Determine the equilibrium constant for a chemical reaction by entering the concentrations of products and reactants with their stoichiometric coefficients. Supports Kc calculations for reactions with up to two products and two reactants.
Every reversible reaction reaches equilibrium — a state where the forward and reverse reactions proceed at equal rates and concentrations stop changing. The equilibrium constant K describes where the balance sits: large K means products dominate, small K means reactants dominate, K ≈ 1 means roughly equal amounts. Once you know K for a reaction (from a table or measurement), you can predict the concentrations at any starting point and answer the central question of practical chemistry: how much product can I actually expect?
This calculator computes K_c (concentration-based equilibrium constant) from the equilibrium concentrations of products and reactants. The general expression is K_c = [products]ⁿ / [reactants]ᵐ, with each concentration raised to its stoichiometric coefficient from the balanced equation. For a reaction aA + bB ⇌ cC + dD, K_c = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ. Plug in concentrations and exponents and the calculator returns K.
Equilibrium constants run from very small (10⁻³⁰ for some unfavorable reactions) to very large (10²⁰ for strongly product-favored reactions), spanning more orders of magnitude than almost any other chemistry quantity. They're at the heart of pH calculations (K_w = 10⁻¹⁴ for water), solubility (K_sp), acid strength (K_a), buffer design, biochemistry (enzyme binding, protein folding), industrial chemistry, and environmental fate of pollutants. Mastering the K_c expression unlocks all of them.
**Scenario:** N₂ + 3 H₂ ⇌ 2 NH₃. At 25 °C and equilibrium: [N₂] = 0.50 M, [H₂] = 1.5 M, [NH₃] = 0.30 M. Compute K_c. **Calculation:** K_c = [NH₃]² / ([N₂][H₂]³) = (0.30)² / (0.50 × 1.5³) = 0.090 / 1.6875 = 0.0533. **Result:** K_c = 0.053 at 25 °C — small, meaning reactants are favored. Industrial Haber-Bosch synthesis runs at 400–500 °C and 200 atm to shift equilibrium toward NH₃ (despite the fact that the high temperature actually reduces K — pressure dominates).
**Scenario:** Acetic acid in water: CH₃COOH ⇌ H⁺ + CH₃COO⁻. At equilibrium in a 0.1 M solution: [H⁺] = 1.3 × 10⁻³ M, [CH₃COO⁻] = 1.3 × 10⁻³ M, [CH₃COOH] ≈ 0.1 M (since only ~1% dissociates). **Calculation:** K_a = [H⁺][CH₃COO⁻] / [CH₃COOH] = (1.3 × 10⁻³)² / 0.1 = 1.69 × 10⁻⁶ / 0.1 = 1.69 × 10⁻⁵. **Result:** K_a ≈ 1.7 × 10⁻⁵, pK_a = 4.76 — matches the literature value for acetic acid. This explains why vinegar (5% acetic acid) has pH ~2.5, not pH 0 (which would require complete dissociation like HCl).
**Scenario:** Reaction A ⇌ B has K_c = 5.0 at 25 °C. You mix [A] = 0.20 M and [B] = 0.40 M. Will the reaction proceed forward or backward? **Calculation:** Reaction quotient Q = [B] / [A] = 0.40 / 0.20 = 2.0. Compare to K = 5.0: Q < K, so reaction proceeds forward (toward more product). Equilibrium will continue forming B from A until [B]/[A] = 5.0. **Result:** Q < K → reaction proceeds forward. Final equilibrium: if total = 0.60 M, then [A]_eq + [B]_eq = 0.60 and [B]_eq/[A]_eq = 5.0 → [A]_eq = 0.10 M, [B]_eq = 0.50 M. So 0.10 M of A will convert to B as the system equilibrates.
**Use equilibrium constant math for:**
- **Predicting reaction extent**: K large → goes nearly to completion; K small → barely any product forms. - **Designing industrial processes**: Haber, contact (H₂SO₄), Ostwald (HNO₃), all use equilibrium analysis to choose T, P, and recycle strategies. - **Buffer design**: K_a determines the useful pH range of a buffer; Henderson-Hasselbalch is a rearrangement of K_a expression. - **Solubility predictions**: K_sp tells you the concentration at which precipitate forms. - **Acid/base strength**: pK_a is just −log₁₀(K_a); strong vs weak distinction comes from K. - **Biochemistry**: enzyme binding (K_d), protein folding (K_unfold), receptor-ligand interactions. - **Environmental chemistry**: partitioning of pollutants between water/air/soil phases, all equilibrium-driven. - **Geochemistry**: mineral solubility, carbonate equilibria controlling ocean pH.
**Practical guidelines for using K:**
- **K > 1000**: reaction is essentially irreversible (goes to completion). - **K = 10 to 1000**: products strongly favored; high but not complete yield. - **K = 0.1 to 10**: mixture of products and reactants at equilibrium. - **K = 10⁻³ to 0.1**: reactants strongly favored; little product forms. - **K < 10⁻³**: essentially no reaction occurs.
**Le Chatelier — practical levers:**
- **Increase reactant concentration**: shifts toward more product. - **Remove product as formed**: shifts further toward product (Haber recycles unreacted N₂/H₂). - **Increase pressure** (gas reactions with fewer moles of gas product): shifts toward product. - **Increase temperature for endothermic reactions**: increases K. - **Decrease temperature for exothermic reactions**: increases K (but slower reaction). - **Catalyst**: speeds equilibration but doesn't change K.
**K depends on temperature:**
K_eq(T) is a strong function of temperature via van't Hoff equation:
ln(K₂/K₁) = −ΔH°/R × (1/T₂ − 1/T₁)
So K reported at one temperature is different at another. Always check temperature when comparing K values.
Calculate Gibbs free energy using ΔG = ΔH - TΔS.
Calculate pH from H+ concentration and convert between pH, pOH, [H+], and [OH-].
Calculate cell potential using E = E0 - (RT/nF)ln(Q).
Calculate percent yield from actual and theoretical yield values.
Calculate theoretical yield from stoichiometry, reactant mass, and molar masses.
Determine the empirical formula from mass percentages of elements.
Leave 0 if only one product
Leave 0 if only one reactant
Keq
5.000e+0
Favored
Products favored
ΔG°
-3.99 kJ/mol
| Parameter | Value |
|---|---|
| Product 1: [P1]^n1 | 0.5^1 = 5.0000e-1 |
| Product 2: [P2]^n2 | N/A |
| Reactant 1: [R1]^n1 | 0.1^1 = 1.0000e-1 |
| Reactant 2: [R2]^n2 | N/A |
| Keq | 5.0000e+0 |
| log(Keq) | 0.6990 |
| Favored Side | Products favored |
| ΔG° at 298 K | -3.9895 kJ/mol |