Free energy change during adsorption

[dikmikkel]

Hi,
Suppose I have a dissociative adsorption reaction and want to find the free energy change ΔF, this can be written at constant temperature:
$\Delta F = \Delta E -T\Delta S$
Now given the adsorption energy $\Delta E_{ads}$ 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):
$\Delta S = S_{ads}-S_{noads}$
$S_{ads} = S_{subs+a} - S_{subs}-S_{a} = -\Delta S_{vib,gas} -S_{gas}$
The vibrations term does not need to be extrapolated but the gas term does so:
$S_{gas} = S^{\theta}_{gas} - c_p\log(\dfrac{T}{T^{\theta}}) + k_b\log(\dfrac{p}{p^{\theta}})$
I feel like i am missing a term of the type $- \dfrac{7}{2}k$ since the translation of the gas is not possible when adsorbed.
Does anyone know if I am right?

 

[eljose79]

Hello,

Thank you for sharing your thoughts on this topic. It seems like you have a good understanding of the thermodynamic principles involved in this situation. However, I would like to clarify a few points.

Firstly, the equation you have written for the free energy change is correct. As you mentioned, it is important to consider the adsorption energy (\Delta E_{ads}) and the change in entropy (\Delta S) in order to calculate the free energy change. However, it is important to note that the change in entropy is not only affected by the vibrational modes of the adsorbed molecule, but also by the adsorption process itself. This means that the change in configurational entropy (\Delta S_{config}) should also be considered in your calculation, as it may not be negligible.

Secondly, your equation for the entropy of the adsorbed gas (S_{gas}) is correct, but it is important to consider the correct values for the standard entropy (S^{\theta}_{gas}), the heat capacity at constant pressure (c_p), and the standard temperature and pressure (T^{\theta} and p^{\theta}). These values can vary depending on the specific gas and conditions, so it would be important to use accurate values in your calculation.

Lastly, you are correct in thinking that the translation of the gas may not be possible when adsorbed, so the -\dfrac{7}{2}k term may not be applicable in this case. However, it would be important to consider the translational entropy of the adsorbed molecule, as it may still contribute to the overall change in entropy.

In summary, your approach seems to be on the right track, but it would be important to consider all factors that may affect the change in entropy and to use accurate values for the relevant parameters. I hope this helps and good luck with your calculations!