Problem 135 - A Complete Resource Book in Chemistry for JEE Main

Question

The colligative properties of electrolytes require a slightly different approach than the one used for the colligative properties of non- electrolytes. The electrolytes dissociate into ions in solution. It is the number of solute particles that determine the colligative properties of a solution. The electrolyte solutions, therefore show abnormal colligative properties. To account for this effect we define a quantity; called the van't Hoff factor which is given by [solution] \(i=\) dissociation \(\mathrm{i}=1\) (for non - electrolytes); \(\mathrm{i}>1\) (for electrolytes, undergoing dissociation) \(\mathrm{i}<1\) (for solute, undergoing association) Benzoic acid undergoes dimerisation in benzene solution. The van't Hoff factor 'i' is related to the degree of association ' \(\alpha\) ' of the acid as (a) \(i=1+\alpha\) (b) \(i=1-\alpha\) (c) \(i=1+\frac{\alpha}{2}\) (d) \(i=1-\frac{\alpha}{2}\)

Step-by-Step Solution

Answer

The correct answer is (d) \(i = 1 - \frac{\alpha}{2}\).

Step 1: Understanding Dimerization

In the context of benzoic acid, dimerization refers to the process where two benzoic acid molecules associate to form a dimer. This association reduces the number of particles in solution, affecting the van't Hoff factor.

Step 2: Consider Van't Hoff Factor Formula

The van't Hoff factor \(i\) is a measure of the effect of solute particles on the colligative properties of a solution. For association reactions like dimerization, \(i\) is typically less than 1 because fewer particles are present due to association.

Step 3: Relationship Between 'i' and Degree of Association 'α'

The degree of association \(\alpha\) represents the fraction of original benzoic acid molecules that dimerize. In the case of complete dimerization, half of the molecules would reduce to dimers, decreasing the number of particles in solution by half, which simplifies to \(i = 1 - \frac{\alpha}{2}\).

Step 4: Selecting the Correct Option

Based on the understanding that \(i = 1 - \frac{\alpha}{2}\), we can identify the correct option as (d) \(i = 1 - \frac{\alpha}{2}\). This formula accounts for the association and the reduction in the number of solute particles.

Key Concepts

Colligative Properties

Colligative properties are unique characteristics of solutions that depend entirely on the number of solute particles, not their identity. This means that regardless of what the solute is, if you have the same amount of particles, the colligative properties will be the same. Common colligative properties include:

• Boiling point elevation - The boiling point of a solution is higher than that of the pure solvent.
• Freezing point depression - The freezing point of a solution is lower than that of the pure solvent.
• Osmotic pressure - The pressure required to stop the flow of solvent into the solution through a semipermeable membrane.
• Vapor pressure lowering - The vapor pressure of a solution is lower than that of the pure solvent.

Electrolytes and non-electrolytes can demonstrate different behaviors in terms of colligative properties due to the presence or absence of ions.

Association and Dissociation

In chemistry, association and dissociation refer to how molecules or ions interact in a solution.

• Association - This occurs when molecules come together to form a complex, such as a dimer in dimerization. Association lowers the number of solute particles in a solution, affecting its colligative properties by making them appear less pronounced.
• Dissociation - Opposite to association, dissociation involves molecules or ionic compounds splitting into individual ions. This increases the number of particles in the solution, leading to greater colligative effects. For example, when table salt (NaCl) dissolves in water, it dissociates completely into Na⁺ and Cl⁻ ions, effectively doubling the number of particles in the solution compared to non-dissociating compounds.

Degree of Association

The degree of association, often denoted by the Greek letter theta ( ), is the measure of the extent to which molecules in a solution form associated complexes like dimers.

• When equals 0, there is no association, meaning all molecules exist as separate entities.
• A value of 1 indicates complete association, where molecules have paired entirely.

The degree of association is crucial in calculating the correct coll gative properties because it relates directly to the van't Hoff factor, where i = 1 - /2 for dimerizing substances. Quantifying the degree of association allows scientists to account for these changes in solute behavior.

Dimerization

Dimerization is a specific type of chemical association where two molecules bind together to form a single entity called a dimer. This process is significant in solutions where certain conditions favor the association of molecules.

• An example of dimerization is the formation of dimers of benzoic acid in a benzene solution. During this process, two benzoic acid molecules join to form a stable dimer.
• This transition decreases the total number of individual molecular entities in the solution.

Since dimerization reduces the number of solute particles in a solution, it leads to a lower van't Hoff factor (i < 1), impacting the solution's colligative properties. Understanding and evaluating dimerization is essential when calculating accurate colligative properties.

Electrolytes versus Non-electrolytes

Electrolytes and non-electrolytes behave differently in solutions because of their ability or inability to dissociate into ions.

• Electrolytes - These are substances that dissolve in water to produce a solution that conducts electricity. They dissociate into ions, thereby increasing the number of solute particles and enhancing the solution's colligative properties. Common examples include sodium chloride (NaCl) and potassium nitrate (KNO₃).
• Non-electrolytes - These substances dissolve in water but do not dissociate into ions. They do not affect the conductivity of water significantly, as they do not produce ions in solution. Non-electrolytes such as sugar or benzoic acid do not increase the number of particles, unless they undergo processes like dimerization.

Understanding the distinction between electrolytes and non-electrolytes is crucial when examining their respective effects on colligative properties in solutions.