Ideal Gas Law
The Ideal Gas Law is an equation of state for a hypothetical ideal gas, combining the empirical gas laws of Boyle, Charles, and Gay-Lussac into a single relationship between the pressure, volume, amount, and absolute temperature of a gas. It assumes gas molecules have negligible volume and no intermolecular forces, making it an excellent approximation for real gases at low pressures and high temperatures. It is foundational to thermodynamics, chemistry, and engineering, used in everything from weather balloon calculations to industrial gas storage and the analysis of respiratory physiology.
Key Formula
P × V = n × R × T
LaTeX: PV = nRT
| Symbol | Meaning | Unit |
|---|---|---|
| P | Absolute pressure of the gas | Pa (N m⁻²) |
| V | Volume of the gas | m³ |
| n | Amount of substance (moles) | mol |
| R | Universal gas constant (8.314 J mol⁻¹ K⁻¹) | J mol⁻¹ K⁻¹ |
| T | Absolute temperature | K |
Worked Example
Problem
A container holds 2 mol of an ideal gas at a temperature of 300 K and a pressure of 200 000 Pa. What is the volume of the gas?
Solution
Step 1: Write the ideal gas law: PV = nRT. Step 2: Solve for V: V = nRT / P. Step 3: Substitute values: V = (2 × 8.314 × 300) / 200 000 = 4988.4 / 200 000 = 0.02494 m³.
Answer
V ≈ 0.0249 m³ = 24.9 litres
Summary of Empirical Gas Laws Unified by the Ideal Gas Law
| Law | Constant Variables | Relationship | Formula |
|---|---|---|---|
| Boyle's Law | n, T | P inversely proportional to V | PV = constant |
| Charles's Law | n, P | V directly proportional to T | V/T = constant |
| Gay-Lussac's Law | n, V | P directly proportional to T | P/T = constant |
| Avogadro's Law | P, T | V directly proportional to n | V/n = constant |
| Ideal Gas Law | None | Combines all above | PV = nRT |
Interactive Tools
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Related Terms
Boyle's Law
Boyle's Law states that for a fixed amount of an ideal gas at constant temperature, the pressure of the gas is inversely proportional to its volume — when volume doubles, pressure halves, and vice versa. Mathematically, the product PV remains constant. This relationship arises because compressing a gas into a smaller volume increases the frequency of molecular collisions with the container walls, thereby raising pressure. It is applied in everyday contexts from tyre pumps and syringes to scuba diving depth calculations and the design of pneumatic systems.
Charles's Law
Charles's Law states that for a fixed amount of an ideal gas at constant pressure, the volume of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), volume doubles. This is an isobaric (constant pressure) process, and the ratio V/T remains constant. The law explains why a balloon expands when warmed, why hot air rises in atmospheric convection, and why gas-filled containers must be stored away from heat sources to prevent rupture.
Gay-Lussac's Law
Gay-Lussac's Law states that for a fixed amount of an ideal gas at constant volume, the pressure of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), pressure doubles. This isochoric (constant volume) relationship arises because higher temperatures cause gas molecules to collide with the container walls more frequently and with greater force. It explains why sealed aerosol cans or vehicle tyres can burst if overheated, and why pressure cookers build up pressure as the internal temperature rises above 100 °C.
The term "ideal gas" (from Latin "idealis" — of an idea/concept) was introduced to describe a theoretical gas obeying a perfectly simple equation. The combined law PV = nRT was formalised by Émile Clapeyron in 1834 after assembling the earlier empirical observations of Boyle (1662), Charles (1787), Gay-Lussac (1809), and Avogadro (1811).