Problem 6 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non volatile solute are together sealed in a container. Over time: (a) the volume of the solution increases and the volume of the solvent decreases (b) the volume of the solution decreases and the volume of the solvent increases (c) the volume of the solution and the solvent does not change (d) the volume of the solution does not change and the volume of the solvent decreases

Step-by-Step Solution

Answer

(a) The volume of the solution increases and the volume of the solvent decreases.

Step 1: Understand the Setup

We have two beakers in a sealed container. One beaker has pure solvent, and the other has a mixture of solvent and a non-volatile solute. Remember, a non-volatile solute does not evaporate easily.

Step 2: Consider Vapor Pressure

Pure solvent and the solvent in the mixture both have vapor pressures, but the pure solvent has a higher vapor pressure because adding a solute decreases vapor pressure (Raoult's Law). This means more solvent molecules will evaporate from the pure solvent beaker compared to the mixture beaker.

Step 3: Account for Transference

Since the pure solvent has a higher vapor pressure, more solvent molecules will evaporate in the air and eventually condense into the mixture beaker where the vapor pressure is lower. This results in a mass transfer from the pure solvent to the solution.

Step 4: Analyze the Outcome

Due to this mass transfer, the volume of pure solvent decreases as it loses molecules to evaporation while the volume of the solution increases as it gains those solvent molecules.

Step 5: Match to Options

Given the analysis above, the correct answer is (a) - the volume of the solution increases and the volume of the solvent decreases.

Key Concepts

Vapor Pressure

Vapor pressure is a term that many students come across in chemistry classes. It refers to the pressure exerted by the vapor of a liquid when it is in equilibrium with its liquid phase. Imagine a closed container with a liquid inside. As molecules from the liquid escape into the vapor phase and strike the walls of the container, they create vapor pressure. This pressure is crucial because it indicates how easily a substance can evaporate.

When dealing with pure substances, this vapor pressure is relatively higher compared to a solution with a solute. This is because the intermolecular forces in a pure liquid are consistent, allowing molecules to escape into the vapor phase easily. In a crucial rule of Raoult's Law, adding a non-volatile solute lowers the vapor pressure of the solvent. This happens because the solute particles occupy space at the surface, reducing the number of solvent molecules that can escape into the vapor phase. This reduction in vapor pressure leads to fascinating phenomena when a pure solvent and a solution are placed in the same sealed environment.

Non-Volatile Solute

A non-volatile solute is a substance added to a solvent that doesn't easily evaporate, meaning it remains largely in the liquid phase. These solutes are essential when discussing solutions because they alter the properties of the solvent, like lowering its vapor pressure, a concept derived from Raoult's Law.

Non-volatile solutes affect how the solution behaves compared to the pure solvent. Due to the presence of solute molecules, the overall surface area available for solvent molecules to evaporate from is reduced. This decrease means fewer molecules escape as vapor, resulting in decreased vapor pressure for the solution compared to the pure solvent. It's like covering some of a liquid's surface with a lid — fewer molecules can escape into the air above.

Understanding non-volatile solutes is key to comprehending many natural and industrial processes. For instance, salt (a non-volatile solute) is added to water to create a solution with different boiling and freezing points, an everyday phenomenon seen when making ice cream or cooking pasta.

Mass Transfer

Mass transfer describes the movement of mass from one location to another, often driven by differences in concentrations or pressures. In the context of our scenario with two beakers in a sealed container, mass transfer plays a crucial role.

Since the pure solvent has a higher vapor pressure than the mixture with a non-volatile solute, more solvent molecules evaporate from the pure solvent. These molecules move through the air inside the sealed container, eventually condensing into the mixture beaker, which has a lower vapor pressure due to the presence of the solute. This movement of molecules is a classic example of mass transfer as it results in the shift of solvent molecules from the beaker of pure solvent to the beaker with the solution.

This process continues until the system reaches some equilibrium, leading to observable changes in volumes: the solution's volume increases due to the gained solvent molecules, while the pure solvent's volume decreases as it loses molecules. Understanding mass transfer helps explain everyday processes and is foundational in fields such as chemical engineering, where it impacts the design of separation processes in industrial applications.