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In chemical adsorption of H$_{2}$ molecule, the distance is limited. In the physical adsorption, the distance of adsorption is limited or can be any value? Is there any correspondence to adsorption distance with the van der Waals radius of the adsorbent and adsorbate?. Is there experimental measurements for the minimum and maximum limit for the H$_{2}$ adsorption distance?

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The equilibrium position of the molecule from the surface will be due to the tradeoff between a (relatively) long range Van der Waals force (or electrostatic force if the molecule is charged or dipolar) and the short range exchange repulsion. You would expect the minimum to be when the molecule touches the surface, so it would around the Van der Waals radius. It's hard to see what could maintain the molecule at a greater distance than this.

Force

I suppose in solution the molecule could be hydrated, espcially if it's charged or polar, and the shell of coordinated water molecules would hold the molecule farther away. This seems a bit of a special case though.

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As far as I know, the potential energy of the molecule could be minimum at a distance of approximately one molecular radius of the adsorbate. The energy minimum is in the order of something like $0.01–0.1\ \mathrm{eV}=1–10\ \mathrm{kJ\;mol^{-1}}$. Due to the weakness of the interaction, significant changes are only observed at low temperatures ($<273\ \mathrm{K}$).

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