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: =+, =+.

Step 1: Understanding Positive Deviations

Positive deviation from Raoult's Law occurs when the vapor pressure of a solution is higher than expected. This implies weaker interactions between the solute and solvent compared to the interactions in pure substances.

Step 2: Relation to Enthalpy and Volume

For positive deviation, enthalpy change () and volume change () are related. Positive deviation often leads to an endothermic process, meaning  is positive, and there is an increase in volume, so  is positive too.

Step 3: Analyzing Given Options

Review the options to find which combination matches the expected signs for volume and enthalpy changes: - (a) =+, =+ - (b) =-, =+ - (c) =+, =- - (d) =-, =-. The correct combination for positive deviation is (a).

Step 4: Select the Correct Answer

Identify the option that correctly aligns with the properties of solutions showing positive deviations from Raoult's Law. Option (a) is correct with positive enthalpy and volume changes.

Key Concepts

Raoult's Law

Raoult's Law is a fundamental principle in chemistry that describes how the partial vapor pressure of each component of an ideal solution contributes to the total vapor pressure of the solution. In an ideal solution, the interactions between different molecules are the same as those among the same kind. Therefore, the partial vapor pressure of each component is directly proportional to its mole fraction in the solution. Mathematically, it's expressed as:\[P_i = X_i \cdot P_i^0\]
Where

• \(P_i\) is the partial vapor pressure of component \(i\),
• \(X_i\) is the mole fraction of component \(i\) in the solution,
• \(P_i^0\) is the vapor pressure of pure component \(i\).

However, real solutions can demonstrate deviations from Raoult's Law due to differences in molecular interactions, such as positive or negative deviations. Understanding these deviations helps in analyzing the behavior of solutions.

Enthalpy Change

Enthalpy change, often noted as \(\Delta H\), is an important concept used to describe heat absorbed or released during a process at constant pressure. In chemical reactions or solution formations, it helps determine whether a process is endothermic (absorbs heat) or exothermic (releases heat).
In solutions exhibiting positive deviations from Raoult's Law, the enthalpy change tends to be positive. This positive enthalpy change indicates that the process is endothermic, meaning it requires an input of energy.
What causes this? When the new interactions between solvent and solute molecules are weaker than the interactions within the pure substances, more energy is needed to break the original bond. This need for energy input results in a positive enthalpy value.

Volume Change

Volume change, represented as \(\Delta V\), refers to the change in volume that occurs when forming a solution from pure components. When a solution follows Raoult's Law, the total volume is usually what you would expect by adding the volumes of individual components.
Solutions showing positive deviations from Raoult's Law experience an increase in volume upon mixing. This is due to weaker interactions between solute and solvent molecules than those found within each pure component. As a result, molecules do not pack as efficiently, leading to a larger volume. Hence, \(\Delta V\) is positive for solutions with positive deviations.

Vapor Pressure

Vapor pressure is a measure of the tendency of molecules to escape from a liquid into the vapor phase. In a solution, vapor pressure can provide insight into the interactions between the liquid components.
According to Raoult's Law, the vapor pressure of a solution should equal the sum of the partial pressures, provided the solution is ideal. However, in positive deviations, the vapor pressure of a solution exceeds what is predicted by Raoult's Law. This happens because the weaker intermolecular forces mean molecules more readily evaporate. This makes the solution's overall vapor pressure higher than expected.

Solution Properties

The properties of solutions deviating from Raoult's Law are significant for understanding chemical mixing. Positive deviations particularly highlight unique solution behaviors due to weaker molecular attractions. These deviations impact both physical and thermodynamic properties.
Some key properties to consider include:

• Excess Volumes: Solutions with positive deviations have excess volumes, meaning they are larger than the sum of their constituent volumes.
• Thermodynamic Traits: Positively deviating solutions are often endothermic, necessitating energy input, thus affecting heat regulation in chemical processes.
• Activity Coefficient: This is used to quantify deviations from ideal behavior, offering a numerical way to analyze how far a particular solution strays from ideality.

By examining these aspects, scientists can better predict and control solution behavior in various practical applications such as formulation of pharmaceuticals or manufacturing of chemical products.