Problem 35 - A Complete Resource Book in Chemistry for JEE Main

Question

The molecular weight of benzoic acid in benzene as determined by depression in freezing point method corresponds to (a) ionization of benzoic acid (b) dimerization of benzoic acid (c) trimerization of benzoic acid (d) solvation of benzoic acid

Step-by-Step Solution

Answer

(b) dimerization of benzoic acid

Step 1: Understanding Freezing Point Depression

Freezing point depression is a colligative property of solutions that decreases the freezing point of a solvent when a solute is added. This property depends on the number of particles in solution, not the type of particles.

Step 2: Reviewing Benzoic Acid Behavior in Benzene

Benzoic acid can undergo dimerization in nonpolar solvents like benzene. When two benzoic acid molecules form a dimer, the number of particles in the solution halves, impacting the freezing point depression calculation.

Step 3: Analyzing Alternatives

Other options such as ionization, trimerization, or solvation imply different or incompatible behavior in nonpolar solvents. Benzoic acid is unlikely to ionize or form trimers in a nonpolar environment like benzene.

Step 4: Concluding the Effect Observed

Given that dimerization reduces the number of particles effectively in the solution, it leads to a lower than expected molecular weight when derived from freezing point depression measurements.

Key Concepts

Colligative Properties

When you add a solute to a solvent, one interesting change can happen: the freezing point of the solvent can drop. We call this phenomenon "freezing point depression," which is a prime example of colligative properties. These properties depend solely on the number of solute particles in a solution and not on their identities. Hence, it's not about what the particles are but rather how many there are that matters.

For instance, when a non-volatile solute like salt is added to water, the water's freezing point lowers. The reason for this is that more energy has to be removed from the solution to change it from a liquid to a solid, compared to pure solvent alone. This is why roads are salted in winter. Within solutions, such as when benzoic acid is dissolved in benzene, the decrease in freezing point can clue us into the number of particles in the solution and help us understand how solute molecules behave.

Dimerization

Dimerization is a process where two molecules of the same kind join together to form a new unit. This is particularly common in certain organic compounds, such as benzoic acid, when placed in nonpolar environments like benzene. In this case, a hydrogen bond frequently keeps the two molecules bonded together.

Why does this matter? Well, in our context, dimerization notably affects colligative properties such as freezing point depression. When two benzoic acid molecules bind into a dimer, the expected number of individual molecules in solution reduces by half. Hence, in terms of particle count, you are effectively halving the amount you initially thought was in the solution. This impacts measurements, such as those used to infer molecular weight from freezing point depression, leading to an observed value that is double what you'd expect if the molecules did not dimerize.

Molecular Weight Determination

Molecular weight determination through colligative properties, such as freezing point depression, involves calculating the average mass of a molecule in a solution. To do this, scientists calculate how much the freezing point drops when a known amount of solute is added. However, certain conditions, like dimerization, can complicate this measurement.

Here's how it goes: When molecules form dimers, you're essentially counting fewer particles than you placed into the solution. This discrepancy impacts our numerical results, causing an incorrect molecular weight measurement. Using the depression in freezing point equation, \[\Delta T_f = K_f \cdot i \cdot m\]where \(\Delta T_f\) is the change in freezing point, \(K_f\) is the freezing point depression constant, \(i\) is the van 't Hoff factor, and \(m\) is the molality of the solution. The van 't Hoff factor \(i\) gets reduced by dimerization, effectively altering the calculated molecular weight to seem lower than it actually is.