Chemical equilibrium · five routes to K

One reaction.
Several routes to equilibrium.

Compare equilibrium constants from Gibbs energies, formation properties, enthalpy and entropy, a reference K, and equilibrium activities. Keep the reaction basis, temperature and standard states consistent.

Reaction and property data

Property sources and standard statesEvaluation temperature / KReference temperature / KMinimum valid model T / KMaximum valid model T / KGas standard pressure p° / kPaSolute standard concentration c° / mol L⁻¹

K is dimensionless. All supplied thermodynamic properties must use these same standard states and the reaction as written. Changing p° or stoichiometry does not automatically transform the independent input properties.

Reaction and formation properties Reactants negative; products positive

Species table · CSV or TSV

Header: species,nu,phase,atoms,charge,Gf,n0. Gf is ΔfG° in kJ/mol of species at the stated formation-data T; n0 is mol. Phases: gas, solute, liquid (solution), pureLiquid, solid. Atoms are explicit counts such as N:2;O:4. The synthetic example uses formal atom X.

Formation-data temperature / K

Balance checks use the atom counts and charges you provide; species names are not parsed as chemical formulas. No standard formation energy is guessed.

Direct reaction Gibbs energy

ΔrG° / kJ per mol of reactionTemperature of this ΔrG° / K

Enthalpy, entropy and heat capacity Values at Tref, per reaction as written

ΔrH°(Tref) / kJ mol⁻¹ΔrS°(Tref) / J mol⁻¹ K⁻¹Constant ΔrCp° / J mol⁻¹ K⁻¹

Both ΔCp°=0 and constant supplied ΔCp° are evaluated. The declared temperature interval must exclude phase changes and ranges where these approximations fail.

Reference equilibrium constant

Input conventionReference value at Tref

van ’t Hoff uses this independent reference value and ΔH° above, with or without the ΔCp° correction. Use logarithms for extreme constants.

Composition, activities and Q Independent observations at one T

Activity inputActivity table · CSV or TSV

Header: species,value,coefficient. In composition mode: gas value=y and coefficient=φ; solute value=c in mol/L and coefficient=γ; liquid value=x and coefficient=γ. In direct mode value=a and coefficient=1. Present pure solids/liquids require 1,1. Use positive values for finite ln Q.

Observation temperature / K These observations are asserted to be at equilibrium

Without this assertion the result is Q, not K. An assertion does not independently establish experimental equilibrium. Pure-phase unit activities assume that those phases are present.

Reaction extent example One neutral ideal-gas reaction at fixed T,P

Observation and extent pressure / kPaNonreacting ideal gas in extent feed / molK source for extent and driving force

Initial amounts come from n0 in the species table. The extent solver excludes charged gases, condensed phases, multiple reactions and phase splitting. Nonideal φ/γ supplied for Q are not used as an EOS in this solver.

Compare thermodynamic K

Direct and formation Gibbs energies apply only at their supplied temperature. Scroll the table horizontally on narrow screens. Energy values are per reaction as written.

Temperature plot scale

Teal: constant ΔH° approximation. Amber: constant ΔCp° correction. Solid lines use Kref; dashed lines use ΔH° and ΔS°. Supplied Gibbs-energy data appear as points only. Matching curves can overlap.

Formation-energy sum

Observed activities: Q or inferred K

From K to equilibrium composition

Five routes, one standard-state convention

1. ln K = -ΔrG°/(RT) 2. ΔrG° = ΣᵢνᵢΔfGᵢ° 3. ΔrG°(T) = ΔrH°(T) - TΔrS°(T) 4. ln[K(T)/Kref] = ΔrH°ref/R (1/Tref - 1/T) 5. K = Πᵢaᵢ^νᵢ only at equilibrium

Reaction coefficients are positive for products and negative for reactants. Reversing a reaction gives Knew=1/K; multiplying all coefficients by c gives Knew=K^c. Reaction-level energies and entropies must be transformed on the same basis. The app does not silently reconcile conflicting independent inputs.

For gases aᵢ=φᵢyᵢP/p°. For solutes on the supplied molarity standard aᵢ=γᵢcᵢ/c°. A liquid solution uses aᵢ=γᵢxᵢ relative to the pure-liquid standard. Unit activities for pure solids and liquids require their presence. The composition panel admits one gas phase and one liquid-solution phase; omitted mole fractions can represent nonreacting components.

All formation and reaction properties must use the same species phases and standard states. No automatic conversion of molarity, molality, pure-liquid or gas standards is performed. Individual-ion activity coefficients are convention dependent; no electrolyte model is supplied.

Heat-capacity correction Constant reaction ΔCp° over the declared interval

ΔH°(T) = ΔH°ref + ΔCp°(T - Tref) ΔS°(T) = ΔS°ref + ΔCp° ln(T/Tref) ln[K(T)/Kref] = ΔH°ref/R (1/Tref - 1/T) + ΔCp°/R [ln(T/Tref) + Tref/T - 1]

The two corrected routes agree only if Kref and the reference ΔH°/ΔS° are mutually consistent. A point value of ΔG° does not provide a temperature law. No polynomial Cp, phase-transition correction or external property database is assumed.

ln K is retained when exponentiating would overflow or underflow; such K values are labeled rather than replaced by zero or infinity. A finite ln K does not guarantee that a nearly depleted equilibrium composition can be resolved in floating-point arithmetic.

Ideal-gas extent and validation

nᵢ=nᵢ,0+νᵢξ defines the feasible extent interval. The solver brackets ln Q(ξ)−ln K at fixed T and total pressure, then independently checks atom conservation. For the admitted single neutral ideal-gas reaction, Gibbs energy is convex along ξ, so the resolved stationary state is the global minimum within that model. The reported relative total Gibbs energy divided by RT has units of mol.

Pressure changes the composition even though standard K depends only on temperature for the fixed standard-state convention. Inert gas affects this fixed-pressure calculation by dilution. This is not the same constraint as adding inert gas to a rigid ideal-gas vessel.

No multireaction minimizer, charged-gas solver, nonideal EOS, reaction–phase equilibrium or electrochemical cell is included. Electrochemistry is the next lab.

Sources and reproducibility

IUPAC: standard equilibrium constant · IUPAC: equilibrium constant and stoichiometric convention · Temperature dependence of K · Calculation source · Regenerate figures