Turnover Frequency Calculator

Turnover frequency counts how many times a catalyst completes its catalytic cycle per unit time. The calculation runs in two stages: the turnover number, TON = moles of product divided by moles of catalyst, is a dimensionless count of cycles delivered per catalytic site, and dividing by elapsed time gives TOF in inverse seconds, minutes or hours. Because the catalyst sits in the denominator, TOF is a normalized activity, letting a 0.001 mol charge of a palladium complex be compared directly against a kilogram of supported nickel. Enzyme kcat values, which are simply TOF at substrate saturation, span roughly 1 to 10,000 per second, with carbonic anhydrase near 1,000,000 per second at the extreme, while industrial homogeneous systems such as rhodium hydroformylation catalysts commonly run in the hundreds to low thousands per hour. The number is only as good as its denominator. In heterogeneous catalysis only surface atoms are accessible, so moles of catalyst must mean moles of exposed active sites measured by selective chemisorption or titration, not the total metal charged; using total metal understates TOF, sometimes by an order of magnitude. TOF also varies with temperature, pressure, solvent and substrate concentration, so a reported value is meaningless without stated conditions, and it should be taken at low conversion, commonly under 10 to 20 percent, before product inhibition and deactivation distort the rate. Averaging over a long run blends an active early period with a decayed later one and flatters neither.

The idea comes from enzymology. Leonor Michaelis and Maud Menten published their saturation kinetics treatment in 1913, and George Briggs and J.B.S. Haldane recast it on a steady-state basis in 1925; the maximum rate divided by the enzyme concentration became known as the turnover number, the count of substrate molecules one enzyme molecule processes each second. That per-site accounting was possible in biochemistry because enzyme concentration could be determined, and it gave a way to rank catalysts independently of how much of them was present. Bringing the same normalization to industrial catalysis was largely the work of Michel Boudart at Stanford, who from the 1960s onward argued that heterogeneous rates should be reported per surface site rather than per gram of catalyst or per unit of reactor volume, and who set out the conventions in his 1995 Chemical Reviews article on turnover rates in heterogeneous catalysis. The approach depended on techniques for counting exposed sites, especially the selective chemisorption of hydrogen or carbon monoxide developed through the 1950s and 1960s. IUPAC later fixed the vocabulary in its recommendations and Gold Book entries, separating turnover number as a total count from turnover frequency as a rate. Organometallic chemists adopted both terms as homogeneous catalysis expanded, where TON became the standard measure of how much product a scarce precious-metal complex can deliver before it dies.