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Chapter 5: Problem 69

Benzoic acid undergoes dimerization in benzene solution, the van't Hoff factor 'i' is related to the degree of association ' \(\mathrm{x}\) ' of to the acid as (a) \(\mathrm{i}=(1+\mathrm{x})\) (b) \(\mathrm{i}=(1-\mathrm{x})\) (c) \(\mathrm{i}=(1-\mathrm{x} / 2)\) (d) \(\mathrm{i}=(1+\mathrm{x} / 2)\)

Short Answer

Expert verified
The correct relation is (c) \(i = (1-x/2)\).

Step by step solution

01

Understand the Concept

Benzoic acid dimerizes in benzene, which affects the observed number of particles in solution. The van't Hoff factor, \(i\), indicates the degree of association or dissociation in a solution.
02

Equation for Dimerization

For benzoic acid dimerization, the equation is \(2C_6H_5COOH \rightleftharpoons (C_6H_5COOH)_2\). This shows that 2 moles of monomer combine to form 1 mole of dimer.
03

Relation of \(i\) with \(x\)

The degree of association, \(x\), represents the fraction of moles of the original solute that has dimerized. The total number of moles after association is given by \((1-x) + \frac{x}{2}\), because the dimers each consist of 2 original moles.
04

Calculate the van't Hoff Factor

In terms of solute particles (monomer and dimer), \(i\) is calculated by dividing the total apparent moles by the original moles. Thus, \(i = 1 - \frac{x}{2}\), arriving at option (c).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Benzoic Acid Dimerization
In solution chemistry, benzoic acid is known for its ability to form dimers, especially in non-polar solvents like benzene. Dimerization is a process where two benzoic acid molecules join to form a single larger unit. This occurs via hydrogen bonding between the carboxyl groups of the acid molecules. This reaction can be visualized as:
  • Initially, each benzoic acid molecule exists independently in the solution.
  • As dimerization proceeds, two benzoic acid molecules connect to form a dimer (a new chemical entity), reducing the total number of discrete particles in the solution.
Understanding dimerization is crucial, especially when predicting the behavior of solutions, as it directly influences the solution's properties including its boiling point, vapor pressure, and osmotic pressure.
Degree of Association
The degree of association, denoted by \(x\), is a key concept in solution chemistry illustrating the fraction of a solute that forms associative bonds, like dimers, in solution. For benzoic acid in benzene, the degree of association helps determine how many of the original molecules are associating to form dimers.The formula for determining \(x\) involves considering the initial number of moles versus the number present after association:
  • If \(x = 0\), no benzoic acid molecules are forming dimers, so all exist as monomers.
  • If \(x = 1\), all molecules form dimers, indicating complete association.
By understanding \(x\), chemists can assess how solute concentration affects associating molecules and predict solution behavior based on this degree of association.
Solution Chemistry
Solution chemistry involves studying how substances dissolve, interact, and behave once mixed into a solvent. This field covers the formation of solutions like benzoic acid in benzene and the subsequent reactions, such as dimerization. Key attributes of solution chemistry include:
  • Concentration - Determining how much solute is present compared to the solvent, influencing the rate and extent of reactions.
  • Solvents and Solutes - Understanding the properties of solutes, like benzoic acid, and solvents, like benzene, allows chemists to predict and control solution behavior.
  • Colligative Properties - These are properties that depend on the number of particles in a solution, not their identity. They are influenced by the van't Hoff factor by accounting for dimerization and other associative phenomena.
These attributes are crucial for applications in industrial chemistry, pharmaceuticals, and any domain where solutions are a fundamental element.
Molecular Association
Molecular association refers to the process where molecules interact and form complexes, such as dimers or larger aggregates. These interactions can heavily influence the physical and chemical properties of a solution. Primary characteristics of molecular association include:
  • Hydrogen Bonding - This is a common force driving molecular associations, especially in the formation of dimers like benzoic acid dimers.
  • Impacts on Properties - The van't Hoff factor measures how molecular association affects the number of solute particles in a solution, altering properties such as osmotic pressure.
  • Reversibility - Frequently, these associations are reversible, allowing a dynamic equilibrium between associated and free molecules, important for understanding solution behavior.
Exploring molecular associations helps chemists comprehend how solutions interact on a molecular level, essential for numerous scientific and practical applications.

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