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Equilibrium Constant Calculator

Calculate an equilibrium constant from equilibrium concentrations, convert between Ka, Kd and pKd, and predict K at another temperature by the van 't Hoff equation.

Formula

K=∏[products]ν∏[reactants]νK = \dfrac{\prod [\text{products}]^{\nu}}{\prod [\text{reactants}]^{\nu}}
Ka=1Kd;pKd=−log⁡10KdK_{\mathrm{a}} = \dfrac{1}{K_{\mathrm{d}}};\quad \mathrm{p}K_{\mathrm{d}} = -\log_{10}K_{\mathrm{d}}
ln⁡K2K1=−ΔHR(1T2−1T1)\ln\dfrac{K_2}{K_1} = -\dfrac{\Delta H}{R}\left(\dfrac{1}{T_2} - \dfrac{1}{T_1}\right)
KK
equilibrium constant for the reaction as written
KdK_{\mathrm{d}}
dissociation constant, the reciprocal of the association constant Ka
ΔH\Delta H
reaction enthalpy, assumed constant between the temperatures

How it works

At equilibrium, the ratio of the concentrations of products to reactants, each raised to its stoichiometric coefficient, is a constant at a given temperature. A large K means products are favoured, and a small one that reactants are. For binding, the association constant Ka is the inverse of the dissociation constant Kd, and the pKd expresses the Kd on a logarithmic scale like pH.

The constant depends on temperature. The van 't Hoff equation predicts it at a second temperature from the reaction enthalpy: an exothermic reaction (negative ΔH) has a smaller K at a higher temperature, and an endothermic one a larger K.

Worked example

A + B ⇌ AB with [A] = 0.02 M, [B] = 0.05 M and [AB] = 0.30 M at equilibrium.

  1. K = [AB] / ([A] [B]) = 0.30 / (0.02 × 0.05) = 300 M⁻¹.

K = 300 M⁻¹, products favoured. For K = 100 at 25 °C and ΔH = −40 kJ/mol, K at 37 °C would be 53.6.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • The concentrations are those at equilibrium, not the initial ones.
  • Concentrations stand in for activities, which holds for dilute solutions.
  • ΔH is constant over the temperature interval for the van 't Hoff prediction.

Common mistakes

  • Using starting concentrations instead of equilibrium ones.
  • Writing the reaction in one direction and using K for the other.
  • Extrapolating the van 't Hoff equation far from the measured temperature, where ΔH changes.

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