TON = Moles of desired product formed/number of active centers or surface area (heterogeneous catalyst)

TOF = TON/time of reaction

I agree with Elham Samadi Following additional information may help in developing a better understanding.

TON and TOF both are calculated based on the active sites present in the heterogeneous Catalyst.

Accurate TOFs for heterogeneous catalysts are not so simply explained 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 atom (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.

You may refer to these useful papers & book:

[1] 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.

[2] Vannice, M. A. Kinetics of Catalytic Reactions; Springer, 2005. (see chapter 2.4 page no. 7)

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

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

I do hope that this will help you

Turn over frequency (TOF) is number of reactant molecule converted per minute per active site.

Let initial reaction rate be r0, = moles of reactant converted per gram of active metal per hour

Let 'M' be atomic weight of active metal

Let 'D' be dispersion of active metal on catalyst support (Determined by using CO-chemisorption or H2-Chemisorption)

Then TOF = (r0*M)/D

Hello, Good day! You can get the required (TON/TOF) help from the following articles.

thanks alot