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When trying to develop mathematical models to show the concentration in a reaction, where can one find a database or good source of known equilibrium constants if it is not necessarily very convenient to find them empirically?

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First, a question: what kinds of reactions are we talking about? Is it a more specialized (in this context) field like biochemistry, or more general chemical reactions? In practice, finding data for the latter is probably simpler than finding data for the former without doing any experimental work.

In general, I would use the information about Gibbs free energy of formation that can be found here (among many other places) for the reactants and products, and then calculate the equilibrium constant from

$$ K = \exp \left(\frac{-\Delta G^\circ_{\mathrm{rx}}}{RT}\right) $$

where $\Delta G_{\mathrm{rx}}$ is the change in Gibbs free energy for the reaction. Beware that if your reaction conditions - e.g. temperature or pressure - is different from standard conditions, this should be taken into account.

Hope this helps a bit!

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