Problem 148 - A Complete Resource Book in Chemistry for JEE Main

Question

In a mixture of \(\mathrm{A}\) and \(\mathrm{B}\), components show negative deviation when: (a) \(\mathrm{A}-\mathrm{B}\) interaction is stronger than \(\mathrm{A}-\mathrm{A}\) and \(\mathrm{B}-\mathrm{B}\) interaction (b) \(\mathrm{A}-\mathrm{B}\) interaction is weaker than \(\mathrm{A}-\mathrm{A}\) and \(\mathrm{B}-\mathrm{B}\) interaction (c) \(\Delta \mathrm{V}_{\text {mix }}>0, \Delta \mathrm{S}_{\operatorname{mix}}>0\) (d) \(\Delta \mathrm{V}_{\operatorname{mix}}=0, \Delta \mathrm{S}_{\operatorname{mix}}>0\)

Step-by-Step Solution

Answer

(a) \( \mathrm{A-B} \) interaction is stronger than \( \mathrm{A-A} \) and \( \mathrm{B-B} \) interaction.

Step 1: Understanding Negative Deviation

Negative deviation from Raoult's Law occurs when the vapor pressure of the mixture is lower than expected. This is typically due to stronger intermolecular forces between different components of the mixture than between similar components.

Step 2: Analyzing the given options

Evaluate each option based on the definition of negative deviation: - **Option (a):** Stronger \(\mathrm{A-B}\) interaction implies stronger attraction between different components than themselves, which leads to negative deviation.- **Option (b):** Weaker \(\mathrm{A-B}\) interaction suggests weaker attraction, leading to positive deviation.- **Option (c):** \(\Delta \mathrm{V}_{\text{mix}} > 0\) implies expansion, indicative of weaker interactive forces, suggesting positive deviation.- **Option (d):** \(\Delta \mathrm{V}_{\text{mix}} = 0\) does not suggest negative deviation as this indicates ideal mixing conditions, while negative deviation is found in sub-ideal conditions.

Step 3: Selecting the correct answer

Since negative deviation indicates stronger attractions between \(\mathrm{A}\) and \(\mathrm{B}\) than within themselves, option (a) fits this pattern with stronger \(\mathrm{A-B}\) interactions causing the observed negative deviation.

Key Concepts

Negative Deviation

Raoult's Law states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the components. However, when a mixture displays negative deviation, it indicates that the observed vapor pressure is lower than predicted. This occurs when the forces between unlike molecules (e.g., A and B in the mixture) are stronger than the forces among the like molecules (A-A or B-B). Such enhanced attraction between different components results in less tendency for molecules to escape into the vapor phase, hence leading to reduced vapor pressure. This behavior suggests a strong affinity between dissimilar particles in the mixture.

Intermolecular Forces

Intermolecular forces are fundamental in determining how mixtures behave, especially under Raoult's Law deviations. These forces include hydrogen bonding, London dispersion forces, and dipole-dipole interactions. When A-B interactions are stronger than A-A or B-B, negative deviation occurs, as the mixture prefers to stay in a liquid state due to these stronger forces. For example:

• Hydrogen bonds can significantly contribute to stronger intermolecular forces between components.
• Polar-polar interactions, such as those between polar solvent molecules, can enhance attraction.

Understanding these forces gives insight into why certain mixtures don't behave ideally.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature. In mixtures, deviations from the ideal behavior as described by Raoult's Law affect vapor pressure.
Negative deviation results in a lower vapor pressure since stronger intermolecular attractions limit the number of molecules transitioning to the gas phase.
Understanding vapor pressure helps explain:

• How substances vaporize when intermolecular forces alter due to mixing.
• The observed phenomena where the vapor pressure is reduced due to specific component interactions.

Vapor pressure is thus a key concept in studying mixture behavior under non-ideal conditions.

Mixture Behavior

The behavior of mixtures, especially when considering deviations from Raoult's Law, can reveal much about component interactions. Negative deviation implies sub-ideal mixing conditions where there is stronger affinity between different components.
This can lead to:

• Decreased volume changes upon mixing, often resulting in no expansion or even contraction.
• Unexpected thermodynamic properties, such as changes in enthalpy and entropy.

Grasping the underlying chemistry helps predict and manipulate mixture behaviors for various applications, such as crafting solutions with specific properties for industrial or pharmaceutical purposes.