What a learner can do afterwards
- Converts pressure to pascals, volume to cubic metres and temperature to kelvin before substituting anything
- Calculates the amount in moles of a gas from measured pressure, volume and temperature
- Finds the molar mass of an unknown gas from the mass of a measured volume of it
- Says which assumptions of the ideal model break down at high pressure or low temperature
1 · Read
One equation ties the four measurable properties of a gas together: pV equals nRT. Pressure times volume equals the amount in moles times the gas constant times absolute temperature. Use R as 8.314 joules per mol per kelvin, pressure in pascals, volume in cubic metres, and temperature in kelvin. The amount n comes out in moles.
Bench readings need converting before they go in. Multiply kilopascals by 1000 to reach pascals, divide cubic decimetres by 1000 to reach cubic metres, and add 273 to Celsius to reach kelvin. Most slips come from skipping these conversions, not from the algebra.
Try a sample at 25 C, 150 kilopascals and 2.0 cubic decimetres. Converted, that is 298 kelvin, 150000 pascals and 0.002 cubic metres. Rearrange to n equals pV over RT and the moles drop out. Weigh the flask full and empty for the mass, then divide mass by n to get the molar mass.
Real gases stray when particles crowd or slow down. At high pressure each particle occupies a noticeable chunk, so the free space is less than V. Near condensing, attractions tug particles together and the pressure drops below ideal. Point particles with no attractions is the model; squeeze or chill, and it breaks.
Convert to pascals, cubic metres and kelvin, then pV equals nRT turns bench readings into moles. Divide a measured mass by that mole count to get the molar mass. Real gases only match this when they are not too cold or too squeezed.
More to read
9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
One equation ties the four measurable properties of a gas together: pV equals nRT. Pressure times volume equals the amount in moles times the gas constant times absolute temperature. Before touching it, convert everything: kilopascals times 1000 into pascals, cubic decimetres divided by 1000 into cubic metres, and Celsius plus 273 into kelvin. Most lost marks come from skipping these conversions, not from the algebra.
9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions
The gas equation doubles as a weighing scale for invisible gases. Measure p, V and T of your sample, rearrange to n equals pV over RT, and you know how many moles sit in the flask. Weigh the flask full and empty to get the mass, then divide mass by n for the molar mass. The same trick feeds into reacting gas volumes and partial pressures.
9.6 Non-Ideal Gas Behavior
Real gases only behave ideally when particles are far apart and moving fast. Squeeze them to high pressure and each particle occupies a noticeable chunk of the volume, so the free space is less than V. Chill them toward condensing and attractions tug particles together, dropping the pressure below ideal. The kinetic theory assumes point particles with no attractions. High pressure breaks the first half and low temperature breaks the second.
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2 · Watch
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Optional connections
8 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.