---
title: "The Gas Laws and the Ideal Gas Equation"
description: "Boyle's law, Charles's law and the pressure law are three slices of one relationship, pV = nRT, once the temperature is in kelvin. The equation gives any one of the four quantities when the other thre"
canonical: https://lightmysky.com/learn/science/the-gas-laws-and-the-ideal-gas-equation-mt_G7DOTVl4KM
source: https://lightmysky.com/learn/science/the-gas-laws-and-the-ideal-gas-equation-mt_G7DOTVl4KM.md
retrieved: 2026-09-12
---

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# The Gas Laws and the Ideal Gas Equation

Boyle's law, Charles's law and the pressure law are three slices of one relationship, pV = nRT, once the temperature is in kelvin. The equation gives any one of the four quantities when the other three are known.

Subject: Science · Area: Matter & Materials · Ages 15 to 17
Page: https://lightmysky.com/learn/science/the-gas-laws-and-the-ideal-gas-equation-mt_G7DOTVl4KM

## Ready when they can

- Uses pV over T staying constant to compare one fixed mass of gas in two states
- Applies pV = nRT with the amount in moles and the temperature in kelvin
- Sketches p against V and p against T and says what the shape of each line shows

## Lesson: One equation for every gas

For a fixed mass of gas, p V over T stays constant. Squeeze it at fixed temperature and pressure climbs as volume falls. Heat a sealed can from 300 K to 600 K and the pressure doubles with it.

The full form is p V equals n R T. Amount goes in as moles, temperature in kelvin, and R is 8.31. Convert Celsius first, since 200 degrees is 473 K and skipping that step wrecks the answer.

**Example.** Gas at 100 kPa fills 2.0 L, then expands to 4.0 L at fixed temperature. So 100 times 2.0 equals the new pressure times 4.0, giving 50 kPa. And 2.0 mol in 3.0 m3 at 300 K gives 2 times 8.31 times 300 over 3.0, which is 1662 Pa.

**Tip.** Read the graphs by shape. At fixed temperature, p against V is a falling curve. At fixed volume, p against T is a straight line through the origin. Mass over molar mass gives the moles to feed in.

**Recap.** Compare states with p V over T, solve all four with p V equals n R T in kelvin, and read curves for shape.

## Practice

13 questions on this page, each with its working shown.

## Needs first

- [Relative Formula Mass and the Mole](https://lightmysky.com/learn/science/relative-formula-mass-and-the-mole-mt_-SiMKJK4rH)
- [The Particle Model](https://lightmysky.com/learn/science/the-particle-model-mt_b6kZgqolEd)

## Opens up

- [Kinetic Theory: Pressure from Molecular Motion](https://lightmysky.com/learn/science/kinetic-theory-pressure-from-molecular-motion-mt_2ARUheICqu)
- [Thermodynamic State Variables and PV Diagrams](https://lightmysky.com/learn/science/thermodynamic-state-variables-and-pv-diagrams-mt_G3EYx84GZK)