Same chemistry as the 3D reactor, viewed through a reactor cross-section plus a live optimization curve. The reaction is the 1913 Haber-Bosch synthesis:
N2(g) + 3H2(g) ⇌ 2NH3(g) ΔH° ≈ -92.4 kJ/mol, ΔS° ≈ -198.1 J/(mol·K)
The equilibrium constant is computed from the integrated van't Hoff relation (constant ΔH°, ΔS°): ΔG°(T) = ΔH° - T·ΔS°, so
Kp(T) = exp( -ΔH°/(R·T) + ΔS°/R )
For a stoichiometric 1:3 N2:H2 feed with N2 conversion x, the ideal-gas mole fractions are y_N2=(1-x)/(4-2x), y_H2=3(1-x)/(4-2x), y_NH3=2x/(4-2x), and the equilibrium expression Kp = y_NH3²/(y_N2·y_H2³)·P⁻² is solved for x by bisection every time a slider moves — that x_eq is the thermodynamic ceiling, higher at lower T and higher P exactly as Le Chatelier's principle predicts, since the forward reaction is exothermic and loses 2 mol of gas per mol of N2.
But the reactor only spends a finite residence time τ in the catalyst bed, so it never fully reaches that ceiling. A simplified Arrhenius rate constant k(T) = A·exp(-Ea/(R·T)) (Ea ≈ 110 kJ/mol, scaled by catalyst activity) sets how fast the gas relaxes toward equilibrium:
x_achievable(T) = x_eq(T) · [ 1 - exp( -k(T)·τ ) ]
This is the real kinetics-vs-equilibrium tradeoff that governs industrial ammonia converters: raise the temperature and k(T) grows fast (more conversion per second), but x_eq(T) shrinks (less conversion is thermodynamically allowed). The product of a rising rate term and a falling equilibrium ceiling produces a hump — a single interior optimum temperature — visible on the live achievable-yield curve below the reactor. Real multi-bed converters approximate this optimum with a falling temperature profile from bed to bed, and typically settle around 400-500 °C, 150-300 atm as the practical compromise this simulator lets you rediscover by hand.