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.
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
Compare states with p V over T, solve all four with p V equals n R T in kelvin, and read curves for shape.
More to read
9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
Squeeze a gas and pressure climbs; heat it and pressure climbs too. The ideal gas law packs all of this into p V = n R T. Amount goes in as moles, temperature as kelvin, and R = 8.31 bridges the units. One equation answers how tires, lungs, and syringes behave. Learn its rearrangements until they feel automatic.
13.3 The Ideal Gas Law
Kinetic theory pictures gases as crowds of tiny elastic balls. Their battering on the walls is pressure, and their average energy sets temperature. This model predicts the gas laws instead of just describing them. When molecules crowd or attract, reality drifts from the ideal. The model still anchors everything that follows.
9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions
Gases meet chemistry through the mole. Convert grams to moles, run the gas equation, then convert back to whatever the question wants. Car airbags, breathing calculations, and industrial tanks all reduce to this pipeline. Volumes scale with moles at fixed T and p, which simplifies reacting gas questions.
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2 · Watch
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Where it sits
Learn first
Optional connections
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
13 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.