The ideal gas equation is one of the most powerful and widely used formulas in chemistry. It connects pressure, volume, temperature, and number of moles into a single relationship that describes how gases behave under many conditions. In IB Chemistry, PV = nRT shows up repeatedly in stoichiometry, gas law problems, thermodynamics, and even equilibrium. Understanding how to apply it confidently is essential for success in the course.
The Ideal Gas Equation
The equation is:
PV = nRT
Each variable represents:
- P = pressure (Pa or kPa)
- V = volume (m³ or dm³)
- n = number of moles
- R = gas constant (8.314 J mol⁻¹ K⁻¹)
- T = temperature (K)
This equation works because ideal gases are assumed to behave perfectly—meaning particles don’t attract each other and occupy negligible volume.
When to Use the Ideal Gas Equation
You apply PV = nRT when:
- Temperature, pressure, or volume changes
- You need to find moles of gas
- You want to convert between mass and volume
- You analyze gas behavior under non-extreme conditions
- You perform gas stoichiometry
- You analyze molar volume at standard conditions
- You handle thermodynamic calculations involving gases
Because moles appear in the equation, PV = nRT is a bridge between gas law relationships and stoichiometric relationships.
Key Requirements: Correct Units
The most common IB exam mistakes come from incorrect units.
For PV = nRT to work properly:
Pressure
Use Pascals (Pa) or convert kPa → Pa
1 kPa = 1000 Pa
Volume
Use m³
1 dm³ = 0.001 m³
Temperature
Use Kelvin (K)
K = °C + 273
Small errors in unit conversion can lead to answers being off by factors of 10 or 100, so always check before substituting values.
Understanding Each Part of the Equation
Pressure (P)
Increasing pressure compresses gas particles into a smaller space, raising collision frequency.
Volume (V)
A larger volume spreads particles out, reducing collisions.
Number of Moles (n)
More moles → more particles → greater pressure at constant volume.
Temperature (T)
Higher temperature increases kinetic energy, causing more forceful collisions.
Gas Constant (R)
A universal constant that maintains consistency between units in the equation.
Together, these relationships describe gas behavior in a predictable way.
Rearranging PV = nRT
You may need to solve for different variables:
To find moles:
n = PV / RT
To find volume:
V = nRT / P
To find pressure:
P = nRT / V
To find temperature:
T = PV / nR
Rearranging correctly is essential for exam accuracy.
Worked Example (IB-Style)
Question: Calculate the number of moles of gas in a 2.50 dm³ container at 100 kPa and 298 K.
Step 1: Convert units
V = 2.50 dm³ = 0.00250 m³
P = 100 kPa = 100,000 Pa
Step 2: Use PV = nRT
n = (100000 × 0.00250) ÷ (8.314 × 298)
n ≈ 0.101 mol
This type of calculation appears frequently on Paper 1 and Paper 2.
Limitations of the Ideal Gas Equation
Real gases deviate from ideal behavior at:
- Very high pressure
- Very low temperature
- Conditions where intermolecular forces become significant
- Situations involving large, heavy, or polar molecules
However, under standard laboratory conditions, gases behave close enough to “ideal” that PV = nRT works well.
FAQs
Why do gases need to be in Kelvin?
Temperature must be proportional to kinetic energy, which begins at absolute zero (0 K). Celsius scale does not reflect this physics correctly.
Does the ideal gas equation work for all gases?
It works well for many common gases at moderate temperature and pressure. For extreme conditions, the van der Waals equation or real gas corrections are needed.
Why do we convert volume to m³?
Because R uses SI units, and consistency is required to ensure correct calculations.
Conclusion
The ideal gas equation, PV = nRT, unifies several gas laws into one powerful formula that describes the behavior of gases under most practical conditions. By mastering its variables, units, rearrangements, and applications, you can confidently tackle gas-related questions in IB Chemistry and understand real-world gas behavior more clearly.
