Properties of Substances and Mixtures
Gas Laws — AP CHEMISTRY Revision Notes & Topical Questions
5 min read 9 parts Lesson 4 of 20 Unit quiz
Lesson summary
Gas Laws — AP CHEMISTRY notes: Apply the ideal gas law, Dalton's law and the gas laws, interpret the kinetic molecular theory and the Maxwell-Boltzmann distribution, and explain non-ideal behaviour.Gas properties are defined by pressure P, volume V, temperature T and amount n in …
- Ideal gas equation
- Ideal gas assumptions
- Pressure units
- Partial pressure
- Gas collected over water
- Absolute zero is 0 K
Section 1 of 9The ideal gas law
Gas properties are defined by pressure P, volume V, temperature T and amount n in moles.
Ideal gas equation
- PV = nRT.What the symbols mean: p = pressure (Pa) · V = volume (m3) · n = amount of gas (mol) · R = 8.31 J mol−1 K−1 · T = temperature (K = °C + 273)
- R = 8.314 J mol−1 K−1 or 0.08206 L atm mol−1 K−1 or 62.36 L torr mol−1 K−1.
- Temperature must be in kelvin, and the units of R must match those of P and V.
Ideal gas assumptions
- Ideal gas assumptions particle volume is negligible compared with the container, and there are no intermolecular forces.
Pressure units
- 1 atm = 760 mmHg = 760 torr = 101.325 kPa = 1.01325 × 105 Pa.
At STP one mole occupies about 22.4 L.
Section 2 of 9Partial pressure and Dalton's law
Partial pressure and Dalton's law
Pressure
Pressure force per unit area, caused by collisions of particles with the container walls.
Dalton's law
- Dalton's law the total pressure of a mixture equals the sum of the partial pressures, PT = PA + PB + PC.
Partial pressure
Partial pressure mole fraction × total pressure, PA = XAPT, where XA = nA/ntotal.
Volume fraction can also give partial pressure.
Gas collected over water
- Pdry gas = Ptotal − PH2O, using the vapour pressure of water at that temperature.
Section 3 of 9The individual gas laws
| Law | Constant | Relationship | Graph |
|---|---|---|---|
| Boyle | T, n | P1V1 = P2V2 | V against P is a curve; V against 1/P is a straight line |
| Charles | P, n | V1/T1 = V2/T2 | V against T (kelvin) is a straight line to zero at 0 K |
| Avogadro | P, T | V1/n1 = V2/n2 | V against n is a straight line |
Combined
- P1V1/T1 = P2V2/T2 for a fixed amount of gas.
Gay-Lussac: at constant volume pressure is proportional to temperature.
Absolute zero is 0 K
−273.15 °C; real gases liquefy before reaching it.
Avogadro's hypothesis
- Avogadro's hypothesis equal volumes of gas at the same temperature and pressure contain equal numbers of molecules.
Section 4 of 9Kinetic molecular theory
1
Gas particles are tiny compared with the distances between them.
2
They move randomly in straight lines in all directions at various speeds.
3
Forces between them are negligible except in collisions.
4
Collisions are elastic, conserving total kinetic energy.
5
Average kinetic energy is proportional to absolute temperature.
KE
½mv2,
- so two gases at the same temperature have the same average kinetic energy but lighter particles move faster.What the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)
Pressure depends on how often and how forcefully particles strike the walls.
Section 5 of 9Maxwell-Boltzmann distribution
1
The curve shows how many molecules have each speed (or kinetic energy) at a given temperature.
2
The peak is the most probable speed.
3
Raising the temperature moves the peak to higher speed and flattens the curve, with the area under the curve unchanged.
4
Lowering the temperature moves the curve to the left with a higher peak.
5
Lighter gases give a broader curve with the peak at higher speed.
Section 6 of 9Non-ideal behaviour
For an ideal gas PV/RT
1 at all pressures.
Real gases deviate when intermolecular attractions and particle volume become significant.
- At low temperature the molecules have less kinetic energy and attract one another.
- At high pressure molecules are crowded, so attraction and their own volume matter.
Gases behave most ideally at high temperature and low pressure (large volume, high average kinetic energy).
Deviation from ideal behaviour decreases as temperature rises.
Section 7 of 9More from the specification
More from the specification
Absolute thermodynamic temperature scale
- Absolute thermodynamic temperature scale adopting the kelvin temperature scale provides a reliable physical means to formulate ideal gas volume relations.
Hydrogen
- A gas that gives a squeaky pop with a lighted splint.
Oxygen
- A gas that relights a glowing splint.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Ideal gas | Hypothetical gas obeying PV = nRT exactly. |
| Partial pressure | Pressure a gas would exert alone in a mixture. |
| Mole fraction | Moles of one gas divided by total moles of gas. |
| Elastic collision | Collision that conserves total kinetic energy. |
| Maxwell-Boltzmann distribution | Distribution of molecular speeds at a given temperature. |
| Absolute zero | 0 K, the lowest possible temperature. |
Section 9 of 9Exam technique
1
Using Celsius temperature in gas equations — use kelvin
2
Using an R value with units that do not match P and V
3
Forgetting to subtract water vapour pressure for a gas collected over water
4
Saying two gases at the same temperature have the same average speed — they have the same average kinetic energy
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