Short on time? This page is the recap. For explanations, graphs and worked examples, use the full study guide.
Recap
- Four properties describe a gas sample: pressure P, volume V, absolute temperature T and amount n.
- For an ideal gas they obey PV = nRT.
- Hold two variables fixed and the other two are either directly or inversely proportional.
- In a mixture, each gas exerts its own partial pressure, as if it were alone in the container. Partial pressures add up to the total.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| PV = nRT | R = 0.08206 L atm mol⁻¹ K⁻¹ or 62.36 L torr mol⁻¹ K⁻¹ | find any one of P, V, n, T |
| P₁V₁ / T₁ = P₂V₂ / T₂ | fixed n; T in K | find new conditions after a change |
| P_A = X_A × P_total | X_A = n_A ÷ n_total (no unit) | find a partial pressure in a mixture |
| P_total = P_A + P_B + … | same pressure units throughout | find the total, or one gas by subtraction |
| M = dRT / P | d in g L⁻¹ | find a molar mass from gas density |
| K = °C + 273.15; 1 atm = 760 torr | conversions | make units consistent |
Graph shapes
- V against T (K), P against T (K), V against n: straight lines through the origin.
- P against V at fixed n and T: a curve that falls and flattens. P against 1/V: straight line through the origin.
- V against T (°C): straight line that extrapolates to zero volume at −273.15 °C.
Assumptions behind the numbers
- The gas is ideal: particles have negligible volume and no attractions. This works best at low pressure and high temperature.
- No gas leaks in or out unless the question says so.
- In mixtures, the gases do not react with each other.
Mistakes to avoid
- Celsius instead of kelvin. Convert first, every time.
- R with the wrong units. torr needs 62.36, or convert to atm.
- Mass fractions instead of mole fractions.
- “Heavier gas, more pressure.” Pressure depends on moles, not mass.
- Calling P against V a straight line. It is a curve.
- Rounding early. Keep full values until the end.
Quick self-check
- What pressure does 1.00 mol of an ideal gas exert in 22.4 L at 273.15 K? (1.00 atm)
- At constant P and n, the temperature rises from 10 °C to 20 °C. By what factor does V change? (293.15 ÷ 283.15 = 1.035)
- A gas has mole fraction 0.25 in a mixture at 2.0 atm. What is its partial pressure? (0.50 atm)
Next: practice questions.