Ammonia Equilibrium Haber–Bosch synthesis, general chemistry
N2(g) + 3 H2(g) ⇌ 2 NH3(g)
Kinetic energy of the molecules (Maxwell–Boltzmann)
Free energy vs reaction quotient
Conditions
25 °C
1.0 atm
Pressures (atm)
Equilibrium? No
PN₂
0.25
25.0 %
PH₂
0.75
75.0 %
PNH₃
0.00
0.0 %
Readouts
How this simulation works
What you control
Temperature (25–600 °C) changes both the equilibrium constant Kp and the rate at which the mixture moves toward equilibrium.
Pressure (1–300 atm, total) does not change Kp, but compresses the mixture so the reaction quotient Q changes and the mixture shifts toward the side with fewer moles of gas.
Add N2 / Add H2 / Remove NH3 change the amounts in the vessel; the mixture is then out of equilibrium and relaxes back.
Catalyst sets the activation energy shown on the Maxwell–Boltzmann plot and the speed of the approach to equilibrium. No catalyst: nothing happens on any human time-scale, at any temperature in range.
The simulation runs in real time: the "time to reach equilibrium" readout tells you how long the wait will be at the current settings.
Thermodynamics
ΔH°(T) and ΔS°(T) are computed at every temperature from the NIST-JANAF Shomate functions of N2, H2 and NH3; Kp = exp(−ΔG°/RT) with the 1 atm standard state used by the gauges. At 25 °C Kp ≈ 5.6×105; at 450 °C ≈ 5×10−5. The lower plot is the free energy of the whole mixture at fixed T and P as the reaction proceeds, drawn against log Q; its minimum is at log Kp, and the marker shows where the vessel is now.
Kinetics
The vessel relaxes toward its equilibrium composition with a first-order rate constant k(T) = kref·exp[−(Ea/R)(1/T − 1/723 K)]. Iron (promoted magnetite, the Haber–Bosch catalyst) is calibrated so that 95 % of the approach takes 20 s at 450 °C, a realistic converter residence time; its apparent activation energy of ≈70 kJ/mol comes from Temkin–Pyzhev and Somorjai's Fe(111) measurements. Ruthenium (Cs–Ru/MgO type) uses the literature apparent Ea ≈ 100 kJ/mol and is set 10× faster than iron at 450 °C, matching the 10–20× activity advantage reported for industrial Ru catalysts. "No catalyst" uses the computed gas-phase barrier of 524 kJ/mol (N2 + H2 → NNH2, Hwang & Mebel 2003); no homogeneous rate has ever been measured.
The Maxwell–Boltzmann curve is the true distribution of molecular kinetic energies at the set temperature. On a linear scale the fraction of molecules above 70 kJ/mol is invisible (about 1 in 105 at 450 °C); switch on the log scale to see the tail and how it grows with temperature. The table under the plot gives the exact fraction for each activation energy.
Sources
Chase, NIST-JANAF Thermochemical Tables (1998); Larson & Dodge, JACS 1923; Larson, JACS 1924; Temkin & Pyzhev 1940; Dyson & Simon, Ind. Eng. Chem. Fundam. 1968; Spencer, Schoonmaker & Somorjai, J. Catal. 1982; Kitano et al., Nat. Commun. 2015; Hwang & Mebel, J. Phys. Chem. A 2003; Appl, Ullmann's Encyclopedia 2011. Full reference lists are in the project's literature folder.