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

Question

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) \(i=\underline{1}+\alpha\) (b) \(i=1-\alpha\) (c) \(i=1+\frac{\alpha}{2}\) (d) \(i=1-\frac{\alpha}{2}\)

Step-by-Step Solution

Answer

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

Step 1: Understanding Association

When benzoic acid undergoes dimerisation in benzene, two molecules of benzoic acid associate to form one dimer. This means that if 1 mole of benzoic acid dimerizes, instead of having 2 discrete particles, only 1 particle is observed in the solution.

Step 2: Defining the Van't Hoff Factor 'i'

The Van't Hoff factor (i) is the ratio of the actual number of particles in solution after dimerization to the number of particles if no association occurred. For full association (when all molecules form dimers), the observed number of particles is reduced by half.

Step 3: Relating 'i' to Degree of Association 'α'

The degree of association (α) represents the fraction of molecules that form dimers. If α=1, all molecules are associated, if α=0, none are. For a partial association, the effective number of particles in the solution will be reduced according to the fraction associated.

Step 4: Deriving the Expression for 'i'

Starting with no association, if we have x moles of benzoic acid, ideally we would have x particles. If a fraction α of these associate, then the remaining particles are x(1-α), and associated pairs contribute xα/2 particles. The total is x(1-α) + xα/2 = x(1-α/2). Therefore, the Van't Hoff factor i for the initial moles x becomes i = 1-α/2.

Key Concepts

Degree of Association

The concept of degree of association, denoted by the Greek letter \( \alpha \), is crucial in understanding how certain molecules behave in solution. This term is used to describe the fraction of a solute that joins together, or associates, in a chemical solution. It represents

• How many of the solute molecules in a solution engage in the formation of larger species, such as dimers or polymers.
• If \( \alpha = 1 \), it means that all molecules of the solute are involved in association, for instance forming dimer pairs or larger aggregates.
• Conversely, \( \alpha = 0 \) implies no molecules in the solute are associating.

The degree of association is a crucial factor in determining the properties of solutions, such as their concentration and colligative properties. By understanding \( \alpha \), one can better interpret how the number of particles in solution might differ from what one would expect if no association occurred. Thus, it can significantly alter calculations for properties like freezing point depression or boiling point elevation.

Dimerisation

Dimerisation, a specific type of association, occurs when two identical molecules combine to form a single unit known as a dimer. This process is a common occurrence in chemistry, especially for organic acids like benzoic acid.

• During dimerisation, two molecules of the solute link up, reducing the number of independent particles in the solution.
• For instance, if one starts with 2 moles of a solute, and those moles completely dimerise, there will end up being only 1 "effective" particle per dimer in the solution.
• Dimerisation changes the expected concentration of the solution from an analytical perspective, influencing colligative properties.

Examining the extent to which dimerisation occurs in a particular chemical system allows chemists to predict various properties of the solution, which is crucial for both theoretical understanding and practical applications such as pharmaceuticals and materials science.

Benzoic Acid

Benzoic acid is a simple aromatic carboxylic acid, known for its preservative and antibacterial properties. In solutions like benzene, a nonpolar solvent, benzoic acid has a tendency to undergo dimerisation.

• This behavior results largely from the hydrogen bonding capabilities of the carboxylic acid groups within benzoic acid molecules.
• When dissolved in nonpolar solvents, these benzoic acid molecules pair up to form dimers, effectively altering the solution's physical properties compared to what is expected based solely on the initial concentration of benzoic acid.
• The formation of dimers is one of the reasons why benzoic acid has a profound impact on freezing and boiling points in solutions, as the effective particle count has changed.

By studying how benzoic acid dimerises, scientists and students can gain insights into the broader principles of molecular interaction and solution chemistry.