Can you provide concrete examples of cases in which you have been bothered by differing values?

Generally:

Clausius-Clapeyron is used for phase equilibria in which one phase must be gaseous.

Van't Hoff is a general equation for reactions ethalpies and can of course be applied for adsorption enthalpies.

I know this answer sounds generic, but for an answer examples would really be helpful. Personally, I would prefer values generated e.g. by microcalorimetry (search for Tian-Calvet), but of course those also build on the fundamental thermodynamical equations that are also the basis for the equations you mentioned.

Thanks for your answer. Actually, I haven't been able to find a paper in which dH is calculated with both methods and compared. That is the reason why I wasn't sure if they are equivalent.

I am studying polyphenol adsorption in a resin, and want to know how dH changes with surface coverage (normally studied with Clausius clapeyron), but as polyphenols are not in the gaseous phase, I am not sure if I can do the same with van't Hoff.

In a paper on polyephols, they just apply Clausius clapeyron, but I'm not sure if that's accurate.

You could actually try to measure adsorption isotherm, your system might be sufficiently similar to the system in this experiment at my old institute:

http://www.ipc.kit.edu/download/A45_20181204.en.pdf

From the isotherm parameters you can calculate adsorption energies (see e.g. Desjonqueres/Spanjaard, Concepts in Surface Physics for the procedure).

Wow, I did the nonlinear fitting (for Langmuir and Freundlich) and statistical analysis myself using matlab. This program seems much more straight forward. I wish I would have seen this sooner.

Thanks for your answer, though! I'll review the book you sent me

The starting point of thermodynamic logic is: 1) opposing perpetual motion. 2) The irreversibility of dynamics. Let's look at how to get Carnot efficiency = 1-T1/T2.

1.1 There are many kinds of type 2 perpetual motors, each of which is a natural phenomenon.

A) Machine A: against the irreversibility of thermodynamics (diffusion, heat conduction, friction, etc) - dynamics;

B) Machine B: Utilizing the Difference of Carnot Efficiency (Reversible Thermodynamics) - Thermodynamics

1.2 A and B belong to different disciplines. There is a parallel relationship between them and there is no logical mutual inevitability.

1.3. Logic of the Second Law of Thermodynamics:

Experience induction, deny that A machine==> B machine can not be manufactured==> All material Kano efficiency: 1-T1/T2.

1.4 The logic of the second law of thermodynamics violates the physical logic that A and B cannot be inferred from each other.

1.5 The second law of thermodynamics elevates the "irreversibility", which is in fact only a kinetic experience.

📷 Detailed discussion can be found in the following figure.

1. The second law of thermodynamics loses the ability of quantitative prediction.

2. Data processing method of law 2 of thermodynamics violates scientific discipline: modifying experimental data to satisfy theory

See the picture for details.

3. The second law of thermodynamics can only be called science if it reaches the same quantitative prediction ability as Newton's second law, otherwise it is pseudoscience.

4.Unfortunately, all the charts of enthalpy and entropy are organized in this way.

Comparison of New and Old Thermodynamics

1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.

2. New thermodynamics pursues universality, two theoretical cornerstones:

2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.

2.2. Hydrostatic equilibrium: applicable to gases and liquids.

3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.

3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.

4. See Appendix Pictures and Documents for details.