, the van't Hoff factor is greater than 1. More particles result compared to the undissociated form, which means it leads to an increase in the number of particles in solution.

Step 3: Association

In association, molecules combine to form larger aggregates, resulting in fewer particles than originally present. Thus, the van't Hoff factor is less than 1, indicating a reduction in the number of separate particles.

Step 4: Comparing Options

Analyze the options based on the understanding of dissociation and association. For dissociation, we need a van't Hoff factor greater than 1, and for association, we need it to be less than 1.

Step 5: Selecting the Correct Option

Option (d) reflects the correct understanding: dissociation has a van't Hoff factor greater than 1 and association has a van't Hoff factor less than 1.

Key Concepts

Colligative Properties

Colligative properties are the properties of a solution that depend on the number of solute particles present in the solution, rather than the type of particle. These include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. They arise because adding a solute to a solvent modifies the number of solvent particles available at the surface of the solution, thereby altering how the solution interacts with temperature and pressure changes.
When you dissolve a solute in a solvent, the nature of this interaction changes, leading to observable phenomena:

• **Boiling Point Elevation**: The presence of solute particles means you need a higher temperature to achieve the vapor pressure needed to boil.
• **Freezing Point Depression**: Solute particles interfere with the formation of the solid lattice of ice, thus lowering the freezing point.
• **Vapor Pressure Lowering**: Solute particles at the surface reduce the number of solvent molecules escaping into the vapor phase.
• **Osmotic Pressure**: Solute particles draw solvent through a semipermeable membrane, generating pressure due to the concentration difference.

The van't Hoff factor is a crucial metric in determining these properties, as it indicates the effect solutes will have through dissociation or association, effectively changing the number of particles in the solution. This understanding is critical when predicting the behavior of solutions in various practical and theoretical scenarios.

Electrolyte Dissociation

Electrolyte dissociation refers to the process by which an ionic compound splits into its constituent ions when dissolved in a solvent, typically water. This process significantly impacts the colligative properties as it increases the number of particles in the solution. For instance, common salt (NaCl) dissociates into Na⁺ and Cl⁻ ions. When an electrolyte dissociates, it leads to:

• **Increased Particles**: More particles are present in the solution beyond the initial electrolyte molecules.
• **Higher Colligative Effects**: Due to more particles, there are greater shifts in boiling and freezing points among other properties.

The van't Hoff factor for dissociation is calculated by counting the total number of particles post-dissociation. Simply put, if a compound such as NaCl completely dissociates, then the van't Hoff factor is approximately 2 (one Na⁺ and one Cl⁻). However, other complex compounds might dissociate differently. Therefore, evaluating dissociation helps predict how a solution’s properties change when an electrolyte is dissolved.

Electrolyte Association

Electrolyte association occurs when ions or molecules in a solution come together to form more complex entities like aggregates or dimers, reducing the total number of particles in the solution. This process can happen in solutions with specific environmental conditions, like high concentration or particular solvent types. In association, you find:

• **Reduced Particles**: Fewer particles exist as smaller ions or molecules form larger clusters.
• **Lower Colligative Effects**: Due to less number of active particles, there is a diminished impact on colligative properties.

For instance, in some solutions, carboxylic acids may form dimers, effectively halving the number of particles, which results in a van't Hoff factor of less than 1. Understanding association is crucial when dealing with organic compounds or systems where intermolecular forces dominate at certain concentrations or temperatures, as it affects the overall properties like viscosity and boiling point alteration differently from dissociation.