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If we consider a gas with a known temperature T and chemical potential $\mu$. A surface is in contact with a gas.Gas molecules can be adsorbed at N points on the surface. In this example it was shown that the fugacity of the adsorbed particles is equal to that of the free particles, when the system reaches equilibrium.Adsorption reduces the energy of a gas molecule by the value $\Delta$.

As we know fugacity is given by: $z=e^{\beta \mu}$.

This is possible when :

  1. The temperature of the adsorbed particles is equal to the one of the free particles $T_{adsorbed}=T_{free}$
  2. Their chemical potentials are also equal, meaning $\mu_{adsorbed}=\mu_{free}$

Now, I can understand the first condition happening. Whenever a particle is adsorbed it gives $\Delta$ energy in the form of heat to the surface. After this process happens for a while, the surface ends up having a temperature similar to that of the gas, in other words the adsorbed particles have the same temperature (and average energy since $\bar \epsilon=\frac 3 2KT$) as the free ones.

But I cannot think of a reason as to why the chemical potentials should be equal too. I know that chemical potentials are taken into consideration when we have a chemical reaction or a phase transition. And only for the case when we have phase transition between two arbitray phases $A$ and $B$, I know that $\mu_{A}(P,T)=\mu_{B}(P,T)$. So I don't understand in which category does the above example falls? Is it a reaction, or is it a phase transition?

imbAF
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2 Answers2

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I know that chemical potentials are taken into consideration when we have a chemical reaction or a phase transition.

The chemical potential µ is (well, should be) taken into consideration whenever matter moves, as unconstrained matter moves to the point of lowest chemical potential. This is analogous to heat flowing from hotter to colder objects and volumes shifting to expand high-pressure areas into low-pressure areas. The chemical potential is the partial molar Gibbs free energy G (i.e., $\mu_i\equiv\left(\frac{\partial G}{\partial N_i}\right)$ for material $N_i$), and G is minimized under the familiar setting of constant temperature and pressure. At equilibrium, G for the system is stationary, and µ for any particular material is spatially uniform. This holds regardless of whether the process is considered a phase change or a reaction (or both).

Chemomechanics
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Adsorbtion is a phase change for sure. A substance from a gas phase is transferred into a solid phase.

The underlying mechanism can be a chemical reaction. Or not.

fraxinus
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