Ideal gas law
Relate pressure, volume and temperature of a gas.
This public page keeps the free explanation visible and leaves premium worked solving, advanced walkthroughs, and saved study tools inside the app.
Core idea
Overview
The ideal gas law is an equation of state that relates the pressure, volume, temperature, and amount of a hypothetical ideal gas. It serves as a fundamental approximation for the behavior of many gases under various conditions by combining Boyle's, Charles's, and Avogadro's laws.
When to use: Apply this equation when gas particles are far enough apart that their individual volumes and intermolecular attractions are negligible. It is most accurate at high temperatures and low pressures, typical of many atmospheric and laboratory conditions.
Why it matters: It is essential for calculating the properties of gases in diverse fields such as meteorology, chemical engineering, and respiratory physiology. Understanding this law allows for the prediction of how gases will expand or contract in response to environmental changes.
Symbols
Variables
p = Pressure, V = Volume, n = Moles, R = Gas Constant, T = Temperature
Walkthrough
Derivation
Formula: Ideal Gas Law
An equation of state combining Boyle's, Charles's, and the pressure laws for an idealised gas.
- Gas molecules occupy negligible volume.
- Collisions are perfectly elastic and there are no intermolecular forces.
Combine Experimental Laws:
For a fixed amount of gas, pressure times volume is proportional to absolute temperature (in kelvin).
Macroscopic Form (Moles):
Uses n (moles) and R (molar gas constant).
Microscopic Form (Molecules):
Uses N (number of molecules) and k (Boltzmann constant).
Result
Source: AQA A-Level Physics — Thermal Physics
Visual intuition
Graph
The graph forms a hyperbola because pressure is inversely proportional to volume. For a physics student, this means that as volume increases, the gas particles have more space to move, causing pressure to drop, while small volumes force particles into a tighter space, resulting in high pressure. The most important feature is that the curve never touches the axes, meaning that pressure and volume can never reach zero, as that would imply the gas occupies no space or exerts no force.
Graph type: hyperbolic
One free problem
Practice Problem
Practice Problem 1
A 2.0 mole sample of oxygen gas is contained in a 5.0 liter vessel at a temperature of 300 K. Calculate the pressure exerted by the gas in atmospheres.
Solve for:
Hint: Rearrange the formula to p = nRT / V and ensure the gas constant R is in L·atm/mol·K.
Practice Problem 2
A weather balloon contains 10.0 moles of helium gas at a pressure of 101325 Pa and a temperature of 273 K. Find the volume of the balloon in cubic meters.
Solve for:
Hint: When using SI units (Pascals and Joules), the resulting volume will be in cubic meters.
Practice Problem 3
A 0.5 mole sample of nitrogen gas exerts a pressure of 2.0 atmospheres in a 6.0 liter container. What is the temperature of the gas in Kelvin?
Solve for:
Hint: Isolate the temperature variable by dividing the product of pressure and volume by the product of moles and the gas constant.
The full worked solution stays in the interactive walkthrough.
Where it shows up
Real-World Context
When estimating gas pressure in a cylinder, Ideal gas law is used to calculate Pressure from Volume, Moles, and Gas Constant. The result matters because it helps turn a changing quantity into a total amount such as area, distance, volume, work, or cost.
Study smarter
Tips
- Always convert temperature to Kelvin by adding 273.15 to the Celsius value.
- Check that your units for pressure and volume match the units of the gas constant R being used.
- Remember that n is the amount in moles; if given mass, divide by the molar mass first.
Avoid these traps
Common Mistakes
- Using Celsius instead of Kelvin.
- Mixing liters and m³.
Common questions
Frequently Asked Questions
An equation of state combining Boyle's, Charles's, and the pressure laws for an idealised gas.
Apply this equation when gas particles are far enough apart that their individual volumes and intermolecular attractions are negligible. It is most accurate at high temperatures and low pressures, typical of many atmospheric and laboratory conditions.
It is essential for calculating the properties of gases in diverse fields such as meteorology, chemical engineering, and respiratory physiology. Understanding this law allows for the prediction of how gases will expand or contract in response to environmental changes.
Using Celsius instead of Kelvin. Mixing liters and m³.
When estimating gas pressure in a cylinder, Ideal gas law is used to calculate Pressure from Volume, Moles, and Gas Constant. The result matters because it helps turn a changing quantity into a total amount such as area, distance, volume, work, or cost.
Always convert temperature to Kelvin by adding 273.15 to the Celsius value. Check that your units for pressure and volume match the units of the gas constant R being used. Remember that n is the amount in moles; if given mass, divide by the molar mass first.
References
Sources
- AQA A-Level Physics — Thermal Physics