Problem 30 - Chemistry in 30 days

Question

According to the kinetic theory of gases, in an ideal gas, between two successive collisions a gas molecule 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

(c) in a straight line path

Step 1: Understanding the question

The question asks about the behavior of a molecule in an ideal gas between collisions. The kinetic theory of gases helps explain this movement.

Step 2: Reviewing Kinetic Theory of Gases

According to the kinetic theory of gases, gas molecules are in constant random motion and collide with each other and the walls of their container. Between collisions, the molecules move freely.

Step 3: Identifying the type of path

Between collisions in an ideal gas, molecules are assumed to move in a straight line with a constant velocity because they do not experience external forces or friction.

Step 4: Analyzing the options

Compare the defined movement with the given options: (a) circular path, (b) wavy path, (c) straight line path, (d) accelerated velocity. The movement between collisions matches a straight line path.

Key Concepts

Ideal Gas Behavior

Ideal gas behavior is a theoretical concept describing how gas molecules behave under ideal conditions. In an ideal gas, several assumptions simplify the behavior of the gas for easier analysis. These assumptions include that:

• Gas molecules are in constant, random motion.
• The molecules are perfectly elastic, meaning they collide without losing any kinetic energy.
• The volume of the individual gas molecules is negligible compared to the volume of the gas as a whole.
• There are no forces of attraction or repulsion between the molecules, except during collisions.

Because of these assumptions, the interactions between molecules in an ideal gas are straightforward. The simplicity of these interactions allows scientists and engineers to predict the behavior of gases under varying conditions with mathematical equations like the ideal gas law: \[ PV = nRT \]where \( P \) is the pressure, \( V \) is the volume, \( n \) is the amount of substance, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Molecule Motion

The kinetic theory of gases describes gas molecules as constantly moving in random directions. This motion is a result of the kinetic energy possessed by the molecules. Kinetic energy in gas molecules comes from the heat energy within a system, prompting them to move in various directions.

• Molecules continue this random movement until they collide with either the walls of the container or other molecules.
• These collisions are perfectly elastic, meaning that no kinetic energy is lost, and their speed remains the same unless influenced by changes in temperature or pressure.
• Each molecule acts independently of others, which is why their paths are random and unpredictable beyond a large-scale statistical level.

Molecule motion forms the backbone of gas behavior, affecting properties like pressure and temperature. Without this incessant motion, the existence of gases as we know them would be fundamentally different.

Straight Line Path

When we refer to the straight line path of a gas molecule, we're specifically focusing on how molecules travel between collisions. Ideal gas models assume that gas molecules move in straight lines until they hit another molecule or bounce off the container walls.

• This linear movement arises because there are no external forces like friction in a perfect gaseous environment that would curve or alter the path of the molecules.
• With no forces to deflect them, they maintain a constant velocity on these paths, only changing direction or speed when a collision occurs.
• After a collision, the molecules resume moving in straight lines until the next interaction takes place.

This concept helps in explaining many properties of gases, such as diffusion and pressure exerted on container walls. The straight line motion itself is a significant simplification that allows for analytical studies and practical applications of gas behaviors.