Actually, TOF is not well defined. While, you can calculated TOFap( apparent) as [moles converted]/[moles of metal * time]. [moles of metal] is the total amount of metals involved in the catalytic process, which often is unknown. Therefore, you can report TOFap with respect to each metal. In any case you should clearly defined what is TOF in your paper. Keep in mind that TOF makes sense if the reaction is definitely catalytic, meaning that TON is at least 10 or higher

Dear Professor,

Thank you for your help. It is really meaningful to my problem.

Warm regards,

Vasu

Please look at the following below links which may help you in your analysis:

https://pubs.acs.org/doi/pdf/10.1021/cs3005264

https://www.sciencedirect.com/topics/chemistry/turnover-frequency

http://www.scielo.br/pdf/jbchs/v31n10/0103-5053-jbchs-31-10-2155.pdf

Thanks

Dear Professor,

Thank you for your help. It is really needful.

Warm regards

Vasu

In order to calculate TOF, you should determine the number of active sites on the catalyst. Hence, for bimetallic catalysts, you should understand the surface sensitivity in terms of the contribution of both metals in the catalyst. Most of the time bimetallic catalysts are used in order to eliminate catalyst poisioning. Therefore, the second metal might not necessariliy pariticipate in the catalytic reaction but it might serve just to inhibit the poisoning on the surface of the active sites. We did a structure sensitivity characterization and then Monte Carlo simulation of a bimetallic catalyst in this work (https://journals.tubitak.gov.tr/chem/issues/kim-09-33-1/kim-33-1-2-0809-38.pdf) but didn't calculate TOF but still it might give you an idea. Basically if you have chance to do chemisorption tests, you can find the number of active sites and then can calculate TOF. In a recent work of mine, I also derived a semi-empirical method to make a rough estimation for TOF values but in this method you should first determine the overall catalytic reaction energy. If you are intersted in, I can share more details.

Dear Professor,

Thank you for giving the detail explanation. Yes sure, you can share more details, it would be a great help. Thanks in advance.

Warm regards

Vasu

Ebru Erunal What is "the overall catalytic reaction energy?"

Yurii V Geletii Thank you for your notification. I just noticed that when I say it reaction energy, it is confused with the enthalpy of the reaction. I wanted to mean the Gibbs Free Energy term in the Arrhenius equation for catalytic rate constant, the energy barrier.

Ebru Erunal This sounds even more confusing : "the Gibbs Free Energy term in the Arrhenius equation for catalytic rate constant"

TON and TOF are mainly used for enzymes. It is about efficient use of a given enzyme. In the case of catalysts, its activity and selectivity, as well as lifetime are more important.

Yurii V Geletii The EA term in k = ko.exp(-EA/RT), k is the rate constant

Ebru Erunal

The EA is called the apparent activation energy. The k = ko.exp(-EA/RT) makes sense only for elementary uni- or bimolecular reactions. Commonly, the reaction rate law for a catalytic reaction is neither the first nor the second order. I have a feeling that all my comments are on the level of basics of chemical kinetics. This is a professional but not an educational forum

Mirosław Grzesik "TON and TOF are mainly used for enzymes." Yes, TOF was introduced by Mickaelis and Menten for enzymes. TON came from organometallic catalysts. Now, they are commonly used for homogeneous catalysts and often for heterogeneous catalysts. The activity of a catalyst is quantified by TOF, the life time (stability) is directly related to TON

Yurii V Geletii There are scientists from various disciplines in this platform and therefore may not necessarily have to know every discipline’s “so-called“ basics for each other. The approaches on macro and microspic systems may consider some ”basics” different than each other. The reason of this platform is to bring scientists from different disciplines to share each other’s experience, knowledge and make useful discussions for a reason.By this way, everyone learns different aspects of disciplines. On the other hand, it does not give anyone right to make such nasty comments. Please share your knowledge and keep other personal comments to yourself or write it privately. This forum is not the place for it!

Yurii V Geletii Arrhenius equation is a relation that you can apply in various subjects, it does not have a specific limitation according to the reaction type in physical chemistry and thermodynamics. It is an empirical relationship so if you have experimental data, you can try to fit in this relationship according to your reaction rate assumptions. It is easier to deal with elementary reactions of course but it is not hard to do optimization for different reaction types with computational tools. Even with Excel, this can be done.

Ebru Erunal You are right that the Arrhenius equation, taken as an empirical exponential function, has wider application. However, then the parameters of this function are not physical constants but lumped parameters with no physical meaning.

I started a new discussion related to Arrhenius Equation. Please feel free to write there your opinions but not fill the answer of this question with unrelated answers to the specific question. Thank you. Yurii V Geletii Mirosław Grzesik

Dear Ebru Erunal, There are many of my comments on activation energy on RG. I would have to repeat myself when participating in the discussion you proposed. But I will be curious to hear the opinion of others. Regards,

TOF for bi- or tri- or tetra- etc-metallic catalysts is calculated in the same manner as for monometallic catalysts: e.g. TOF = (moles converted of reactant)/(moles of active site)*(time). Already, Isam Eldin Hussein Elgailani added some nice references mentioning what to take into account for the calculation of the reaction rate -(moles converted of reactant/time)- that should be used for TOF calculations. Therefore, attention must now be paid to the calculation of the "number of active sites". For metallic catalysts, active sites are usually assumed to be exposed metallic atoms. This is why chemisorption of probes such as CO and H2 is taken to be some sort of standard measure for the number of active sites. And, the method works very well most of the time!

In the case of a bimetallic catalyst, the method cannot work so well. In this regard, one may ask what happens if both metals chemisorb the probe? e.g., in a PdPt/support catalyst, both Pt and Pd chemisorb both CO and H2 and the stoichiometry of chemisorption may change! Furthermore, one often assumes that bimetallic catalysts are made of bimetallic particles and this may well not be the case. Therefore, to define what is the active site for a bimetallic catalyst one needs a better understanding of the functionalities of each metal on the studied reaction. For this purpose, one should be able to know if the bimetallic system shows synergistic effects or if its reactivity follows a linear relationship with the concentration of one of the metals. On the other hand, to estimate the number of active sites by chemisorption one should be able to choose adequate probes that selectively adsorb over the exposed atoms of one the metals and not over the other.

In the end, one should keep in mind that the active site is the one responsible for controlling the kinetics of the reaction; e.g. for CH4 oxidation, the active site is, under most reaction conditions, the one responsible for breaking one of the four C-H bonds of the molecule.

P.S. Some publications that we have made on bimetallic PtPd catalysts may be of use for you:

Article Synergetic Behavior of TiO2‐Supported Pd(z)Pt(1−z) Catalysts...

Article Development of the HYD route of hydrodesulfurization of dibe...

Article Factors controlling the development of the HYD route of desu...

Presentation Synergy: a new type of curve

it is easy, TOF for bi catalysts is calculated in the same manner as for monometallic catalysts