This question was asked not long ago for heterogeneous catalysts. The answer is the same. Thus, TON is mol of converted substrate/mol of catalyst. I'd like to emphasize again that there is a big gap about the utility of TON and TOF in academia and industry. While TON can be used for the estimation of the longevity of a catalyst system, TOF says nothing about the real kinetics of a reaction (according to chemical engineers TOF is only an academic gadget as referred elegantly and relevantly by Nicola Pericona in the previous discussion). It can only be used for a very rough comparison of a catalytic activity in the same (or a very similar reaction) under very similar reaction conditions only at low conversions! TOF takes a zero order kinetics for the substrate, which is seldom the case! Thus TOF depends on the rate order !!. It is funny to see TOF values given above 90 or even at 100 % conversion! I would not suggest that the rate order and rate constants should be determined for each and every time, but showing the reaction profile (conversion versus reaction time, 3,4 values) at given reaction conditions (not a lot of work) could give more practical information about the rate and usability of the reaction than a vague TOF. So please don't use 100 % conversion for the determination of TOF. If you really need to, then give a TOF at 10 % conversion or below avoiding big faults due to a higher than zero rate.

In general I agree with Imre.

Both formulas are correct, if you define what does TON mean. In the first case the TON is for the substrate conversion, the second is for the certain product formation. The ratio of these TONs is the selectivity. The term TOF is not well defined. It came from enzymatic catalysis and from organometalic chemistry with different meanings.

I would use the term TOF(apparent), which is simply d(TON)/dT or Initial TON (apparent), which is d(TON)/dt at time = 0. In terms of Michaelis-Menten kinetics TOF = k(cat). The definition of TOF is discussed in our recent paper;

Collecting meaningful early-time kinetic data in homogeneous catalytic water oxidation with a sacrificial oxidant.

James W Vickers, Jordan M Sumliner, Hongjin Lv, Mike Morris, Yurii V Geletii, Craig L Hill

Physical Chemistry Chemical Physics (Impact Factor: 3.83). 03/2014; DOI:10.1039/c3cp55406f

In general I also agree with Yurii :). With giving TOF at or below 10 % conversion I also meant to give initial TOF. The idea of apparent TOF is also practical, although this TOF will also depend on the dT. i.e on the reaction rate and won't be an exact measure. However, in the academic practice of homogeneous catalysis you don't give different TON-s, i.e. based on the substrate and the product. In other words, the selectivity is determined by analysis (GC, HPLC, NMR, etc) and not by dividing the product TON with the substrate TON. Thus, TON and TOF is calculated solely on the basis of converted substrate (based on conversion). That is why it is essential to give the initial substrate to catalysts ratio and the detected selectivity with the results. Furthermore, there might be undetected products in a given analysis. For this reason, selectivity and thus a product based TON/TOF is uncertain unless you determine the mass-balance for every reactions.

Dear Imre, we well understand each other. One quick comments for you. We are doing water oxidation and calculate TON as the ratio of O2 formed to catalyst concentration. We just can't measure the consumption of water.

Dear Nesrine, do you have an answer to your question?

Indeed it would be difficult to determine a substrate (conversion) based TON when the substrate is also the solvent and the conversion is very-very low. You are right Yurii that in our academic discussion we might forgetting Nesrine's question. That is why I'd like to summarize for Nesrine what we suggested. 1. Use TON and TOF on conversion (reacted substrate) basis if you need to and if you can with the knowledge that TOF is not an exact measure. 2. Give then always the initial substrate to catalyst ratio with the detected selectivity. 3. Try to give TOF values at conversion values as low as possible.

4. It is handy to provide the conversion and selectivity profile (curve) of the reactions based on about 4-5 points at least in the supplementary materials. 5. If you cannot detect (calculate) conversion, give then the product TON/TOF with explanation. Good luck!

Interesting. Thanks a lot.

You are welcome Nesrine. The slope of the substrate conversion curve depends also on the reaction rate (thus also not an exact measure). For this reason it doesn't really matter whether you take the slope or a single point at low conversion (this is easier). As earlier said, the best is to give the reaction profile (conversion, selectivity vs reaction time as well, so that everybody can calculate whatever she/he wants to.

Hi

Please read the following article. http://dx.doi.org/10.1016/j.jpowsour.2014.10.087

As I read the answers, most of them were related to the homogeneous catalysts. Does anyone know how I can calculate the TON or TOF based on the rate of reaction constant?

Dear Maryam,

TON is not related to rate constants or to the rate of the reaction. It simply expresses the ratio of the molar amount of substrate converted to the molar amount of catalyst used in a reaction. TOF also ignores the kinetics, but basically it assumes a zero order reaction rate for the reaction. For this reason, you can easily convert a zero order k (M/s) to TOF, by simply dividing k (M/s) by the M' molar concentration of catalyst used. Thus you will get TOF in s-1 units. Be careful to use the same molar concentration forms both for the substrate (product) and the catalyst. The calculation of TOF from higher rate orders is difficult as TOF will depend on the conversion.

Please find the link

https://application.wiley-vch.de/books/sample/3527331654_c01.pdf

Imre Tóth and Yurii V Geletii ,

Thank you so much for your contributions so far that have been rich and helpful. Meanwhile, I would like to understand how to convert a case where rate constants are higher orders, to TOF.

Toyese Oyegoke ,

the concept of TOF is pretty complex. Commonly in the literature the apparent TOFap is reported, which is simply calculated as TON/(reaction time), providing that TON >>1. The real TOF is one of the rate constant of the reaction mechanism, which can be proposed based on kinetic and other studies.

Nesrine Said ,

TOF= TON/Time

I have attached a useful book. In the first chapter you can find your answer as clear as possible.