Equilibrium Constant from Conversion
Compute the equilibrium constant of a simple A ⇌ B reaction from the equilibrium conversion, Keq = X/(1 − X), where X is the fraction of reactant converted when the reaction reaches equilibrium. It shows the direct relation between how far a reaction 'goes' and its Keq: high conversions (X→1) imply a large Keq (favorable reaction); X = 0.5 gives Keq = 1 (equilibrium in the middle). Enter the equilibrium conversion (fraction).
Result
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Equilibrium constant from conversion
For a simple reversible reaction A ⇌ B, there is a direct bridge between how far the reaction proceeds and its equilibrium constant: Keq = X/(1 − X), where X is the equilibrium conversion (the fraction of A converted once the reaction stops progressing). The logic: at equilibrium, [B]/[A] = X/(1−X), and for this reaction Keq = [B]/[A]. The result is intuitive — if the reaction converts 80% before it stalls, Keq = 0.8/0.2 = 4 (products favored); if it converts only 50%, Keq = 1 (reactants and products equally stable); conversions above 50% give Keq > 1, below that they give Keq < 1. This links thermodynamics (Keq, and through it the Gibbs free energy ΔG° = −RT·ln Keq) to the practical outcome measured in the reactor. Reactions with a small Keq are equilibrium-limited: no matter how much time they are given, they never go past a certain conversion — unless equilibrium is 'tricked' by removing the product continuously (Le Chatelier's principle), as reactive distillation does. Enter the equilibrium conversion.
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