The formula
- Ideal gas law
PV = nRT- Comparing two states of a fixed amount of gas
P₁V₁ / T₁ = P₂V₂ / T₂- Using mass and molar mass instead of moles
n = m / M, then PV = nRT- Molar volume at STP, 273.15 K and 1 atm
V / n = 22.4 L/mol
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
P | Pressure of the gas; P₁ and P₂ are the pressures in two different states of the same sample | atm (or Pa, matched to R) |
V | Volume of the container; V₁ and V₂ label the same two states | L (or m³, matched to R) |
n | Amount of gas | mol |
R | Molar gas constant | 0.08206 L·atm/(mol·K), or 8.314 J/(mol·K) |
T | Absolute temperature; T₁ and T₂ label the same two states | K |
m | Mass of the gas sample | g |
M | Molar mass of the gas | g/mol |
When it applies
- Temperature is in kelvin, always. Celsius makes every result wrong and a temperature at or below 0 °C makes it absurd.
- The value of R has to match the other units. Use 0.08206 L·atm/(mol·K) with atmospheres and liters, or 8.314 J/(mol·K) with pascals and cubic meters.
- The gas is far from condensing. Near its boiling point or at very high pressure, a real gas deviates and needs a corrected equation.
- For a mixture, n is the total moles of gas and P is the total pressure; each component contributes its own partial pressure.
Worked example
Problem. A 10.0 L vessel holds 2.50 mol of an ideal gas at 25.0 °C. What is the pressure, in atmospheres and in kilopascals?
- Convert the temperature to kelvin: T = 25.0 + 273.15 = 298.15 K.
- Choose R to match the units. Pressure in atmospheres and volume in liters calls for R = 0.08206 L·atm/(mol·K).
- Rearrange and substitute: P = nRT / V = (2.50 × 0.08206 × 298.15) / 10.0.
- The numerator is 61.17 L·atm, so P = 6.1166 atm, which is 6.12 atm.
- Convert to kilopascals with 1 atm = 101.325 kPa: 6.1166 × 101.325 = 619.8 kPa, so about 620 kPa.
- Cross-check in SI: with R = 8.314 J/(mol·K) and V = 0.0100 m³, P = (2.50 × 8.314 × 298.15) / 0.0100 = 6.197 × 10⁵ Pa = 620 kPa, which agrees.
Answer. 6.12 atm, which is about 620 kPa.
Common mistakes
- Leaving the temperature in Celsius, which is the single biggest source of wrong answers on this equation.
- Pairing the wrong R with the units in the problem, such as using 8.314 with liters and atmospheres.
- Using 22.4 L/mol away from STP. That molar volume belongs to 273.15 K and 1 atm, and at room temperature it is closer to 24.5 L/mol.
- Applying the two-state form when the amount of gas changed. P₁V₁/T₁ = P₂V₂/T₂ holds only while n stays fixed.
Related formulas
- Limiting reactant:
compare n(X) / coefficient(X) across reactants; the smallest value is limiting - Molar mass:
M = Σ (atoms of each element × atomic mass)