Ideal Gas Concept

Simple idea of an ideal gas that perfectly follows the kinetic theory assumptions and gas laws.

1. What Is an Ideal Gas?

An ideal gas is a theoretical gas whose molecules behave exactly as described by the kinetic theory. It does not exist in reality but helps us understand real gases better.

The idea of an ideal gas makes calculations and concepts simpler because the molecules behave perfectly according to certain assumptions.

2. Assumptions of an Ideal Gas

An ideal gas obeys a set of assumptions that make the behavior easy to describe using simple equations.

2.1. 1. Molecules Have Negligible Volume

The size of each molecule is so small compared to the total volume that we treat them as point particles.

2.2. 2. No Intermolecular Forces

Molecules do not attract or repel each other. They move freely until they collide.

2.3. 3. Perfectly Elastic Collisions

When molecules collide, no kinetic energy is lost. They bounce off each other and the walls without losing speed.

2.4. 4. Continuous Random Motion

Molecules move in all possible directions randomly, with speeds that depend on temperature.

3. Equation of State for an Ideal Gas

An ideal gas obeys the famous relation:

PV = nRT

where:

  • P = pressure
  • V = volume
  • n = number of moles
  • R = universal gas constant
  • T = absolute temperature

3.1. Meaning of the Equation

The equation shows how pressure, volume, and temperature are related. Changing any one of these changes the others.

4. Microscopic Interpretation

Using kinetic theory, pressure and temperature can be expressed in terms of molecular motion.

P = \dfrac{1}{3} \rho \bar{c^2}

where:

  • \( \rho \) = mass per unit volume
  • \( \bar{c^2} \) = mean square speed

4.1. Connection to Temperature

Temperature is directly related to average kinetic energy of molecules. That's why ideal gas behavior matches kinetic theory.

5. Ideal Gas vs Real Gas

Real gases behave like ideal gases only under certain conditions:

  • Low pressure
  • High temperature

Under these conditions, intermolecular forces become negligible.

5.1. When Real Gases Deviate

At high pressure and low temperature, molecules come very close. Intermolecular forces become significant, and real gases no longer follow PV = nRT perfectly.

6. Why the Ideal Gas Concept Is Useful

Even though ideal gases don’t exist, the concept is extremely useful because many gases behave almost ideally in normal conditions. This makes predictions easier and helps understand real gas deviations.

6.1. Practical Example

Air behaves nearly as an ideal gas at room temperature and atmospheric pressure, so PV = nRT works well for everyday calculations.