1.5.3Additional lessons
The Ideal Gas Equation — IB Chemistry SL Revision Notes & Topical Questions
5 min read 5 parts Lesson 17 of 98
Part 1 of 5The Equation
The ideal gas equation links four properties of a gas.
Equation
- PV = nRT, where P is pressure, V volume, n amount in moles and T temperature in kelvin.
Gas constant
- R = 8.31 J K⁻¹ mol⁻¹ is the same for all gases, and is given in the data booklet.
SI units
- Use pressure in Pa, volume in m³ and temperature in K so that the units match R.
Rearrangements
- The same equation gives V = nRT ÷ P, P = nRT ÷ V, n = PV ÷ RT and T = PV ÷ nR.
Part 2 of 5Unit Conversions
Most errors arise before the numbers go into the equation.
1
Convert temperature to kelvin by adding 273 to the Celsius value.
2
Convert volume to m³: divide cm³ by 10⁶, or divide dm³ by 1000.
3
Convert pressure to Pa: multiply kPa by 1000, and note that 1 atm is about 1.01 × 10⁵ Pa.
4
Substitute and calculate, then convert the answer back to the unit requested, such as dm³.
| Quantity | Unit needed | Convert from |
|---|---|---|
| Temperature | K | °C + 273 |
| Volume | m³ | dm³ ÷ 1000; cm³ ÷ 10⁶ |
| Pressure | Pa | kPa × 1000 |
Part 3 of 5Real Gases
Real Gases
Close to ideal
- Real gases behave most like ideal gases at high temperature and low pressure.
Deviation at high pressure
- Particles are close together, so their own volume is no longer negligible.
Deviation at low temperature
- Particles move slowly enough for intermolecular forces to matter and the gas may liquefy.
Molar mass
- Using PV = nRT with n = m ÷ M gives M = mRT ÷ PV, which is used to find the molar mass of a gas.
Part 4 of 5Worked Example
Question Calculate the volume, in dm³, of 0.500 mol of an ideal gas at 300 K and 150 kPa.
- P = 150 kPa = 1.50 × 10⁵ Pa; T = 300 K.
- V = nRT ÷ P = (0.500 × 8.31 × 300) ÷ (1.50 × 10⁵) = 8.31 × 10⁻³ m³.
- Convert8.31 × 10⁻³ m³ × 1000 = 8.31 dm³.
Answer 8.31 dm³
Part 5 of 5Exam Checklist & Tips
1.5.3 – Key Points for the Exam
- Ideal gas equation PV = nRT, relating pressure, volume, amount and temperature of an ideal gas.
- Gas constant R, equal to 8.31 J K⁻¹ mol⁻¹.
- Pascal The SI unit of pressure, equal to one newton per square metre.
- Real gas A gas whose behaviour departs from that predicted for an ideal gas.
Common Mistakes
- Leaving the temperature in °C or the volume in dm³ when substituting.
- Using kPa for pressure without converting to Pa.
- Stating that real gases are most ideal at high pressure and low temperature.
- Mixing up the amounts in moles with mass in grams.
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