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Suppose I have a dissociative adsorption reaction and want to find the free energy change ΔF, this can be written at constant temperature:

[itex] \Delta F = \Delta E -T\Delta S[/itex]

Now given the adsorption energy [itex] \Delta E_{ads} [/itex] I would like to extrapolate the Free energy assuming that the adsorbate is an ideal gas since I know the experimental entropy.

I Assume that the vibrations from the adsorped moleule does not perturb the substrate vibrations and also that the configurational entropy is not changes(maybe rough):

[itex] \Delta S = S_{ads}-S_{noads}[/itex]

[itex] S_{ads} = S_{subs+a} - S_{subs}-S_{a} = -\Delta S_{vib,gas} -S_{gas}[/itex]

The vibrations term does not need to be extrapolated but the gas term does so:

[itex] S_{gas} = S^{\theta}_{gas} - c_p\log(\dfrac{T}{T^{\theta}}) + k_b\log(\dfrac{p}{p^{\theta}})[/itex]

I feel like i am missing a term of the type [itex]- \dfrac{7}{2}k[/itex] since the translation of the gas is not possible when adsorbed.

Does anyone know if I am right?

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# Free energy change during adsorption

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