Chemistry 20 · Gases
Four quantities, one equation
Pressure, volume, temperature and amount. Every named gas law is the ideal gas law with two of them held still, which means there is really only one thing to learn — plus one rule about kelvins that causes more lost marks than anything else in the unit.
- 1. The words, first
- 2. The kinetic molecular theory
- 3. The gas laws
- 4. The ideal gas law and molar volume
- 5. What costs marks
The words, first
The idea: Most of the difficulty here is units. Getting them straight in advance removes most of the arithmetic risk.
| Word | What it means |
|---|---|
| Pressure | Force per unit area from particles colliding with the walls. Measured in kilopascals (kPa), atmospheres (atm) or millimetres of mercury. |
| Standard atmospheric pressure | 101.325 kPa = 1 atm = 760 mm Hg. |
| Absolute zero | −273.15 °C, the zero of the Kelvin scale. Nothing is colder. |
| Kelvin | The absolute temperature scale: K = °C + 273. No degree symbol, and never negative. |
| STP | Standard Temperature and Pressure: 0 °C and 101.325 kPa. Molar volume 22.4 L/mol. |
| SATP | Standard Ambient Temperature and Pressure: 25 °C and 100 kPa. Molar volume 24.8 L/mol. |
| Molar volume | The volume occupied by one mole of gas at stated conditions. It is the same for any gas, which is Avogadro's insight. |
| Ideal gas | A model gas whose particles have no volume and no attractions. Real gases follow it closely except at high pressure and low temperature. |
| R | The universal gas constant, 8.314 kPa·L/(mol·K). The units tell you what the other quantities must be in. |
The kinetic molecular theory
The idea: A gas is mostly empty space with particles flying through it at random. Every gas law is a consequence of that picture.
- Particles are in constant, random motion and their own volume is negligible.
- Collisions are elastic — no kinetic energy is lost.
- There are no significant attractions between particles.
- Average kinetic energy depends only on temperature.
That last point does real work. At the same temperature, H₂ and CO₂ have the same average kinetic energy, ½mv². Hydrogen molecules are much lighter, so they must be moving much faster — which is why light gases diffuse and effuse more quickly.
Where the model breaks. Squeeze a gas hard enough and the particles' own volume stops being negligible; cool it enough and attractions start to matter. That is exactly when a real gas stops obeying PV = nRT — and also when it condenses.
The gas laws
The idea: Each named law holds two quantities constant and says how the other two trade off. Learn the combined law and the rest fall out of it.
Boyle. 2.0 L at 100 kPa compressed to 1.0 L: P₂ = (100)(2.0)/1.0 = 200 kPa. Halving the volume doubles the pressure.
Charles. 6.0 L at 300 K heated to 600 K: 12.0 L. This only works in kelvins — doubling 27 °C to 54 °C does not double anything.
Combined. 3.0 L at 200 kPa and 300 K, taken to 100 kPa and 400 K:
V₂ = P₁V₁T₂/(T₁P₂) = (200)(3.0)(400)/[(300)(100)] = 8.0 L
Lower pressure and higher temperature both expand a gas, so an answer above 3.0 L was expected. Checking the direction before checking the arithmetic catches most errors instantly.
The ideal gas law and molar volume
The idea: PV = nRT connects a measurable volume to an amount in moles, which is what links this unit to every calculation in the rest of the course.
Units are not optional. With R = 8.314, pressure must be in kPa, volume in L, temperature in K and amount in mol. Any other combination silently produces a wrong number.
Worked example. 5.0 L at 150 kPa and 300 K:
n = PV/(RT) = (150)(5.0)/[(8.314)(300)] ≈ 0.30 mol
Molar volume as a shortcut. At SATP, one mole of any gas occupies 24.8 L, so a volume converts straight to an amount without touching PV = nRT. A 2.0 g sample occupying 1.24 L at SATP: n = 1.24/24.8 = 0.050 mol, so M = 2.0/0.050 = 40 g/mol.
STP or SATP? 22.4 L/mol is STP; 24.8 L/mol is SATP. Questions state which, and using the wrong one gives an answer that is about 10% out and looks perfectly plausible.
What costs marks
The idea: Three of the four are unit errors, which means they are fixable by habit rather than by understanding.
- Celsius in a gas law. Convert to kelvins first, every time, before you write anything else down.
- Millilitres left unconverted. R expects litres.
- Using 22.4 L/mol at SATP. Read the conditions in the question.
- Not sanity-checking the direction. If you heated a gas and the volume came out smaller, something is wrong.