What is the ideal gas equation?

Short Answer

The ideal gas equation is a mathematical relationship that describes the behaviour of an ideal gas. It combines pressure (P), volume (V), temperature (T), and number of moles (n) into one formula:
PV = nRT.

Here, R is the universal gas constant. This equation helps predict how a gas will behave when temperature, pressure, or volume changes. It is widely used because many gases behave nearly ideally under normal conditions, making the ideal gas equation useful for calculations in chemistry and physics.

Detailed Explanation

Ideal Gas Equation

The ideal gas equation is one of the most important equations in chemistry. It brings together several individual gas laws—Boyle’s law, Charles’s law, Gay-Lussac’s law, and Avogadro’s law—into a single general equation:
PV = nRT

This equation describes how pressure, volume, temperature, and number of moles of a gas are related. It assumes that the gas behaves ideally, meaning the gas particles have no attraction between them and occupy no actual volume. Although real gases do not perfectly follow these assumptions, the ideal gas equation still works well for most gases at normal temperature and pressure.

Meaning of each term in the equation

  • P (Pressure): The force gas molecules exert on the walls of the container, usually measured in atmospheres (atm) or pascals (Pa).
  • V (Volume): The space occupied by the gas, measured in litres (L) or cubic meters (m³).
  • n (Moles): The amount of gas substance, measured in moles (mol).
  • R (Gas constant): A fixed value used in the equation. Common value:
    R = 0.0821 L·atm/mol·K
  • T (Temperature): Must always be in Kelvin (K), not Celsius.

The relationship PV = nRT shows that if one variable changes, the others must adjust to maintain balance.

How the ideal gas equation is derived

The equation combines four basic gas laws:

  1. Boyle’s Law (P ∝ 1/V at constant T and n)
  2. Charles’s Law (V ∝ T at constant P and n)
  3. Gay-Lussac’s Law (P ∝ T at constant V and n)
  4. Avogadro’s Law (V ∝ n at constant P and T)

By putting these proportionalities together, we get:
PV ∝ nT

To convert this proportionality into an equation, we add the gas constant R:
PV = nRT

When gases behave ideally

Gases behave nearly ideally when:

  • Temperature is high
  • Pressure is low
  • Gas particles move freely and have minimal attraction

Under these conditions, the ideal gas equation gives very accurate results.

When gases deviate from ideal behaviour

Real gases do not always behave ideally. Deviations occur when:

  • Pressure is very high
  • Temperature is very low
  • Gas molecules interact strongly with each other
  • Volume of gas molecules becomes significant

In such situations, the ideal gas equation becomes less accurate, and chemists use the van der Waals equation instead. However, for most everyday calculations, PV = nRT works well.

Uses of the ideal gas equation

The ideal gas equation is used widely in chemistry and physics:

  1. Calculating gas volume or pressure

By rearranging the equation, we can find unknown values.
For example, V = nRT / P.

  1. Finding the number of moles of a gas

n = PV / RT is used when gas samples are collected in experiments.

  1. Understanding gas behaviour

It explains how gases expand when heated or compress when pressure increases.

  1. Gas stoichiometry

Used to calculate gas amounts in reactions when gases are not at STP.

  1. Determining molar mass of a gas

If mass and gas conditions are known, molar mass can be calculated.

  1. Environmental and atmospheric studies

Helps model gas behaviour in the atmosphere, pollution levels, and weather patterns.

  1. Engineering applications

Used in designing engines, airbags, gas cylinders, and refrigeration systems.

Examples of using the ideal gas equation

Example 1:
If 1 mole of gas is at 1 atm and 273 K:
V = nRT / P
V = (1 × 0.0821 × 273) / 1
V ≈ 22.4 L
This shows the molar volume of a gas at STP.

Example 2:
To find pressure if 2 moles of gas occupy 10 L at 300 K:
P = nRT / V
P = (2 × 0.0821 × 300) / 10
P ≈ 4.93 atm

Conclusion

The ideal gas equation, PV = nRT, is a powerful equation that describes the relationship between pressure, volume, temperature, and moles of a gas. It is based on the behaviour of ideal gases but works well for many real gases under ordinary conditions. The equation is widely used in chemical calculations, gas stoichiometry, environmental studies, and engineering applications. Understanding the ideal gas equation helps explain how gases behave in different situations and makes gas calculations simple and reliable.