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) \(A-B\) interaction is weaker than \(A-A\) and \(B-B\) interaction (c) \(\Delta \mathrm{V}_{\operatorname{mix}}>0, \Delta \mathrm{S}_{\operatorname{mix}}>0\) (d) \(\Delta \mathrm{V}_{\operatorname{mix}}=0, \Delta \mathrm{S}_{\operatorname{mix}}>0\)

Step-by-Step Solution

Answer

Negative deviation occurs when \( A-B \) interaction is stronger than \( A-A \) and \( B-B \) interaction, so option (a) is correct.

Step 1: Understanding Component Interactions

The exercise involves understanding how different interactions between components in a mixture affect its properties. Negative deviation in a mixture occurs when the interactions between different components, here \( A-B \), are stronger than the interactions among the same components, \( A-A \) and \( B-B \). This means that unlike components attract each other more strongly than like components.

Step 2: Identifying Negative Deviation

Negative deviation is characterized by a mixture showing a reduced vapor pressure compared to what is expected from Raoult's Law. This happens when the \( A-B \) interaction is stronger, leading to lower partial pressures of components in the vapor phase. Consequently, option (a) is consistent with a stronger \( A-B \) interaction and indicates negative deviation.

Step 3: Analyzing Thermodynamic Quantities

Options (c) and (d) involve thermodynamic quantities \( \Delta V_{\text{mix}} \) and \( \Delta S_{\text{mix}} \). Negative deviation usually results in \( \Delta V_{\text{mix}} < 0 \) because the volume decreases as components interact more strongly, reducing spacing between molecules. \( \Delta S_{\text{mix}} \) is typically positive since mixing generally increases disorder, but it doesn't distinguish negative deviation on its own.

Step 4: Conclusion and Correct Choice

In conclusion, the key aspect of negative deviation is the stronger interaction between different components compared to like components. Therefore, option (a), where \( A-B \) interaction is stronger than \( A-A \) and \( B-B \), leads to negative deviation. Options (b), (c), and (d) do not align with the fundamental characteristic of negative deviation.

Key Concepts

Component Interactions in Solutions

When two substances are mixed, the type of interaction between their molecules determines the properties and behavior of the solution. This interaction can significantly influence whether the mixture shows positive, negative, or ideal behavior.
In a solution, the key types of interactions are:

• Like-Like Interactions: These occur between molecules of the same type, for instance, (\(A-A\) and \(B-B\)).
• Unlike Interactions: These occur between molecules of different types (\(A-B\)).

When components in a mixture exhibit stronger unlike interactions (\(A-B\)) than like interactions, we observe phenomena such as negative deviation from Raoult's Law. The stronger attraction between different molecules overpowers their natural tendency to separate into like pairs, resulting in a more cohesive mixture. These interactions can alter various properties of the solution, impacting its stability and behavior. Understanding these interactions is crucial for predicting and manipulating the properties of mixtures.

Raoult's Law Deviations

Raoult's Law describes how the presence of a solute affects the vapor pressure of a solvent. According to Raoult's Law, the partial vapor pressure of each component in a mixture is directly proportional to its mole fraction. This ideal behavior assumes that interactions between different components are the same as those within each component.
However, real solutions often deviate from this ideal behavior due to differing component interactions:

• Negative Deviation: Occurs when \(A-B\) interactions are stronger than \(A-A\) and \(B-B\) interactions. The mixture exhibits a lower vapor pressure than predicted. This is because the enhanced attraction between different components holds them together more tightly in the liquid phase, reducing the number of molecules that can escape into the vapor phase.
• Positive Deviation: Occurs when \(A-B\) interactions are weaker than \(A-A\) and \(B-B\). Here, the mixture has a higher vapor pressure than expected, as weaker attractions allow more molecules to vaporize.

These deviations highlight the importance of molecular interactions in determining the physical properties of solutions.

Thermodynamic Properties of Mixtures

Thermodynamic properties provide insight into the energetic aspects of mixing and how they vary with different interactions. Two important thermodynamic quantities are the change in volume (\(\Delta V_{\text{mix}}\)) and entropy (\(\Delta S_{\text{mix}}\)) during mixing.
For negative deviation, the signs of these changes typically include:

• \(\Delta V_{\text{mix}} < 0\): The volume of the mixture is less than the sum of individual volumes because stronger \(A-B\) interactions bring molecules closer together, reducing overall space.
• \(\Delta S_{\text{mix}} > 0\): Mixing usually increases randomness or disorder, hence a positive entropy change is common. However, this does not specifically signify negative deviation; it is more a consequence of mixing itself.

Together, these properties illustrate the underlying thermodynamic principles that guide how solutions form and behave. By analyzing these attributes, scientists can better predict and control the outcomes of mixing different substances.