Problem 17 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For a dilute solution, Raoult's law states that : (a) the lowering of vapour pressure is equal to the mole fraction of solute. (b) the relative lowering of vapour pressure is equal to the mole fraction of solute. (c) the relative lowering of vapour pressure is proportional to the amount of solute in solution. (d) the vapour pressure of the solution is equal to the mole fraction of solvent.

Step-by-Step Solution

Answer

(b) The relative lowering of vapour pressure is equal to the mole fraction of solute.

Step 1: Understanding Raoult's Law

Raoult's Law is a principle applied to ideal solutions. It states that in a dilute solution, each component of the solution exerts a partial vapor pressure proportional to its mole fraction. The total vapor pressure of the solution is the sum of these partial pressures.

Step 2: Define Key Terms

Mole fraction of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution. Relative lowering of vapor pressure means the change in vapor pressure relative to the original pressure, usually of the pure solvent.

Step 3: Identify Relevant Concept

For a dilute solution, especially when considering the effects of a non-volatile solute, Raoult's Law tells us that the relative lowering of vapor pressure of the solvent is directly proportional to the mole fraction of the solute, which is the key concept in this exercise.

Step 4: Analyze the Options

The exercise presents four statements. We must match these against what Raoult's Law asserts: (a) talks about lowering directly, (b) refers to relative lowering, (c) cites proportionality, and (d) focuses on solvent mole fraction against solution vapor pressure.

Step 5: Select Correct Option

Option (b), stating the relative lowering of vapor pressure is equal to the mole fraction of solute, correctly represents Raoult's Law for dilute solutions. It captures the proportional relationship between the solute mole fraction and the change in vapor pressure compared to the pure solvent.

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase at a given temperature. In a solution, vapor pressure changes depending on the composition. When you add a non-volatile solute, the solution's vapor pressure lowers compared to the pure solvent. This phenomenon occurs because the solute particles occupy space at the liquid surface, hindering solvent molecules from escaping into the vapor phase.
The measurement of vapor pressure is significant in determining the physical properties of solutions. For example:

• It influences boiling points and freezing points.
• It is crucial for understanding weather patterns and cooking at high altitudes.

Understanding vapor pressure helps predict how solutions will behave in different conditions, making it a core concept in chemistry and related fields.

Mole Fraction

Mole fraction is a way to express the concentration of a component in a mixture. It's defined as the number of moles of one component divided by the total number of moles of all components in the mixture. For a binary solution of solvent and a single solute, the mole fraction of the solute (denoted as \( x_2 \)) and of the solvent (denoted as \( x_1 \)) are very straightforward. They are calculated as follows:

• \( x_1 = \frac{n_1}{n_1 + n_2} \), where \( n_1 \) is the moles of solvent and \( n_2 \) is the moles of solute.
• \( x_2 = \frac{n_2}{n_1 + n_2} \).

The sum of the mole fractions in a solution is always 1. Mole fraction is significant because it remains constant regardless of temperature changes, unlike concentration units like molarity or molality.

Dilute Solution

A dilute solution is one where the amount of solute is relatively small compared to the solvent. In such solutions, the properties are almost identical to that of the pure solvent. Raoult's Law becomes particularly useful in dilute solutions for predicting how the vapor pressure is affected by solute addition. Here are some characteristics of dilute solutions:

• They often lead to small changes in the physical properties, making calculations simpler.
• Assumptions based on ideal behavior, like those used in Raoult's Law, tend to be more accurate.

When Raoult’s Law is applied to a dilute solution, it asserts that the relative lowering of vapor pressure is proportional to the mole fraction of the solute. This concept is central when studying solutions because it relates directly to essential phenomena such as boiling point elevation and freezing point depression.