How to use PV = nRT, choose the correct gas constant R, apply Boyle/Charles/Gay-Lussac, and convert temperatures to kelvin.
The ideal gas law relates pressure, volume, amount of substance, and temperature for a gas that behaves ideally:
PV = nRT- P — pressure
- V — volume
- n — moles of gas
- R — universal gas constant (units must match P and V)
- T — absolute temperature in kelvin
Real gases approach ideal behavior at low pressure and moderate-to-high temperature (well above condensation).
Choosing R
| R | Units | Typical use |
|---|---|---|
| 0.082057 | L·atm/(mol·K) | P in atm, V in L |
| 8.314 | J/(mol·K) | SI; energy and thermodynamics |
| 62.364 | L·Torr/(mol·K) | P in Torr or mmHg |
Mismatch of R with pressure/volume units is the most common source of error.
Temperature Must Be Absolute
Always convert Celsius to kelvin before substituting:
T(\mathrm{K}) = T(^\circ\mathrm{C}) + 273.15Special Cases (Constant n)
| Law | Condition | Relation |
|---|---|---|
| Boyle | T fixed | $P_1 V_1 = P_2 V_2$ |
| Charles | P fixed | $V_1/T_1 = V_2/T_2$ |
| Gay-Lussac | V fixed | $P_1/T_1 = P_2/T_2$ |
| Combined | n fixed | $P_1 V_1 / T_1 = P_2 V_2 / T_2$ |
Worked Example
Find the volume of 2.00 mol of an ideal gas at 1.00 atm and 25.0 °C.
$T = 298.15$ K, $R = 0.082057$ L·atm/(mol·K)
$V = nRT/P = (2.00)(0.082057)(298.15)/(1.00) ≈ 48.9$ L
At common chemistry STP (0 °C, 1 atm), one mole occupies about 22.4 L.
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