Dear Zahra,

The difference can be the type of constant. In pseudo second order we determine the initial rate of adsorption ans half tome réaction. Elovich is used to determine the rate constants (adsorption rate and desorpotion rate).

The easiest way is to compare both equations in the form of qt vs t. From the mathematical point of view, in the first case we deal with the hyperbolic function and in the second with the logarithmic function. It is also worth comparing the behavior of both functions at 0 (t --> 0) and in infinity (t --> ∞). You can easily notice the limited use of the logarithmic function in approximation of adsorption kinetic data - which explains the result of fitting. Regards,

All these misconceptions, errors and inconsistencies are the result of not always the correct use of basic concepts of the chemical reaction engineering in the description of the results of kinetic studies of the sorption processes. Where from all "pseudo order kinetics", "pseudo order reaction" or "pseudo order rate constant" terms. And also considering the dependences in the form of qt vs time as kinetic equations, while these equations are suitable at most for the approximation of individual kinetic curves. Thus Elovich's equation is not a kinetic equation, but only an equation by means of which one can approximate a single kinetic curve, and only in a limited range of time changes (logarithmic function). Regards,

Thank you Ngakou, Miroslow and Hai for your responses.

The paper was helpful Hai.

Dear Miroslove, my qt vs. t curve best fitted Pseudo second order model. I thought this model shows chemisorption. so, I thought it might be a paradox that they do not fit Elovich model that also shows chemisorption.

but you propose that I can trust Pseudo second order model rather than Elovich model, because Elovich equation is not actually a model, is it right?

It all depends on what data you have (a single kinetic curve of adsorption for one initial concentration and one constant temperature, or several kinetic curves for different initial concentrations and different temperatures) and what you want to achieve.

A typical kinetic curve of adsorption (qt(0)=0, qt(∞) -> qe), without inflection points) you can approximate both exponential and hyperbolic functions. As an exponential function it is usually used: qt=qe(1-exp(- kt)) (the solution of differential equation: dqt/dt=k(qe-qt), qt(0) = 0). As a hyperbolic function one can use: qt=kqe2t/(1+kqet) (the solution of differential equation: dq/dt=k(qe-qt)2, qt (0) = 0) but not only. For the approximation of a single kinetic curve you can also use the Elovich equation. It does not matter how we call this equation (model or something else), it is important that this equation does not meet the boundary conditions in infinity (qt(∞) -> +∞). It is also important that the Elovich equation and what you call the "pseudo second order model" are empirical functions. Hence, the assignment of physical meaning to the value of their parameters is questionable. The same applies to the equation dqt/dt=k(qe-qt), qt(0)=0 but here one can indicate the theoretical basisis.

It is completely different if you want to describe several kinetic curves with one equation and additionally take into account the influence of temperature. Here, however, it is worth starting by getting acquainted with the basic concepts and terms in the field of chemical kinetics, and then looking for an analogy between chemical reactions, in particular reversible chemical reactions and the sorption processes. Nothing difficult.

And finally. It is worth noting that in the case of adsorption processes, the adsorbent and its properties are much more important than the quantitative description of the process. Regards,

Thank you Dr. Grzesik. it was very helpful for me.

Goodness of fit is rarely a good indicator whether data follow either mechanism or model. It is appropriate to fit the data to a function if you already know, the data follow the mechanism, and you would like to determine some parameters (as rate constants, etc). Using a linearized function of originally nonlinear models is quite risky. This is the case of PSO kinetics model.

"Fitting data to a function" is the way for the best fit. - Hope you do not do that. You are right, however, that non-linerar models should not be transformed into a linear form. There is a publication on RG, where negative values of k were obtained for so-called PFOM. Regards,

Zahra ... Surely you've got excellent discussion of the point. After all they are still models that help us to give a closer picture of the process involved during the adsorption.

How do the scientists justify the chemical nature of adsoprtion throuhh Langmuir isotherm and psedo-second order fitting? How these equations justifying the chemical nature of adsorption and what is the logic?

Aziz Ahmad The Langmuir equation, correctly called Langmuir like equation, results directly from the mass balance equation: dq/dt=kaC(qmax-q)-kdq. As for the so-called PSO, so far no one has developed the physico-chemical foundations of these equations in differential and integral form. These are empirical equations. So there is no logic in using PSO to describe kinetic data and LLE to describe equilibrium data.

This video step by step shows how to fit nonlinear Elovich kinetic model [qt = 1/B ln(A B t +1)] in OriginPro easily! #aminulcheminnovation #AminulSir

https://youtu.be/yF80eY8j-O0

I fell into the same problem choosing between a PSO model and an Elovich model when using the origin in a nonlinear way I got R2 = 0.99 elovich vs. R2 = 0.94 PSO What does this mean

The model should be chosen based on the theoretical background and NOT on fitting the data and resulting R2 parameters.

Each tested model is (or should be) based on theoretical constraints and mechanisms and supported by knowledge of good-quality literature (PSO is not). It is a good practice to consider a model if the mechanism makes sense for your system. Several experiments should be done to verify the model, each designed to answer the scientific hypothesis coming from the theory. Fitting the data can confirm the model but mostly fails by giving often false positive results, as in your case, when R2 indicates both the models are suitable.