turnover number

{{short description|In chemistry, number related to catalysis}}

In chemistry, the term "turnover number" has two distinct meanings.

In enzymology, the turnover number ({{math|k_cat}}) is defined as the limiting number of chemical conversions of substrate molecules per second that a single active site will execute for a given enzyme concentration {{math|[E{{sub|T}}]}} for enzymes with two or more active sites.{{cite book |doi=10.1016/b978-0-12-801238-3.05143-6 |chapter=Michaelis-Menten Kinetics |title=Reference Module in Biomedical Sciences |year=2015 |last1=Roskoski |first1=Robert |isbn=978-0-12-801238-3 }} For enzymes with a single active site, {{math|k_cat}} is referred to as the catalytic constant.{{cite book | title = Fundamentals of Enzyme Kinetics|last= Cornish-Bowden | first = Athel |edition = 4th | year = 2012 | publisher= Wiley-Blackwell, Weinheim | isbn = 978-3-527-33074-4 | pages = 33}} It can be calculated from the limiting reaction rate {{math|V{{sub|max}}}} and catalyst site concentration {{math|e{{sub|0}}}} as follows:

$$k\_\backslash mathrm\{cat\}\; =\; \backslash frac\{V\_\backslash max\}\{e\_0\}$$ (See Michaelis–Menten kinetics).

In other chemical fields, such as organometallic catalysis, turnover number (TON) has a different meaning: the number of moles of substrate that a mole of catalyst can convert before becoming inactivated:{{cite journal |last1=Bligaard |first1=Thomas |last2=Bullock |first2=R. Morris |last3=Campbell |first3=Charles T. |last4=Chen |first4=Jingguang G. |last5=Gates |first5=Bruce C. |last6=Gorte |first6=Raymond J. |last7=Jones |first7=Christopher W. |last8=Jones |first8=William D. |last9=Kitchin |first9=John R. |last10=Scott |first10=Susannah L. |title=Toward Benchmarking in Catalysis Science: Best Practices, Challenges, and Opportunities |journal=ACS Catalysis |date=1 April 2016 |volume=6 |issue=4 |pages=2590–2602 |doi=10.1021/acscatal.6b00183 |doi-access=free }}

$$\backslash mathrm\{TON\}\; =\; \backslash frac\{n\_\backslash mathrm\{product\}\}\{n\_\backslash mathrm\{cat\}\}$$

An ideal catalyst would have an infinite turnover number in this sense, because it would never be consumed. The term turnover frequency (TOF) is used to refer to the turnover per unit time, equivalent to the meaning of turnover number in enzymology.

$$\backslash mathrm\{TOF\}\; =\; \backslash frac\{\backslash mathrm\{TON\}\}\{t\}$$

For most relevant industrial applications, the turnover frequency is in the range of {{nowrap|10⁻² – 10² s⁻¹ (10³ – 10⁷ s⁻¹}} for enzymes).{{Citation |title=Introduction |date=2006-04-20 |url=https://onlinelibrary.wiley.com/doi/10.1002/3527607684.ch1 |work=Industrial Catalysis |pages=7 |place=Weinheim, FRG |publisher=Wiley-VCH Verlag GmbH & Co. KGaA |doi=10.1002/3527607684.ch1 |isbn=978-3-527-60768-6 |access-date=2022-06-03 |archive-date=2022-06-03 |archive-url=https://web.archive.org/web/20220603002425/https://onlinelibrary.wiley.com/doi/10.1002/3527607684.ch1 |url-status=live |url-access=subscription }} The enzyme catalase has the largest turnover frequency, with values up to 4{{x10^|7}} s⁻¹ having been reported.{{Cite journal |last1=Smejkal |first1=Gary B. |last2=Kakumanu |first2=Srikanth |date=2019-07-03 |title=Enzymes and their turnover numbers |url=https://www.tandfonline.com/doi/full/10.1080/14789450.2019.1630275 |journal=Expert Review of Proteomics |language=en |volume=16 |issue=7 |pages=543–544 |doi=10.1080/14789450.2019.1630275 |pmid=31220960 |s2cid=195188786 |issn=1478-9450 |doi-access=free |archive-date=2022-06-03 |access-date=2022-06-03 |archive-url=https://web.archive.org/web/20220603002425/https://www.tandfonline.com/doi/full/10.1080/14789450.2019.1630275 |url-status=live }}