Equilibrium Calculators

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Chemical equilibrium is the state at which the rate of the forward reaction equals the rate of the reverse reaction, resulting in constant concentrations of reactants and products. The equilibrium constant Keq (or Kc for concentration-based) equals the ratio of product concentrations to reactant concentrations, each raised to their stoichiometric coefficients: Keq = [C]^c[D]^d / [A]^a[B]^b for aA + bB ⇌ cC + dD. Le Chatelier's principle predicts how equilibria shift in response to changes in concentration, pressure, or temperature. Biological equilibria govern enzyme kinetics, acid-base balance, protein folding, and receptor-ligand binding.

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Equilibrium Constant (Keq)

For: aA + bB ⇌ cC + dD. Keq = [C]^c [D]^d / [A]^a [B]^b. Pure solids and pure liquids are omitted. Kc: concentration-based (mol/L). Kp: pressure-based (for gases); Kp = Kc × (RT)^Δn. Keq > 1: products favored. Keq < 1: reactants favored. Keq = 1: roughly equal amounts of reactants and products.

Reaction Quotient (Q)

Q has the same form as Keq but uses non-equilibrium concentrations. Q < Keq: reaction proceeds forward. Q > Keq: reaction proceeds in reverse. Q = Keq: equilibrium reached.

Le Chatelier's Principle

When a stress is applied to a system at equilibrium, the system shifts to partially relieve that stress: Adding reactant: shifts right (toward products). Adding product: shifts left. Increasing pressure: shifts toward fewer moles of gas. Increasing temperature: shifts in the endothermic direction. Catalyst: does NOT shift equilibrium; only speeds attainment of equilibrium.

Relationship to ΔG°

ΔG° = −RT ln(Keq) = −2.303 RT log(Keq). At 25°C: ΔG° = −5.71 kJ/mol × log(Keq).

Glossary

Equilibrium Constant (Keq)
Keq = [products]^coeff / [reactants]^coeff; pure solids/liquids excluded; Keq > 1 = products favored; temperature-dependent; related to ΔG° = −RT ln(Keq).
Reaction Quotient (Q)
Q has the same form as Keq but uses actual (non-equilibrium) concentrations; Q < Keq → forward reaction; Q > Keq → reverse reaction; Q = Keq → equilibrium.
Le Chatelier's Principle
A system at equilibrium shifts to minimize applied stress; adding reactant shifts right; increasing T shifts endothermic direction; increasing pressure shifts to fewer gas moles; catalysts do not shift equilibrium.

Frequently Asked Questions

Chemical equilibrium: a dynamic state where forward and reverse reaction rates are equal → concentrations remain constant. Keq expression: for aA + bB ⇌ cC + dD: Keq = [C]^c × [D]^d / [A]^a × [B]^b. Important rules: pure solids (s) and pure liquids (l) are not included in Keq expressions. Keq depends only on temperature — not on concentrations, pressure, or catalysts. Example: N₂(g) + 3H₂(g) ⇌ 2NH₃(g). Keq = [NH₃]² / ([N₂][H₂]³). If Keq = 977 at 25°C: products (NH₃) strongly favored at equilibrium.

Q has the same mathematical form as Keq but uses the actual, current concentrations (not equilibrium concentrations). Comparing Q to Keq predicts reaction direction: Q < Keq: system has too many reactants relative to equilibrium → forward reaction occurs → products form until Q = Keq. Q > Keq: system has too many products → reverse reaction occurs → reactants form until Q = Keq. Q = Keq: system is already at equilibrium → no net change. Example: if Keq = 100 and Q = 0.5: Q < Keq → reaction goes forward. This is the same logic as the Nernst equation in electrochemistry: both use the ratio Q/Keq to predict direction.

Le Chatelier's principle: if a stress is applied to a system at equilibrium, the system responds to minimize that stress. Concentration change: Add reactant → shifts right (more products form to consume the added reactant). Remove product → shifts right (same logic). Add product → shifts left. Temperature change: Increase T → shifts in endothermic direction (because adding heat is the stress; endothermic reaction absorbs heat to oppose it). Decrease T → shifts in exothermic direction. Pressure change (gases): Increase pressure → shifts toward fewer moles of gas. Decrease pressure → shifts toward more moles of gas. Catalyst: doesn't shift equilibrium — only speeds up both forward and reverse reactions equally; equilibrium is reached faster but at the same Keq.

Biological systems are governed by equilibrium principles: Acid-base: Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA]); blood pH maintained near equilibrium of bicarbonate buffer. Receptor-ligand binding: Kd = [R][L]/[RL] (dissociation constant = inverse of binding constant Ka); determines fraction of receptors occupied at a given ligand concentration. Enzyme kinetics: Km approximates the Ks (substrate-enzyme dissociation constant) for simple mechanisms. Protein folding: ΔG of folding = RT ln(Keq_unfold/Keq_fold); folded state is stabilized by negative ΔG. ATP hydrolysis: highly exergonic (ΔG°' = −30.5 kJ/mol); far from equilibrium in cells (actual ΔG ≈ −50 kJ/mol due to low [ADP] and [Pi]) — cells maintain far-from-equilibrium conditions by coupling to metabolism.