The Ideal Gas Equation
\(pV = nRT\)
Mandatory SI Units
To use this equation, you must convert all values into strict SI units. Failure to do so guarantees an incorrect answer.
| Symbol | Quantity | SI Unit | Common Conversion |
|---|---|---|---|
| \(p\) | Pressure | Pa (N m⁻²) | kPa × 1000 = Pa |
| \(V\) | Volume | m³ | dm³ ÷ 1000 = m³ ; cm³ ÷ 10⁶ = m³ |
| \(n\) | Moles | mol | - |
| \(R\) | Gas constant | 8.31 J K⁻¹ mol⁻¹ | Given in Data Booklet |
| \(T\) | Temperature | K | °C + 273 = K |
Worked Example: Determining Molar Mass
Problem
A 0.250 g sample of a volatile liquid vaporises to occupy 98.0 cm³ at 100°C and 103 kPa. Calculate the relative molecular mass.
Step 1: Unit conversions
T = 100 + 273 = 373 K
V = 98.0 ÷ 10⁶ = 9.80 × 10⁻⁵ m³
p = 103 × 1000 = 103000 Pa
Step 2: Rearrange for n
\(n = \frac{pV}{RT} = \frac{103000 \times 9.80 \times 10^{-5}}{8.31 \times 373}\)
\(n = 3.255 \times 10^{-3}\) mol
Step 3: Calculate molar mass
\(M = \frac{m}{n} = \frac{0.250}{3.255 \times 10^{-3}}\)
\(M = \) 76.8 g mol⁻¹
⚠️ Examiner Trap. Unit Mismatching
The vast majority of marks lost in S1.5 calculations come from unit mismatching. Common errors:
- Using kPa instead of Pa
- Using cm³ or dm³ instead of m³
- Forgetting to convert °C to K (Celsius can produce negative values, breaking the equation)
Always convert units FIRST, before substituting into the equation.
Try the Gas Law Calculator
Practise your own PV = nRT calculations with instant unit conversions and step-by-step solutions.
The Combined Gas Law
For a sealed system where the amount of gas stays constant:
\[\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}\]
Units for p and V just need to be consistent on both sides. Temperature must always be in Kelvin.
Molar Volume at STP
📘 IB Standard Conditions
At STP (Standard Temperature and Pressure: T = 273.15 K, P = 100 kPa), the molar volume of any ideal gas is:
\(V_m = 22.7 \text{ dm}^3 \text{ mol}^{-1}\)
This means one mole of any gas occupies 22.7 dm³ at STP, regardless of which gas it is. This value is in the Data Booklet.
⚠️ Examiner Tips
- The IB will not assess the names of individual gas laws (Boyle's, Charles's, Gay-Lussac's). You only need the equations and how to apply them.
- The constant R = 8.31 J K⁻¹ mol⁻¹ requires SI units (Pa, m³, K). If your answer is off by a factor of 1000, you probably forgot a unit conversion.
- Unit conversions are the number one source of lost marks in gas law questions. Always convert before substituting.