Labor für ideale Gase
Hüpfende Moleküle, echte Physik: Der Druck entsteht aus Wandstößen, während P·V = n·R·T live erhalten bleibt.
Das ist echte Molekulardynamik — kein vorgetäuschter Druck. Teilchen fliegen und prallen elastisch von den Wänden ab, und der Druck wird aus dem Impuls gemessen, den sie auf die Wände übertragen (er entspricht dem theoretischen N·k_B·T/A). Heizen Sie das Gas, damit die Moleküle schneller werden, ziehen Sie den Kolben, um das Volumen zu ändern, fügen Sie Teilchen hinzu und beobachten Sie, wie P·V = n·R·T mit R = 8,314 J/(mol·K) im Gleichgewicht bleibt.
Voreinstellungen
Messwerte
Formeln & Quellen
P·V = n·R·T (R = 8.314 J/mol·K)
P from wall-collision impulse (measured)
½m⟨v²⟩ ∝ T (kinetic theory)
Boyle P∝1/V · Charles V∝T · Gay-Lussac P∝T
The units and constants behind this gas
pV = nRT carries four units at once — pascal, litre, kelvin and mole. Since 2019 the gas constant R is not measured at all: it is the product of two numbers the SI fixes by definition.
Where R comes from
- R = 8.314462618 J mol⁻¹ K⁻¹ Molar gas constant · exact, because R = N_A · k_B and both of those are fixed by definition
- N_A = 6.02214076 × 10²³ mol⁻¹ Avogadro constant · defines the mole — one mole is this many particles, by definition
- k_B = 1.380649 × 10⁻²³ J K⁻¹ Boltzmann constant · defines the kelvin — it turns a temperature into an energy per particle
How much room one mole of any ideal gas takes up
| Condition | Temperature | Pressure | Molar volume |
|---|---|---|---|
| IUPAC standard (0 °C, 100 kPa) | 273.15 K | 100 kPa | 22.711 L/mol |
| 0 °C at one atmosphere | 273.15 K | 101.325 kPa | 22.414 L/mol |
| Room temperature (25 °C) | 298.15 K | 101.325 kPa | 24.465 L/mol |
| Boiling water (100 °C) | 373.15 K | 101.325 kPa | 30.620 L/mol |
Computed live as V/n = R·T/p, using the exact molar gas constant from our constants page. The answer does not depend on which gas it is — that is what makes it ideal.
R stopped being a measured number in 2019
The 2019 SI redefinition fixed the Boltzmann constant (which defines the kelvin) and the Avogadro constant (which defines the mole). The gas constant is their product, R = N_A · k_B, so it inherited their exactness — 8.314 462 618… J mol⁻¹ K⁻¹, with no uncertainty left to measure.
See the seven defining constants →