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.