Also contains definitions of: observed rate coefficient, partial order of reaction, pseudo-first-order rate coefficient, rate constant, \(k\)

https://doi.org/10.1351/goldbook.O04322

If the macroscopic (observed, empirical or phenomenological) @[email protected] (

Green Book, 2

PAC, 1993,

PAC, 1994,

PAC, 1996,

*v*) for any reaction can be expressed by an empirical differential rate equation (or rate law) which contains a factor of the form \(k\ \left[\text{A}\right]^{\alpha }\ \left[\text{B}\right]^{\beta }\) ... (expressing in full the dependence of the @[email protected] on the concentrations \(\left[\text{A}\right]\), \(\left[\text{B}\right]\) ...) where \(\alpha \), \(\beta \) are constant exponents (independent of concentration and time) and \(k\) is independent of \(\left[\text{A}\right]\) and \(\left[\text{B}\right]\) etc. (rate constant, @[email protected]), then the reaction is said to be of order \(\alpha \) with respect to A, of order \(\beta \) with respect to B, ... , and of (total or overall) order \(n=\alpha +\beta\: +\,...\) The exponents \(\alpha \), \(\beta \), ... can be positive or negative integral or rational nonintegral numbers. They are the reaction orders with respect to A, B, ... and are sometimes called 'partial orders of reaction'. Orders of reaction deduced from the dependence of initial rates of reaction on concentration are called 'orders of reaction with respect to concentration'; orders of reaction deduced from the dependence of the @[email protected] on time of reaction are called 'orders of reaction with respect to time'. The concept of order of reaction is also applicable to chemical rate processes occurring in systems for which concentration changes (and hence the @[email protected]) are not themselves measurable, provided it is possible to measure a @[email protected] For example, if there is a dynamic equilibrium according to the equation: \[a\text{A}\rightleftharpoons p\text{P}\] and if a @[email protected] is experimentally found, (e.g. by NMR @[email protected]) to be related to concentrations by the equation: \[\frac{\varphi _{-\text{A}}}{\alpha } = k\ \left[\text{A}\right]^{\alpha }\ \left[\text{L}\right]^{\lambda }\] then the corresponding reaction is of order \(\alpha \) with respect to A ... and of total (or overall) order \(n(=\alpha +\lambda\: +\,...)\). The proportionality factor \(k\) above is called the (\(n\)th order) '@[email protected]'. Rate coefficients referring to (or believed to refer to) @[email protected] are called 'rate constants' or, more appropriately 'microscopic' (hypothetical, mechanistic) rate constants. The (overall) order of a reaction cannot be deduced from measurements of a '@[email protected]' or '@[email protected]' at a single value of the concentration of a species whose concentration is constant (or effectively constant) during the course of the reaction. If the overall @[email protected] is, for example, given by: \[v=k\ \left[\text{A}\right]^{\alpha }\ \left[\text{B}\right]^{\beta }\] but [B] stays constant, then the order of the reaction (with respect to time), as observed from the concentration change of A with time, will be \(\alpha \), and the @[email protected] of A can be expressed in the form: \[v_{\text{A}}=k_{\text{obs}}\ \left[\text{A}\right]^{\alpha }\] The proportionality factor \(k_{\text{obs}}\) deduced from such an experiment is called the 'observed rate coefficient' and it is related to the \((\alpha +\beta )\)th order @[email protected] \(k\) by the equation: \[k_{\text{obs}}=k\ \left[\text{B}\right]^{\beta }\] For the common case when \(\alpha = 1\), \(k_{\text{obs}}\) is often referred to as a 'pseudo-first order @[email protected]' (\(k_{\psi }\)). For a simple @[email protected] a partial order of reaction is the same as the @[email protected] of the reactant concerned and must therefore be a positive integer (see @[email protected]). The overall order is then the same as the @[email protected] For @[email protected] there is no general connection between @[email protected] numbers and partial orders. Such reactions may have more complex rate laws, so that an apparent order of reaction may vary with the concentrations of the @[email protected] involved and with the progress of the reaction: in such cases it is not useful to speak of orders of reaction, although apparent orders of reaction may be deducible from initial rates. In a @[email protected], orders of reaction may in principle always be assigned to the elementary steps.

*See also:*kinetic equivalence

*Sources:*Green Book, 2

^{nd}ed., p. 55 [Terms] [Book]

PAC, 1993,

*65*, 2291. (

*Nomenclature of kinetic methods of analysis (IUPAC Recommendations 1993)*) on page 2296 [Terms] [Paper]

PAC, 1994,

*66*, 1077. (

*Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)*) on page 1147 [Terms] [Paper]

PAC, 1996,

*68*, 149. (

*A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)*) on page 176 [Terms] [Paper]