Problem 147 - A Complete Resource Book in Chemistry for JEE Main

Question

According to the kinetic theory of gases, in an ideal gas, between two successive collisions the gas molecules travels (a) in a circular path (b) in a wavy path (c) in a straight line path (d) with an accelerated velocity

Step-by-Step Solution

Answer

In an ideal gas, molecules travel in a straight line path between collisions.

Step 1: Understanding the Problem

The problem asks us to determine the path that gas molecules travel in, according to the kinetic theory of gases, between two successive collisions. The options given are: circular path, wavy path, straight line path, and accelerated velocity.

Step 2: Reviewing Kinetic Theory of Gases

According to the kinetic theory of gases, molecules are in constant random motion. Between collisions with each other or with the walls of their container, the molecules move in straight lines with constant velocity, assuming no forces act on them.

Step 3: Identifying the Correct Path

Based on the kinetic theory, molecules move in straight lines when not colliding. This excludes circular or wavy paths, as well as accelerated motion, because these would require a change in velocity or direction from an external force.

Step 4: Conclusion

Given that molecules move in straight lines between collisions, the correct option is (c) in a straight line path.

Key Concepts

Ideal Gas Behavior

In the realm of physics, the ideal gas is a concept that simplifies the behavior of gases. This model assumes that gas molecules:

• Are in constant, random motion
• Have no significant volume compared to the space they occupy
• Do not exert significant forces on each other except during collisions

The beauty of the ideal gas law, which is articulated as \( PV = nRT \), lies in its simplicity. Here, \( P \) represents pressure, \( V \) is volume, \( n \) denotes the amount of gas in moles, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.
Under this model, the only interactions considered are perfectly elastic collisions, meaning energy is conserved. Perfect elasticity implies no energy is lost to sound or heat during these collisions.
While real gases deviate slightly from these assumptions due to factors like intermolecular forces, the ideal gas model provides a foundation for understanding more complex gas behaviors. It serves well in many conditions, such as high temperature and low pressure, where real gases tend to exhibit behavior closer to that of an ideal gas.

Molecular Motion

Molecular motion in gases is a key element of the kinetic theory. Gas molecules are in perpetual, erratic motion. This movement is random and quick, contributing to the high energy state of gases compared to solids or liquids.
Here are some aspects of molecular motion:

• Randomness: Molecular motion is completely unpredictable in terms of individual particle paths.
• Speed and energy: The speed of molecules relates directly to the temperature of the gas. Higher temperatures yield faster average molecular speeds.
• Elastic collisions: When molecules collide, they do so elastically, meaning kinetic energy before and after the collision remains constant.

This chaotic motion is what prevents gas molecules from sticking together and is essential for the diffusion of gases where they spread to occupy any available volume. This randomness also leads to a distribution of speeds among the molecules, typically described by the Maxwell-Boltzmann distribution.

Straight Line Path

In the context of the kinetic theory of gases, the concept of a straight line path provides insight into how gas molecules move between collisions.
Between any two successive collisions, a gas molecule travels in a straight line path. There are no net forces acting on the molecule after the collision until it interacts with another molecule or the surface of the container. This means:

• The molecule travels at constant velocity between collisions, as no external forces alter its motion.
• The trajectory of the molecule is unaffected by gravity at the molecular level, assuming it's moving in an isolated system.

Hence, the idea of straight line paths is fundamental in distinguishing the behavior of gases, under ideal conditions, from liquids and solids. This simplifies many calculations and predictions within thermodynamics and provides a clear picture of the molecular dynamics inherent in gaseous states.