# Free energy change during adsorption

1. May 8, 2013

### 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?

Last edited: May 8, 2013