Problem 36 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is correct for a solution showing positive deviations from Raoult's law? (a) \(\Delta \mathrm{V}=+\mathrm{ve}, \Delta \mathrm{H}=+\mathrm{ve}\) (b) \(\Delta \mathrm{V}=-\mathrm{ve}, \Delta \mathrm{H}=+\mathrm{ve}\) (c) \(\Delta \mathrm{V}=+\mathrm{ve}, \Delta \mathrm{H}=-\mathrm{ve}\) (d) \(\Delta \mathrm{V}=-\mathrm{ve}, \Delta \mathrm{H}=-\mathrm{ve}\)

Step-by-Step Solution

Answer

Option (a) is correct: \(\Delta \mathrm{V}=+\mathrm{ve}, \Delta \mathrm{H}=+\mathrm{ve}\).

Step 1: Understanding Positive Deviations from Raoult's Law

When a solution shows positive deviations from Raoult's law, the intermolecular forces between unlike molecules in the mixture are weaker than those in the pure individual components. Hence, the molecules are not as strongly held together, leading to new characteristics.

Step 2: Examine Volume Change (ΔV)

For positive deviations, since the molecules are less tightly held together compared to the pure components, they tend not to fit as closely. As a result, the solution's volume increases, leading to \(\Delta \mathrm{V} = +\mathrm{ve}\).

Step 3: Examine Enthalpy Change (ΔH)

With weaker interactions in the mixture compared to the pure components, more energy is required to separate the molecules than would be expected for an ideal solution. Therefore, the process is endothermic, resulting in \(\Delta \mathrm{H} = +\mathrm{ve}\).

Step 4: Determine the Correct Option

Matching these explanations with the options provided, option (a) correctly represents a solution showing positive deviations from Raoult's law. Hence, \(\Delta \mathrm{V} = +\mathrm{ve}\) and \(\Delta \mathrm{H} = +\mathrm{ve}\) are the expected signs.

Key Concepts

Positive Deviations

In the context of Raoult's Law, solutions can demonstrate either positive or negative deviations. Positive deviations occur when the intermolecular attractions between different components in a mixture are weaker than those in the pure substances themselves. This means that when you mix these substances, they don't hold each other as tightly as they do when they are apart.
This phenomenon leads to several important consequences:

• The vapor pressure of the solution is higher than predicted by Raoult's Law.
• The mixture tends to separate more easily because the components are not strongly bound.
• Typically, this suggests that the components are more volatile than expected.

These deviations are important when considering the mixing of liquids and how they behave in different concentrations.

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion between molecules. These determine how molecules interact and bond with each other. In solutions showing positive deviations, intermolecular forces between differing molecules are weaker compared to those in pure substances.
When these forces are weak:

• The molecules don't stick together as tightly, making the solution expand as the molecules move more freely.
• This often results in an increase in vapor pressure as more molecules can escape into the vapor phase.
• Weak forces can lead to higher volatility of the components in the mixture.

Understanding the strength of intermolecular forces helps us predict and explain deviations from ideal solution behavior.

Volume Change

Volume change is an essential indicator of how substances mix in a solution. For mixtures showing positive deviations from Raoult's law, the total volume of the solution is often greater than the sum of the volumes of its components. This is due to the weak intermolecular forces in the mixture compared to the pure substances.
When mixing:

• Molecules do not pack as closely together, resulting in an increase in the overall volume of the mixture.
• The repulsive forces might become significant as the molecules push each other apart more than they do in the pure substances.

This phenomenon leads to a volume change (\(\Delta V = +\text{ve}\)), which can be measured and predicted to assess the nature of the mixture.

Enthalpy Change

Enthalpy change (\(\Delta H\)) in solutions is an indicator of the energy change when components mix. In the case of positive deviations, this change is usually positive, indicating an endothermic process.
During mixing:

• The weaker interactions between unlike molecules mean that energy is absorbed to break the initial interactions and allow the new weaker ones to form.
• This absorption of energy increases the enthalpy of the system.
• Mixing processes that demand energy imply that the new interactions formed are less stable than those in pure substances.

Recognizing this energy absorption is crucial in predicting how solutions will behave under different conditions.