TOF and TON calculations

In brief

Before digging into a more elaborate discussion, let’s briefly state that the turnover frequency (TOF) is a measure of how active a catalytic site is, while the turnover number (TON) is a measure of the stability of such active site. With this in mind, let’s now dive in conceptual details.

The misinterpretation 

The misinterpretation of these terms is understandable considering that one finds ambiguous definitions in reliable sources of information. As an example, the IUPAC Gold Book defines the turnover frequency (TOF) as “Commonly called the turnover number, N, and defined, as in enzyme catalysis, as molecules reacting per active site in unit time” [1] (See IUPAC’s definition here). Judging from this description, it seems that the TOF and the TON are the same, but in the context of catalysis they are not. The common pitfalls are [2]:

• The TOF is calculated as an average value, dividing all molecules converted in a given period by the number of sites. This approach conditions the resulting TOF as it skews its value to a lower number.
• The TON is calculated as the total number of transformations per site in a given time, even though the catalyst might still be active at the end of this period [2]. This calculation is highly sensitive to the reaction time considered.    

Turnover frequency (TOF)

Definition

The TOF is defined as the number of rotations of the catalytic cycle per unit of time [3]. It is calculated as the number of molecules converted per active site per time [2], as shown in equation (1) [4]:

Here, dNi/dt is the differential concentration change of i with time, NAv is Avogadro’s number and S is the number of active sites.

It should be highlighted that the TOF is only valid for a specific set of reaction conditions and reactant concentration. Therefore, the TOF should be reported together with the method for measuring surface sites, concentrations species and testing conditions [2, 3].

Advantages of reporting TOF

Reporting catalytic activity as function of TOF has many advantages, which have been reported elsewhere [3, 5]. Some of them are:

• Reporting TOF could be used to directly compare catalysts, even across laboratories. Ribeiro et al. [6] have shown the value of this approach for the ethylene hydrogenation and the CO methanation reactions.
• The presence of heat and mass transport effects can unequivocally be assessed by measuring the TOF of catalysts with different number of active sites. Of course, some considerations must be accounted for. Please refer to the method proposed by Koros and Nowak [7].
• The TOF could be used to identify if a reaction is structure sensitive or insensitive, in other words, to identify the relevance of crystalline anisotropy. This is illustrated in Figure 1 (data extracted from Bezemer et al. [8]), where one can observe that the reaction becomes structure insensitive once the cobalt particles reach a size of approximately 6 nm.

Opposing arguments

For the sake of stimulating a fair discussion, I would like to point out that there are some arguments against the use (or importance) of the TOF and TON [9-11]. I would strongly recommend you (the reader) to review some of these documents, so that you can balance the content of the present article and draw your own opinion on the subject. Unfortunately, the description of their content is out of the scope of this document.

In a similar note, I should point out that measurements of catalytic activity per unit volume are more interesting for industrial applications than TOF measurements [12]. This does not diminish the usefulness of TOF measurements, but allows one to put the information into perspective.

The turnover number (TON)

The TON is a measure of catalyst stability. In the words of Kozuch and Martin [13] “the TON deals with its lifetime robustness”. It is calculated as the number of catalytic cycles a site can perform until it deactivates completely [2], meaning that the catalytic test must be perform until the catalyst is completely deactivated [2]. The calculation is given by equation (2) [13]:

Considering that the TON is expressed as function of the TOF, further discussions on the TON are excluded from this article.

Final remarks and further references

The measurement of TOF is not easy task. As Vannice wrote [4]:

“precise TOFs for heterogeneous catalysts are not so readily definable as those in homogeneous or enzyme catalysis because adsorption sites typically measured by the chemisorption of an appropriate gas and used to count surface metal atoms, for example, do not necessarily correspond to ‘active’ sites under reaction conditions on a one-to-one basis. The exact atom or grouping of atoms (ensemble) constituting the active site is typically not known for any heterogeneous reaction and, in fact, it is very likely that a variety of active sites may exist, each with its own rate, thus the observed TOF then represents an average value of the overall catalyst activity”

Therefore, one must pay close attention while measuring and reporting TOF values. In essence, (i) one must measure and report TOF values in a wide range of operating conditions, and under conditions that guarantee the absence of heat and mass transport effects; (ii) one should clearly state the experimental conditions used during the determination of the TOF (T, P, and concentration of species); and, (iii) one must report the method used to determine the number of active sites on the catalysts. Additional guidelines and detailed information for solid acids and metal catalysts can be found in elsewhere [3, 6].

I would like to close this brief article with an excerpt from Kozuch and Martin [13] in reference to the TOF definition:

“The debate is far from finished, but it may come the day when the catalyst will be neatly tabulated according to their kinetic behavior, much like the standard thermodynamic tables”

Author information

Carlos Ortega || [email protected]

Orcid: 0000-0003-1696-2389

References

[1] Burwell, R. L. Manual of symbols and terminology for physicochemical quantities and units - APPENDIX II. Definitions, Terminology and Symbols in Colloid and Surface Chemistry. PART II: HETEROGENEOUS CATALYSIS. Pure and Applied Chemistry 1976, 46, 71–90.

[2] Schüth, F.; Ward, M. D.; Buriak, J. M. Common Pitfalls of Catalysis Manuscripts Submitted to Chemistry of Materials. Chemistry of Materials 2018, 30, 3599–3600.

[3] Boudart, M. Turnover Rates in Heterogeneous Catalysis. Chemical Reviews 1995, 95, 661–666.

[4] Vannice, M. A. Kinetics of Catalytic Reactions; Springer, 2005.

[5] Ertl, G., Kn?zinger, H., Schüth, F., Weitkamp, J., Eds. Handbook of Heterogeneous Catalysis; Wiley-VCH Verlag GmbH & Co. KGaA, 2008.

[6] Ribeiro, F. H.; von Wittenau, A. E. S.; Bartholomew, C. H.; Somorjai, G. A. Reproducibility of Turnover Rates in Heterogeneous Metal Catalysis: Compilation of Data and Guidelines for Data Analysis. Catalysis Reviews 1997, 39, 49–76.

[7] Koros, R.; Nowak, E. A diagnostic test of the kinetic regime in a packed bed reactor. Chemical Engineering Science 1967, 22, 470.

[8] Bezemer, G. L.; Bitter, J. H.; Kuipers, H. P. C. E.; Oosterbeek, H.; Holewijn, J. E.; Xu, X.; Kapteijn, F.; van Dillen, A. J.; de Jong, K. P. Cobalt Particle Size Effects in the Fischer-Tropsch Reaction Studied with Carbon Nanofiber Supported Catalysts. Journal of the American Chemical Society 2006, 128, 3956–3964.

[9] Ritter, S. K. The Turnover Fallacy. Chemical & Engineering News Archive 2013, 91, 46–47.

[10] Lente, G. Deterministic Kinetics in Chemistry and Systems Biology; Springer-Verlag GmbH, 2015.

[11] Lente, G. Comment on "Turning Over" Definitions in Catalytic Cycles. ACS Catalysis 2013, 3, 381–382.

[12] Chorkendorff, I.; Niemantsverdriet, J. W. Concepts of Modern Catalysis and Kinetics; Wiley-VCH, 2003.

[13] Kozuch, S.; Martin, J. M. L. "Turning Over" Definitions in Catalytic Cycles. ACS Catalysis 2012, 2, 2787–2794.