Equilibrium Engine
Solve a nonlinear gas equilibrium. Explore reaction quotients, Gibbs energy and temperature dependence.
Gas-phase equilibrium vessel
Square particles represent A. Circular particles represent B.
Concept figure: reaction quotient
The system responds until its reaction quotient matches the equilibrium constant.
Set the equilibrium
Species amounts during equilibration
Gibbs energy landscape
Van 't Hoff relationship
The chemistry
Model reaction: A(g) ⇌ 2B(g). Standard pressure p° = 1 bar. All gases behave ideally.
Amounts at extent ξ: nA = nA,0 − ξ; nB = nB,0 + 2ξ. Units: mol.
Pressure quotient: Qp = (pB/p°)² / (pA/p°), where pi = yiP.
Standard Gibbs energy: ΔᵣG° = ΔᵣH° − TΔᵣS° = −RT ln Kp.
Van 't Hoff: ln Kp = −ΔᵣH°/(RT) + ΔᵣS°/R. The gradient of ln K against 1/T is −ΔᵣH°/R.
Reaction direction: ΔᵣG = RT ln(Qp/Kp). Forward if Q < K, reverse if Q > K.
Equilibrium calculation: numerically solve Qp(ξ) = Kp for an admissible ξ. A minimum of G(ξ) occurs at equilibrium.
Assumptions: ideal gases, fixed total pressure and temperature within each equilibrium calculation, constant ΔᵣH° and ΔᵣS°, no inert gas or side reactions. Kp and Qp are dimensionless.
R = 8.31 J mol⁻¹ K⁻¹. Temperature is in K, pressure in bar, and Gibbs energy in kJ.