Kinetic Theory of Gases | Chemistry for EmSAT Achieve PDF Download

Kinetic Theory of Gases

The kinetic theory of gases delves into the microscopic nature of atoms and molecules constituting a gas to elucidate its three major properties. While solids and liquids can be characterized by tangible attributes like size and shape, gases lack a fixed shape or size, making direct measurements of mass and volume challenging. This theory proves invaluable in understanding gases under such conditions.

By leveraging the kinetic theory of gases, the physical attributes of any gas can be predominantly defined through three measurable macroscopic properties: the pressure, volume, and temperature of the container in which the gas resides. Let's explore this concept further.

Table of Contents

• What Is the Kinetic Theory of Gases?
• Kinetic Theory of Gases Assumptions
• Kinetic Theory of Gases Postulates
• Understanding Gas Behaviour
• Maxwell and Boltzmann Distribution of Energy and Velocity

Exploring the Kinetic Theory of Gases

• The Kinetic Theory of Gases: An Overview
• Assumptions Underlying the Kinetic Theory of Gases
• Key Postulates of the Kinetic Theory of Gases
• Insight into Gas Behavior
• Examining Maxwell and Boltzmann's Energy and Velocity Distributions

The kinetic theory of gases serves as a theoretical framework that delineates the molecular composition of gases in terms of myriad submicroscopic particles, encompassing atoms and molecules. Moreover, it elucidates that gas pressure emanates from particles colliding with each other and the container walls. Notably, this theory defines fundamental properties like temperature, volume, and pressure, alongside transport properties such as viscosity, thermal conductivity, and mass diffusivity, encapsulating all phenomena linked to the microscopic realm.

Kinetic Theory of Gases Overview

• The kinetic theory of gases is crucial for establishing a connection between the macroscopic properties and microscopic behaviors.
• It aids in examining the movement of gas molecules, which are in constant motion, colliding with each other and container walls.
• This theory also enhances our comprehension of phenomena like Brownian motion.

Kinetic Theory of Gases Assumptions

• Gas consists of a vast number of atoms or molecules.
• Atoms or molecules within a gas are minute particles with negligible mass.
• Particles are widely spaced apart, with inter-particle distances significantly greater than their sizes.
• Particles do not interact with each other and are autonomous.
• Gas particles are constantly in motion, moving randomly in various directions in a straight line due to the absence of interactions and ample free space.

Kinetic Theory of Gases

• Volume of Gas: Gas particles fill the total volume of the container they are in, regardless of its size, considering the container's volume as the gas volume.
• Mean Free Path: This represents the average distance a particle travels before colliding with another particle.
• Kinetic Energy of the Particle: Gas particles, being in constant motion, possess kinetic energy that is directly proportional to the gas temperature.
• Constancy of Energy/Momentum: When gas particles collide with each other or the container, these collisions are perfectly elastic, meaning they do not alter the energy or momentum of the particles.
• Pressure of Gas: Gas particles striking the container walls exert a force, resulting in pressure. The gas pressure is related to the frequency of collisions per unit time and area on the container walls.

The kinetic theory of gases aids in comprehending how macroscopic properties emerge from microscopic behaviors.

Key Concepts About Gases:

• Gases are composed of numerous tiny particles, such as atoms and molecules. These particles are significantly smaller than the spaces between them, with most of the gas volume being empty.
• The gas particles are in constant random motion, leading to collisions among themselves and with the container walls. When gas molecules collide with the container walls, they transfer momentum, creating measurable force known as pressure.
• Collisions between gas molecules and container walls are perfectly elastic, meaning no kinetic energy is lost during collisions. As a result, gas molecules maintain a constant speed without slowing down.
• The average kinetic energy of gas particles changes with temperature. Higher temperatures correspond to higher average kinetic energy of the gas.
• Gas molecules do not exert any attractive or repulsive forces on each other except during collisions.

Gas Laws of Ideal Gases:

In understanding the behavior of ideal gases, we explore how pressure relates to the number of gas particles at a constant volume.

• Pressure is directly proportional to the number of gas particles present in a container at a constant volume. More gas particles lead to a higher frequency of collisions with the container walls, resulting in increased pressure.

Summary of Gas Laws

• Relationship between Gas Amount and Pressure

  When the amount of gas in a container is increased at constant temperature and volume, the pressure also increases. This is because a larger number of gas particles result in more collisions with the container walls, leading to higher pressure.

• Avogadro's Law

  Avogadro's Law states that at constant pressure, the volume of a gas is directly proportional to the number of particles present. If the pressure is to remain constant, increasing the volume reduces the frequency of collisions per unit area.

• Boyle's Law

  Boyle's Law explains that at constant temperature, the pressure of a gas is inversely proportional to its volume. When the volume decreases, the particle density increases, leading to more collisions per unit area and higher pressure.

• Amonton's Law

  Amonton's Law states that at constant volume, the pressure of a gas is directly proportional to its temperature. As temperature increases, the kinetic energy of particles rises, causing more frequent collisions with the container walls and thus increasing pressure.

• Charles's Law

  Charles's Law describes the direct proportionality between the volume of a gas and its temperature at constant pressure. When temperature increases, the volume occupied by the gas also increases to maintain a constant pressure.

Key Concepts in Gas Laws

• Boyle's Law: When the pressure of a gas increases, its volume decreases proportionally, provided the temperature remains constant.
• Charles's Law: At constant pressure, volume changes proportionally to temperature.
• Avogadro's Law: Equal volumes of gases at the same temperature and pressure contain the same number of molecules.
• Graham Law of Diffusion: The velocity of gas molecules is inversely proportional to the square root of their molecular weights.

Understanding Non-ideal Gas Behavior

All gas molecules adhere to ideal gas laws under specific conditions of low pressure and high temperature. However, deviations from ideal gas behavior occur due to incorrect assumptions in the postulates. These deviations include:

• Wrong Assumptions: Real gases deviate from ideal behavior due to flawed assumptions made in the gas laws.
• Causes of Deviation: The main reasons behind the deviation of real gases are attributed to factors like molecular interactions and volume occupied by gas molecules.
• Van der Waals Equation: This equation corrects the ideal gas law by considering the volume occupied by gas molecules and the attractive forces between them.
• Critical Point: The point at which a gas can no longer be liquefied, regardless of pressure applied, is known as the critical point.

The Kinetic Theory of Gases

• The particles in a gas are not point charges and possess some volume. This is evident as gases cannot be compressed to zero volume.
• Gas particles interact based on their nature, influencing gas pressure. Interactions and volumes vary among different gases, leading to the development of gas laws with correction factors.
• Particle collisions in gases are elastic, involving energy exchange. As a result, gas particles exhibit a range of energies rather than possessing the same energy.

Maxwell–Boltzmann Molecular Distribution of Energy and Velocity

The kinetic theory of gases asserts that gas particles are in constant motion and their kinetic energy is directly proportional to the gas temperature.

Maxwell–Boltzmann utilized this theory to determine the energy distribution of gas particles from zero to infinity, enabling the calculation of the most probable, average, and root mean square velocities of particles.

For additional study material, refer to JEE Main Kinetic Theory of Gases Previous Year Questions with Solutions on EduRev.

Frequently Asked Questions on Kinetic Theory of Gases

What is the main concept behind the kinetic theory of gases?

• Kinetic theory provides insights into gas behavior by suggesting that gases are made up of swiftly moving atoms or molecules.

Could you explain what real gases are?

• Real gases are those that exhibit behaviors departing from those of ideal gases.

Define mean energy in the context of gases.

• Mean energy, also known as the internal energy of a gas denoted by U, is the kinetic energy of one mole of gas.

What are the fundamental assumptions of the kinetic model?

• The simplest kinetic model is based on the following assumptions:
  • The gas comprises numerous identical molecules moving randomly and independently in all directions, with significant distances between them.
  • Molecules engage in perfectly elastic collisions with each other and the container walls, without any energy loss, and do not interact otherwise.
  • Heat transfer occurs through the exchange of kinetic energy between molecules.

Can you elaborate on the concept of degree of freedom (n)?

• Degree of freedom refers to the count of independent ways in which a system's configuration and position can alter.

What is the degree of freedom for a monoatomic gas molecule?

• The degree of freedom for a monoatomic gas molecule is n = 3.

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