Problem 61 - A Complete Resource Book in Chemistry for JEE Main

Question

Osmotic pressure observed when benzoic acid is dissolved in benzene is less than that expected from theoretical considerations. This is because (a) benzoic acid is an organic solute (b) benzoic acid has higher molar mass than benzene (c) benzoic acid gets associated in benzene (d) benzoic acid gets dissociated in benzene

Step-by-Step Solution

Answer

(c) benzoic acid gets associated in benzene

Step 1: Understanding Osmotic Pressure

Osmotic pressure () is a colligative property which depends on the number of solute particles in solution. The formula for osmotic pressure is given by \(  = i \frac{nRT}{V} \), where \( i \) is the van't Hoff factor, \( n \) is the moles of solute, \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( V \) is the volume of solution. The van't Hoff factor \( i \) represents the degree of dissociation or association of the solute.

Step 2: Analyzing Benzoic Acid in Benzene

Benzoic acid is a known self-associating compound, particularly when dissolved in non-polar solvents like benzene. In such non-polar solvents, benzoic acid molecules tend to form dimers. This means that instead of separating into individual molecules (dissociation), they pair up (association), effectively reducing the number of solute particles contributing to the osmotic pressure.

Step 3: Interpreting the Effect on Osmotic Pressure

The association of benzoic acid in benzene reduces the number of particles in solution, which decreases the osmotic pressure compared to what would be expected if benzoic acid dissociated fully. Therefore, the van't Hoff factor \( i \) becomes less than 1.

Step 4: Identifying the Correct Option

Given the reduced osmotic pressure due to the association of benzoic acid in benzene, we can conclude that the correct answer to why the observed osmotic pressure is lower than expected is that "benzoic acid gets associated in benzene."

Key Concepts

Benzoic Acid Association

Benzoic acid is an interesting compound, especially when it comes to its behavior in solution. When benzoic acid is dissolved in non-polar solvents like benzene, it doesn't behave like typical solutes. Instead of breaking apart into individual molecules (a process called dissociation), benzoic acid does the opposite. It tends to come together to form pairs, known as dimers. This process is called association, and it significantly impacts the properties of the solution.

In non-polar environments, the tendency for benzoic acid to associate is heightened because there are no strong interactions pulling the molecules apart. Thus, benzoic acid molecules prefer to pair up, reducing the total number of particles present in the solution. This association effect directly influences colligative properties such as osmotic pressure. You'll find that because there are fewer "particles" in the solution than you might initially expect, the solution's osmotic pressure is lower than theoretical predictions suggest.

Colligative Properties

Colligative properties are fascinating aspects of solutions that depend on the number of solute particles, not their identity. Properties like boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure are all considered colligative. These phenomena arise because the solute particles disrupt the solvent's normal behavior.

When discussing benzoic acid in benzene, osmotic pressure is the focus. Osmotic pressure is essentially the pressure required to stop the solvent from naturally diffusing through a semipermeable membrane to balance concentrations. It's directly related to the number of solute particles in the solution, according to the formula: \[\Pi = i \frac{nRT}{V}\]

Here, \( \Pi \) represents the osmotic pressure, \( i \) is the van’t Hoff factor, \( n \) is the number of moles of solute, \( R \) is the ideal gas constant, \( T \) is temperature, and \( V \) is volume. Association affects this by reducing the effective number of solute particles, which in turn results in a lower than expected osmotic pressure.

Van't Hoff Factor

The van’t Hoff factor, \( i \), is essential for understanding how solutes behave in a solution, especially for colligative properties. It helps us determine how many particles a solute produces when dissolved. This factor is crucial because it accounts for the effects of both dissociation and association of solutes.

For solutes that dissociate, like salts dissolving in water, the factor \( i \) would be greater than 1, reflecting the increase in particle numbers. However, for benzoic acid solutions in benzene, \( i \) becomes less than 1 due to association. This is because the molecules come together to form fewer 'effective' particles, reducing the expected impact on colligative properties.

In summary, the van’t Hoff factor adjusts the relationship between the apparent and theoretical behavior of solutes, helping explain why some experiments yield results that deviate from initial expectations due to solute association or dissociation.