Problem 20 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

When \(25 \mathrm{ml}\) of \(\mathrm{CCl}_{4}\) and \(25 \mathrm{ml}\) of toluene is mixed, the total volume of the solution will be (a) \(50 \mathrm{~m} /\) (b) \(>50 \mathrm{ml}\) (c) \(<50 \mathrm{ml}\) (d) Indefinite

Step-by-Step Solution

Answer

The total volume of the solution will be slightly less than 50 ml, leading to the correct answer being (c) <50 ml.

Step 1: Understand the Concept of Miscibility and Volume Additivity

When two liquids are mixed, the total volume of the resulting solution can be either additive (equal to the sum of the individual volumes), less than additive (the total volume is less than the sum), or in rare cases more than additive. For most miscible liquids, the volumes are not strictly additive due to molecular interactions.

Step 2: Apply Knowledge of CCl_4 and Toluene Mixture

CCl_4 (carbon tetrachloride) and toluene are both non-polar solvents and when mixed, they are known to form a nearly additive mixture. However, due to intermolecular forces, the molecules can pack more efficiently together, slightly decreasing the total volume.

Step 3: Choose the Correct Option

Given that the CCl_4 and toluene form a nearly additive but slightly less than additive mixture upon combining, the total volume of the solution will be slightly less than the sum of the individual volumes. Hence, the correct option is (c) <50 ml.

Key Concepts

Miscibility in Chemistry

Understanding miscibility is crucial when predicting how two substances mix to form a solution. Miscibility refers to the ability of two fluids to mix in all proportions, forming a homogenous solution without separating into two phases. For instance, water and ethanol are completely miscible, meaning they can be mixed in any ratio to create a uniform solution.

However, just because two liquids are miscible doesn't mean the volume of their mixtures will be strictly additive. When evaluating miscibility, it’s essential to consider molecular size, polarity, and the types of intermolecular forces at play. Sometimes, the space between molecules in a solution allows for a more compact arrangement than when the liquids are separate, which can lead to a decrease in total volume upon mixing.

Volume Additivity

Volume additivity is a concept in chemistry that deals with the combined volumes of substances. In an ideal scenario, if two substances are mixed, the total volume is expected to be the sum of their individual volumes. This is called perfect volume additivity and it is a key assumption in classical chemistry, especially when dealing with gases or dilute solutions.

In the real world, however, this perfect additivity rarely holds true for liquids. Due to molecular interactions such as intermolecular forces, volumes can deviate from being strictly additive. Those forces affect how closely molecules can pack together, which in turn affects the total volume of a solution. In the case of the CCl₄ and toluene mixture, while they are nearly additive in nature, the intermolecular forces cause a slightly more efficient packing, resulting in a combined volume that is less than the sum of their separate volumes.

Intermolecular Forces

Intermolecular forces are forces of attraction or repulsion that act between neighboring particles (atoms, molecules, or ions). They are the forces that hold substances together and are fundamental in understanding why materials have the physical properties they do, including why certain liquids mix and how their volumes change upon mixing.

These forces can be categorized into several types such as hydrogen bonding, dipole-dipole interactions, Van der Waals forces, and London dispersion forces. Non-polar substances like CCl₄ and toluene primarily experience London dispersion forces. These are the weakest of the intermolecular forces but can still lead to significant effects, such as the slight decrease in total volume when these two liquids are mixed. When designing a mixture like the one in the exercise, one must always take into consideration these subtle but impactful intermolecular interactions.