The equilibrium constant is the cornerstone of quantitative chemistry: it tells you exactly how far any reversible reaction proceeds before the forward and reverse rates equalise. This calculator bundles four tools into one tabbed interface — direct Kc/Kp evaluation, a full ICE-table solver, the van’t Hoff temperature-shift equation, and a reaction-quotient comparator — so you can tackle any equilibrium problem without switching between separate pages.
The equilibrium expression
For a generic reaction aA + bB ⇌ cC + dD the concentration-based equilibrium constant is:
Kc = [C]^c · [D]^d / ([A]^a · [B]^b)
where each bracket denotes equilibrium molar concentration in mol/L. The pressure-based equivalent uses partial pressures and satisfies Kp = Kc(RT)^Δn, where Δn is the net change in moles of gas. When Δn = 0 the two constants are numerically identical.
The Kc/Kp tab accepts the pre-computed product-activity numerator and reactant-activity denominator directly, letting you solve for Kc, for a product concentration, or for a reactant concentration. It also reports log₁₀(Kc), ln(Kc), and the standard Gibbs free energy change ΔG° = −RT ln Kc at 298 K as a quick thermodynamic reality-check.
ICE table mode
The ICE (Initial–Change–Equilibrium) method is the standard approach for exam and lab problems. You fill in species labels, stoichiometric coefficients, initial concentrations and — in “calculate Kc” mode — the net change column. The tool computes Kc immediately.
Switch to find-x mode, enter a target Kc instead, and the calculator runs a bisection algorithm (500 iterations, converges to 12 significant figures) to find the extent-of-reaction x. Every equilibrium concentration appears in the table, and the result is verified by back-substituting x into the Kc expression so you can check the solver’s accuracy.
van’t Hoff equation
The van’t Hoff equation links Kc at two temperatures via the standard enthalpy of reaction:
ln(K₂/K₁) = −(ΔH°/R)(1/T₂ − 1/T₁)
R = 8.314 J mol⁻¹ K⁻¹; temperatures must be in kelvin. The van’t Hoff tab solves for K₂, for ΔH°, or for T₂ depending on which quantity you need. A plain-English sentence interprets the sign of ΔH° — endothermic reactions shift right when heated, exothermic reactions shift left — translating the equation into Le Chatelier language.
Reaction quotient Q vs Kc
Before a system reaches equilibrium you can compute the reaction quotient Q using instantaneous (non-equilibrium) concentrations with the same formula as Kc. Comparing Q to Kc instantly predicts reaction direction:
- Q < Kc — forward reaction is spontaneous; more products will form.
- Q > Kc — reverse reaction is spontaneous; products decompose back to reactants.
- Q = Kc — the mixture is already at equilibrium.
The Q vs Kc tab highlights the result with a colour-coded banner (green, amber, red) so the conclusion is impossible to miss.
Worked example
A 1 L flask contains 0.50 mol/L N₂O₄ initially (no NO₂). At 298 K the equilibrium constant Kc for N₂O₄ ⇌ 2 NO₂ is 4.64 × 10⁻³.
Open the ICE Table tab, set N₂O₄ as a reactant (coeff = 1, initial = 0.50) and NO₂ as a product (coeff = 2, initial = 0). Switch to find-x mode, enter Kc = 0.00464 and press Calculate. The solver returns x ≈ 0.0332 mol/L, giving equilibrium concentrations of about 0.467 mol/L for N₂O₄ and 0.0664 mol/L for NO₂. Back-substituting: Kc = (0.0664)² / 0.467 ≈ 0.00464 — verified.
Now open the van’t Hoff tab: set K₁ = 0.00464 at T₁ = 298 K, ΔH° = +57 200 J/mol, and solve for K₂ at T₂ = 350 K. The result is K₂ ≈ 0.157 — the reaction shifts strongly toward NO₂ at higher temperature, consistent with its endothermic character.
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