The formula
- Molar form
pV = nRT- Molecular form
pV = Nk_BT- Comparing two states of the same fixed amount of gas
p₁V₁ / T₁ = p₂V₂ / T₂
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
p | Absolute pressure | Pa |
V | Volume | m³ |
n | Amount of gas | mol |
R | Molar gas constant | 8.314 J/(mol·K) |
T | Absolute temperature | K |
N | Number of molecules | dimensionless count |
k_B | Boltzmann constant | 1.38 × 10⁻²³ J/K |
When it applies
- The gas is dilute enough that molecules rarely interact, which covers nearly every classroom and laboratory condition.
- Temperature in kelvin, never degrees Celsius, and pressure absolute rather than gauge.
- The combined form applies when the amount of gas is fixed and you are comparing a before and an after state.
Worked example
Problem. What pressure does 2.0 mol of an ideal gas exert at 300 K inside a 0.025 m³ container?
- List the knowns: n = 2.0 mol, T = 300 K, V = 0.025 m³, R = 8.314 J/(mol·K).
- Rearrange the molar form: p = nRT / V.
- Evaluate the numerator: (2.0)(8.314)(300) = 4988.4 J.
- Divide by the volume: p = 4988.4 / 0.025 = 199,536 Pa, which is 2.0 × 10⁵ Pa to two significant figures.
Answer. About 2.0 × 10⁵ Pa, close to two atmospheres.
Common mistakes
- Leaving the temperature in degrees Celsius. 27 °C is 300 K, and using 27 changes the answer by a factor of more than ten.
- Mismatching the units of R with the units of pressure and volume. R = 8.314 J/(mol·K) requires pascals and cubic meters.
- Substituting a volume in liters. One liter is 1 × 10⁻³ m³.
- Applying the law near condensation or at very high pressure, where real gases stop behaving ideally.
Related formulas
- Bernoulli's equation:
p + ½ρv² + ρgy = constant - Pressure formula:
p = F / A