The Langmuir constant (K) indicates the extent of interaction between the adsorbate and the surface. If the value of K is relatively larger it indicates that there is a strong interaction between adsorbate and adsorbent, while smaller value implies a weak interaction. So up to which value it is accepted, or from what value it is called higher?
The Langmuir constant can be derived from statistical thermodynamics, so it is
q=qmono,max*(KC/[1+KC])=p/(p+p0(T))
with p0(T)=(2PiMkBT/h2)kBTexp(-Eads/kBT)
For the derivation of this, see e.g. chapter 6.2 of
Book Concepts in Surface Physics
The Langmuir isotherm is usually applied for physisorption phenomena, so if the adsorption energy Eads (in eV) you get from this reaches the 1eV per binding atom range, your enter the strong chemisorption area for which Langmuir doesn't regularly get applied.
I would think one should be careful with using the Langmuir constants per se, since they are always experimentally determined, depending on concentration (or pressure) units (derived from the concentration scale used for solutions or partial pressures in the gas phase). Thus, -RTlnK as an experimentally determined value is a solute concentration unit-dependent; changing the concentration (and the reference state), the absolute value of the Langmuir affinity (as well as the free energy change for the selected reference states) will change, in contrast to the adsorption enthalpy. However, generally, I assume, it is a separate story to obtain, based on the Langmuir affinity, per se, the enthalpy change, since the entropy changes associated with the interactions with a sorption site are not necessarily easily accountable. Certainly, it is a problem for liquid phase adsorption, and/or for less well-defined materials, anyway. Hence, I consider for myself two points helping in evaluating how strong or weak the Langmuir- model-based interaction is: (1) obtaining enthalpies, if possible, from the temperature dependence, which will give a direct idea about energies that may be compared with many other data and calculations, (2) in terms of chemistry, the Langmuir model is just a simple 1:1 complex formation; formally and physically, it is the same (or essentially similar) process controlled by a stoichiometric reaction. In such a case, I compare the Langmuir affinity with any other quantified and characterized complexes formed in solutions or at the surfaces; for example, the equilibrium constant about 1 L/mol will be well comparable with equilibrium constants determined for middle-scale strength hydrogen bonding; it would give a some idea. When talking about the metal adsorption, their interactions with a surface are often interpreted in terms of chemical speciation models; the Langmuir affinity could be compared with the similar constants determined for the complexes studied in solutions. It may give a more broad perspective for ranking and comparing.
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