A catalyst increases the rate of a reaction by lowering the activation energy so that more reactant molecules collide each other with enough energy to surmount the smaller energy barrier .

What does "conversion rate" mean? Just use the term "conversion". What do you mean by "the reaction is very complex? As one can imagine, you mean a system of several reactions. In such a case, the activation energy must be determined for each reaction separately, unless you use the lumped kinetic approach. And then, it will not be the activation energy, nor the apparent activation energy, but only a measure of the sensitivity of overall rate to temperature change. This is for start.

Chenhao Wei, To answer your basic question: there is no relationship between the the value of activation energy/apparent activation energy and the rate of a chemical reaction or the overall rate of the process. However, obviously, the chemical reaction and the type of catalyst determine the value of activation energy.

I have study used two catalysts on same fuel under same operating conditions, the higher activation energy gave higher conversion

Ghazwan Saleh Ahmed, It can happen, but it cannot be generalized. Let me give you an example. Catalysts of various concentrations can be used in homogeneous reactions. Increasing the catalyst concentration does not change the activation energy, but increases the rate of the chemical reaction.

@Mirosław Grzesik : according to Arrhenius equation increasing activation energy lead to higher value of rate constant and then rate of reaction

Ghazwan Saleh Ahmed, You narrow the problem down to the effect of one parameter in the Arrhenius equation, but there are two. The value of the rate constant is determined not only by the activation energy value, but also by the value of the pre-exponential factor, often called the frequency factor.

Mirosław Grzesik . This true ,we have different values for pre-exponential factor, thank you for information

I would also add that the conversion is often controlled by the reaction thermodynamics, which does not depend on catalyst. A catalyst can decrease the time to achieve an equilibrium but does not shift the equilibrium

Dear Mirosław Grzesik, thank you for your reply. I realize the expression of "the reaction is very complex" might lead to misunderstanding. The reason I used the word "complex" is that the target reaction is always accompanied with side reactions, and they are all composed of several elementary reactions. Besides, physical processes play an important role in the overall reaction.

First, I want to try to explain the difference between AE and AAE, to better express my confusion.

According to some textbooks, Activation Energy (AE) is for an single elementary reaction, it describes the sensitivity to temperature change and also the minimum energy required for this reaction to proceed (energy barrier). While the concept "Apparent Activation Energy (AAE)" is for reactions composed of several elementary reactions. In this situation, the value for AAE is just the simple summary of AE values. (physical processes were not mentioned) So, I speculate it should also have the meaning of an energy barrier in some degree.

However, on the website of AICHE, https://www.aiche.org/ccps/resources/glossary/process-safety-glossary/apparent-activation-energy ,I found a different defination: In practice, reaction rates are often determined by physical processes (e.g. mass flow, diffusion, mass transfer area) as well as by chemical processes. The activation energy observed in these cases is called the apparent activation energy. Here, physical processes are concluded. And I think this is more convincing, because it's hard to separate chemical reactions and physical processes when determining AAE in practice.

Second, my confusion.

Assume there are two elementary reactions, M and N, and the AE value is higher for M than for N. Does it mean at a specific temperature, N is eaiser to proceed than M? If yes, then for the same time length, the reactant of N should be consumed more, thus the conversion should be higher.

Now assume a specific complex reaction (composed of several elementary reactions) is proceeding on two catalysts. Then the AAE we calculated are based on these two systems. If in one system, the AAE is lower, does it mean this complex reaction is eaiser to proceed? If yes, then for the same time length, more reactant should be consumed, thus the conversion should be higher. Am I right?

The discussion became too general with too many assumptions, and therefore useless. The statement: " While the concept "Apparent Activation Energy (AAE)" is for reactions composed of several elementary reactions. In this situation, the value for AAE is just the simple summary of AE values" IS NOT CORRECT

Dear Yurii V Geletii, Unfortunately, I cannot agree, the type of catalyst has no effect on the conversion. The type of catalyst has no influence on the equilibrium conversion in the reversible reaction, but it does influence the current conversion in both the reversible and the irreversible reactions. However, enzymes are known whose active sites may not detect the presence of one of the products of a reversible reaction, e.g. water. Then the concept of equilibrium conversion loses its meaning.

Dear Mirosław Grzesik ,

There is some misunderstanding. Actually I wrote that the equilibrium does not depend on catalyst. This is the same as yours " The type of catalyst has no influence on the equilibrium conversion in the reversible reaction." The time required to achieve the equilibrium does depend on the type of catalyst. The irreversible reactions are reversible, but the equilibrium is significantly shifted to one side.

Dear Yurii V Geletii,

If you used the term "equilibrium conversion" instead of "conversion" there would be no reason to discuss it a bit. Of course I know your view on irreversible reaction, which does not mean that I agree with it. There are chemical reactions where the product is a volatile substance that is spontaneously removed from the liquid reaction medium. Can such a reaction be called reversible? The reaction product can also be a substance with very low solubility in the reaction medium. There are many more such examples, as e.g. spontaneous combustion or explosion.

"Can such a reaction be called reversible? " Yes, if you keep mass balance (the total numbers of atoms should be constant)

Dear Yurii V Geletii, We don't have to agree on everything. The law of mass conservation in the macro-world must be fulfilled. But I don't recall that in the cases I have mentioned, the arrows between the substrates and the products were pointing in both directions. Nor do I intend to treat, for example, the esterification reaction with continuous water removal as a reversible reaction. Well, it is time to return to the issue raised in the question.

Dear Mirosław Grzesik ,

Ok,

I guess that the question is not clearly formulated. Therefore,

" The discussion became too general with too many assumptions, and therefore useless."

In addition, the statement: " While the concept "Apparent Activation Energy (AAE)" is for reactions composed of several elementary reactions. In this situation, the value for AAE is just the simple summary of AE values" IS NOT CORRECT

Dear Yurii V Geletii,

It is not about what you wrote, with which of course I agree, but what the author wrote in the question and later. Worst of all, that this is not an isolated view point.

Dear Mirosław Grzesik ,

This is a reason why I suggested to close this discussion. I'm no longer willing to waste my time. I was going to write you a personal message, but finally I decided to to express my opinion publicly. No personal attack, just the SCIENCE

Dear Yurii V Geletii, I really appreciate that you have devoted so much of your precious time to me. Thanks a lot.

Activation Energy determine Conversion Rate in a catalysis reaction . The role of catalyst is to decrease the energy of activation while the reactants are converted into products. So more reacts are converted into products by decreasing the energy of activation. so that the rate of the reaction is enhanced.

To all. I will repeat again. There is no clear relationship between the activation energy value of a given chemical reaction and its rate (initial or estimated on the basis of conversion for a given time/residence time). I also note with sadness that another person, following the author of the question, uses the wrong term "conversion rate".

This is the similar endless discussion

https://www.researchgate.net/post/Relationship_that_exist_between_reaction_rate_and_activation_energy_in_either_catalytic_and_non-catalytic_reactions_kinetics

This is a real problem of this professional forum that a wrong pseudo-scientific terminology is used, e.g. " Activation Energy determine Conversion Rate in a catalysis reaction ." What is the activation energy of a catalytic reaction? Conversion and rate are two different terms. The rewording of this statement is something like " some not well defined parameter controls something non-existing in a catalytic reaction."

That's what it's all about. The questioners use a variety of pseudoscientific terms and I try to draw attention to this. Unfortunately, it is like "fighting windmills".

Can Apparent Activation Energy determine Conversion Rate in a catalysis reaction? Yes, although other factors can as well contribute to that effect.

Respected scholars, Mirosław Grzesik, Yurii V Geletii

I think the word "conversion rate" used by the author in the question presented above could possibly be meant to imply the rate of transformation just like the rate of disappearance of the feeds (i.e. reactant).

I feel you can help the author by sharing an interpretation of his/her question so that he/she can have it revised if that's not his intended message. Especially in a case like this, that would help us to learn fast without any complications. I feel that help.

Toyese Oyegoke, According to definition: conversion = (nAo-nA)/nAo, A - reference component, reaction rate = ± (1/X) dnA/dt, X = V, mc or S. The "conversion rate" is not used in the chemical reactions/reactors engineering. Moreover, the search for the relationship between the activation energy value and conversion as well as the reaction rate (what: initial ?, for t1/2 ?, average ?) does not make sense.

Thank you sir for your feedback. I totally with your expressions for the conversion and reaction rate. And in line with the expressions,

Reaction rate = ± (1/X) dnA/dt, where, X = V, mc or S

And I understood that the reaction rate above can still be expressed as a function:

Reaction rate = f (X, nA, k), where, X = V, mc or S and k = ko exp(-Ea/RT)

The reaction rate here shows a direct relationship with rate constant, k, and the rate constant shows an indirect linear relation with Ea. Taking Ea as the apparent activation energy, it is expected that the rate constant would be small if Ea is high, and when Ea low, the rate would high.

My key question is that:

what are the possible factors that can alter the indirect linear relationship that exists between Reaction rate & Ea (App. Act. E) or Rate constant & Ea (App. Act. E).

Expressing in another way (in line with the other person's question):

What can make a catalyst with higher Apparent Activation Energy display a higher Reaction Rate? What factors could be responsible?

Thank you for your resourceful responses, Mirosław Grzesik