Real Gas Explorer
Molecular laboratory
Real molecules experience finite-size repulsion and intermolecular attraction.
Concept figure · Molecular speed distribution
For a Maxwell–Boltzmann gas, the most probable, mean and r.m.s. speeds are different.
Investigation
Compressibility against pressure
Ideal gas Z = 1. Real-gas values depend on pressure and temperature.
Maxwell–Boltzmann distribution
Characteristic speeds are marked for the current temperature.
Adjust the molecular state, then Check.
The chemistry
Ideal gas: pV = nRT. For university calculations use R = 8.314 J K⁻¹ mol⁻¹ and T(K) = θ(°C) + 273.15.
van der Waals equation: (p + an²/V²)(V − nb) = nRT, so p = nRT/(V − nb) − an²/V².
Constants: a has units Pa m⁶ mol⁻² and b has units m³ mol⁻¹. The parameters in each challenge are supplied for the named gas.
Compressibility: Z = pV/(nRT). Ideal gases have Z = 1. Values below 1 indicate attractive effects dominate the departure from ideality; values above 1 indicate repulsive or excluded-volume effects dominate.
Maxwell–Boltzmann speed density: f(v) = 4π(m/(2πkT))³ᐟ² v² exp(−mv²/(2kT)), where m is the mass of one molecule.
Speeds: v_mp = √(2kT/m), v_mean = √(8kT/(πm)), v_rms = √(3kT/m).
Constants: k = 1.38 × 10⁻²³ J K⁻¹ and N_A = 6.02 × 10²³ mol⁻¹. Molecular mass = molar mass/N_A.
Conventions: work done BY the gas is positive on expansion and negative on compression. Reversible boundary work is W_by = ∫p dV. No cyclic processes are included.
Assumptions: single-component gas in thermal equilibrium; classical, non-relativistic molecules; van der Waals equation used as an approximate single-phase equation of state; no chemical reactions. Calculations require T above 0 K, V above 0, and V greater than nb.