Incorrect equilibrium constant for reactions with multidentate species

[bjkreitz]

Issue

I think that the calculation of the concentration equilibrium constant is wrong for reactions involving multidentate species.
The concentration equilibrium constant is calculated for surface reactions according to the following equation:

$$K_{ci}=\frac{p}{RT}^{\sum{\nu_{gi}}} \Gamma^{\sum{\nu_{si}}}K_{pi} $$

where the first sum is over all gas-phase species $g$ in reaction $i$ and the second is over all surface species $s$. According to the Chemkin manual (https://github.com/ReactionMechanismGenerator/RMG-Py/files/12370978/chemkin11surfacechemkin.pdf, page 64), the calculation of the equilibrium constant is different when adsorbates with more than one binding site are involved. The correct equation should be:

$$K_{ci}=\frac{p}{RT}^{\sum{\nu_{gi}}} \Gamma^{\sum{\nu_{si}}}\prod{\sigma_{s}^{-\nu_{si}}} K_{pi} $$

If a reaction involves only monodentate species, the term $\prod{\sigma_{s}^{-\nu_{si}}}$ is 1. Otherwise a small factor is used to multiply $K_{pi}$.

The question is whether the second equation is correct. I haven't found a detailed derivation of this equation yet.
If the second equation is correct, I can start a PR since I have already written the code to fix this.