Equilibrium Constant Calculator – Kc, Kp and the Reaction Quotient
This equilibrium constant calculator applies the law of mass action. Type a balanced reaction, enter the amounts at equilibrium, and it writes the expression and works out Kc or Kp. It can also solve for one missing concentration, compare a mixture's reaction quotient Q with K, and combine the constants of several reactions.
The law of mass action
Cato Guldberg and Peter Waage proposed in 1864 that, at equilibrium, a fixed ratio holds between products and reactants. For aA + bB ⇌ cC + dD:
K = [C]^c [D]^d / ([A]^a [B]^b)
The exponents come from the balanced equation, not from the rate law. The two only agree for an elementary step, where K equals the ratio of the forward and reverse rate constants, K = k_f / k_r. For a multi-step reaction the rate law can look completely different, but K is still products over reactants.
Heterogeneous equilibria: solids and liquids drop out
A pure solid or a pure liquid has an activity of 1. Its "concentration" is fixed by its density, so adding more of it does not shift the equilibrium. For limestone, CaCO₃(s) ⇌ CaO(s) + CO₂(g), the whole expression is Kp = P(CO₂). Water is a special case. As the solvent in a dilute solution it is written H₂O(l) and left out. As steam, H₂O(g) is a gas and belongs in K. Mark phases with (s), (l), (aq) or (g) and the calculator decides what goes in.
Reading the size of K
Equilibrium constants span an enormous range, so the tool places K on a logarithmic scale. A common rule of thumb is that K above about 10³ means the mixture is mostly products, and K below about 10⁻³ means it is mostly reactants. In between, both sides are present in noticeable amounts. Textbooks draw these lines at 10², 10³ or 10⁴, so treat them as a guide. K does not depend on the starting amounts: whatever you begin with, the mixture settles at the same ratio. It does depend on temperature. The Van't Hoff equation describes how K changes when you heat or cool the system.
Q vs K and Le Chatelier's principle
The reaction quotient Q uses the same expression with the amounts you have right now. It answers "where are we?" compared with "where will we end up?". In ammonia synthesis, N₂ + 3H₂ ⇌ 2NH₃, a mixture with little ammonia has Q < K, so the reaction runs forward until Q rises to K. Too much product gives Q > K, and the reaction runs backward. This is Le Chatelier's principle with numbers attached. The free-energy change follows from the same ratio: ΔG = RT ln(Q/K). The Gibbs Free Energy Calculator covers ΔG° from formation data.
Manipulating K: reverse, scale and add
K always belongs to the equation exactly as written, so three rules follow:
- Reverse the reaction and K becomes
1/K. - Multiply every coefficient by n and K becomes
Kⁿ. Halving gives √K. - Add two reactions and their constants multiply:
K = K₁ × K₂.
For example, take N₂ + O₂ ⇌ 2NO and N₂ + ½O₂ ⇌ N₂O. Reversing the second and adding it to the first gives N₂O + ½O₂ ⇌ 2NO, with K = K₁ / K₂. This is Hess's law in multiplicative form. Because ΔG° = −RT ln K, log K adds up the same way ΔG° does. The Combine reactions tab can find the reversals and factors for you.
Units and activities
Strictly, K is dimensionless. Each concentration is divided by 1 mol/L and each pressure by 1 bar before it enters the expression. If you use the raw numbers you get apparent units such as M⁻² or atm, which the calculator reports so you can compare like with like. Kc and Kp differ by a factor of (RT)^Δn, and the choice of atm or bar only changes the number when Δn(gas) is not zero. A Kp to Kc Converter handles that conversion. Acid and base constants have their own tools: see the Ka & pKa Converter and the Solubility Product Calculator.