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Equilibrium Constant Kc (A + B ⇌ C + D)

Kc=[C][D][A][B]K_c = \frac{[\mathrm{C}][\mathrm{D}]}{[\mathrm{A}][\mathrm{B}]}

Worked example: [C]=[D]=0.60 M over [A]=0.20, [B]=0.30 M → Kc = 6.00 — press Try an example to run it live, then adjust anything.

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Equilibrium Constant Kc (A + B ⇌ C + D) explained

[A][B][C][D]Kc

Cato Guldberg and Peter Waage, two brothers-in-law working in Kristiania (now Oslo), published the law of mass action in 1864: at equilibrium the products of the concentrations, each raised to its stoichiometric coefficient, sit in a fixed ratio. For the common one-to-one case A + B ⇌ C + D that ratio is just [C][D]/([A][B]). Their paper appeared in Norwegian and was ignored for a decade until a French translation reached van 't Hoff and Ostwald.

The identical expression evaluated with any set of concentrations — not necessarily equilibrium ones — is the reaction quotient Q, and comparing Q with Kc predicts which way the reaction will run: Q < Kc means it goes forward, Q > Kc means it reverses, Q = Kc means it is already there. Worked example: with [C] = [D] = 0.60 M and [A] = 0.20 M, [B] = 0.30 M, the quotient is 0.36/0.060 = 6.0, so if Kc were 2.0 the mixture would run backwards to consume product. Note that this calculator assumes all four coefficients are 1; with other coefficients each concentration needs its own exponent.

Equilibrium Constant Kc (A + B ⇌ C + D) formula

Kc=[C][D][A][B]K_c = \frac{[\mathrm{C}][\mathrm{D}]}{[\mathrm{A}][\mathrm{B}]}
Where
  • KcK_c= Equilibrium constant (or quotient Q)
  • [C][\mathrm{C}]= Concentration of product C (M)
  • [D][\mathrm{D}]= Concentration of product D (M)
  • [A][\mathrm{A}]= Concentration of reactant A (M)
  • [B][\mathrm{B}]= Concentration of reactant B (M)

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Part of this formula set

Chemical equilibrium constants

6 formulasKc, Kp, the reaction quotient Q, Ksp and the link to Gibbs free energy — every way of asking which side a reaction favours.