Q.If x is the amount of adsorbate and m is the amount of adsorbent, which of the following relations is not related to the adsorption process?

A solid surface attracts contacting gas or liquid species because atoms sitting right at the surface — unlike atoms buried in the bulk — have unsatisfied ('residual') valency, and this attraction happens strictly at the surface, which is what marks adsorption out as a surface phenomenon, distinct from absorption, where the absorbed substance spreads uniformly through the whole bulk of the absorbing material. The solid that does the attracting is the adsorbent; the substance attracted and held is the adsorbate; the surface of separation where the adsorbate's concentration builds up is the interface; and removing the adsorbed substance again is desorption. Where adsorption and absorption both occur together, the combined process is called sorption (M.C. Bain), and the specific case of gases taken up within a metal (e.g. hydrogen in palladium) is called occlusion (T. Graham).

Adsorption can occur at any interfacial surface — gas–solid, liquid–solid, liquid–liquid, solid–solid or gas–liquid — and is always spontaneous, so $\Delta G < 0$, reaching equilibrium exactly when $\Delta G = 0$. Because molecules moving from a free, disordered phase into an ordered adsorbed layer necessarily lose randomness, $\Delta S < 0$ for adsorption; since $\Delta G = \Delta H - T\Delta S$ and $-T\Delta S$ is therefore positive, $\Delta H$ must be sufficiently negative for $\Delta G$ to stay negative overall — so adsorption is always exothermic, a conclusion that follows directly from the entropy decrease. Adsorption is also characteristically fast, much faster than the comparatively slow, diffusion-limited process of absorption. …