Engineering · Chemical Engineering · Thermochemistry
Equilibrium Constant Calculator
Calculates the equilibrium constant (Kc) for a chemical reaction from the molar concentrations of reactants and products at equilibrium.
Calculator
Formula
For a general reaction aA + bB ⇌ cC + dD: [A] and [B] are the molar concentrations of reactants A and B (mol/L); [C] and [D] are the molar concentrations of products C and D (mol/L); a, b, c, d are the stoichiometric coefficients of each species. Kc is dimensionless when referenced to a standard concentration of 1 mol/L.
Source: IUPAC Compendium of Chemical Terminology (Gold Book), 2nd Ed.; Atkins' Physical Chemistry, 11th Ed., Oxford University Press.
How it works
When a reversible reaction reaches equilibrium, the ratio of product concentrations to reactant concentrations — each raised to their stoichiometric coefficient — remains constant at a given temperature. This constant, Kc, is derived from the law of mass action and is a thermodynamic property that depends only on temperature, not on initial concentrations or the path taken to reach equilibrium.
For the general reaction aA + bB ⇌ cC + dD, the equilibrium constant is expressed as Kc = ([C]^c × [D]^d) / ([A]^a × [B]^b), where square brackets denote molar concentrations in mol/L at equilibrium. Pure solids and pure liquids are excluded from the expression by convention, as their activities are defined as unity. This calculator supports reactions with up to two reactant and two product species; if a species is absent, set its concentration to 1 and its coefficient to 0.
Kc values are widely applied in reactor design, chemical process engineering, environmental chemistry, and biochemistry. A large Kc (≫ 1) indicates the reaction strongly favors products; a small Kc (≪ 1) indicates the reverse reaction is favored. The natural and base-10 logarithms of Kc are also output because they directly link to Gibbs free energy change: ΔG° = −RT ln Kc, enabling thermodynamic feasibility analysis.
Worked example
Consider the synthesis of ammonia via the Haber process: N₂ + 3H₂ ⇌ 2NH₃
At equilibrium, suppose the concentrations are measured as: [N₂] = 0.50 mol/L, [H₂] = 0.20 mol/L, and [NH₃] = 0.80 mol/L.
The stoichiometric coefficients are: a = 1 (N₂), b = 3 (H₂), c = 2 (NH₃). There is no second product, so set [D] = 1 mol/L and d = 0.
Step 1 — Numerator (products): [NH₃]² × [D]⁰ = (0.80)² × (1)⁰ = 0.6400 × 1 = 0.6400
Step 2 — Denominator (reactants): [N₂]¹ × [H₂]³ = (0.50)¹ × (0.20)³ = 0.50 × 0.0080 = 0.004000
Step 3 — Kc: Kc = 0.6400 / 0.004000 = 160.0
Step 4 — ln Kc: ln(160.0) ≈ 5.0752
Step 5 — log₁₀ Kc: log₁₀(160.0) ≈ 2.2041
A Kc of 160 indicates the equilibrium strongly favors ammonia production under these conditions, consistent with the Haber process being economically viable.
Limitations & notes
This calculator assumes ideal solution behavior, where activity coefficients are equal to unity and concentrations directly represent thermodynamic activities. In real concentrated solutions or high-pressure gas-phase reactions, activity coefficients deviate significantly from 1, requiring the use of thermodynamic activity-based equilibrium constants (Ka). Additionally, Kc strictly applies to homogeneous equilibria in solution; for gas-phase reactions, Kp (in terms of partial pressures) is often more appropriate, related to Kc via Kp = Kc(RT)^Δn, where Δn is the change in moles of gas. The calculator supports up to two reactants and two products; more complex multi-species reactions require a generalized approach. Pure solids and liquids must be manually excluded by setting their concentration to 1 and coefficient to 0. Temperature changes will alter Kc, so all equilibrium concentrations must be measured at the same, well-defined temperature.
Frequently asked questions
What does a large Kc value mean for a chemical reaction?
A large Kc value (much greater than 1) means the equilibrium position lies far to the right, strongly favoring the formation of products. In practical terms, nearly all of the reactants will be converted to products before equilibrium is established, making the reaction highly efficient from a yield perspective.
What is the difference between Kc and Kp?
Kc is the equilibrium constant expressed in terms of molar concentrations (mol/L) and is most commonly used for reactions in solution. Kp is expressed in terms of partial pressures and is typically used for gas-phase reactions. They are related by the equation Kp = Kc(RT)^Δn, where Δn is the change in the number of moles of gas, R is the gas constant, and T is the absolute temperature in kelvin.
How is the equilibrium constant related to Gibbs free energy?
The standard Gibbs free energy change ΔG° is directly related to the equilibrium constant by ΔG° = −RT ln Kc, where R is the universal gas constant (8.314 J/mol·K) and T is the absolute temperature. A negative ΔG° corresponds to Kc > 1 (product-favored), while a positive ΔG° corresponds to Kc < 1 (reactant-favored). This linkage makes ln Kc a critical output for thermodynamic analysis.
Do pure solids or liquids appear in the equilibrium constant expression?
No. By convention in thermodynamics, the activities of pure solids and pure liquids are defined as exactly 1, so they do not appear in the Kc expression. For example, in the reaction CaCO₃(s) ⇌ CaO(s) + CO₂(g), only the concentration (or pressure) of CO₂ appears in the equilibrium expression. In this calculator, exclude such species by setting their concentration to 1 and their stoichiometric coefficient to 0.
Does Kc change if I add more reactant to the system at equilibrium?
No. Kc is a constant at a given temperature and does not change when concentrations are altered. However, adding more reactant will temporarily shift the reaction quotient Q away from Kc, and the reaction will proceed in the forward direction to re-establish equilibrium, consistent with Le Chatelier's principle. Only a change in temperature will change the value of Kc itself.
Last updated: 2025-01-15 · Formula verified against primary sources.