chemical flux, \(\varphi\)
A concept related to @[email protected], particularly applicable to the progress in one direction only of component reaction steps in a complex system or to the progress in one direction of reactions in a system at dynamic equilibrium (in which there are no observable concentration changes with time). Chemical flux is a derivative with respect to time, and has the dimensions of @[email protected] per unit volume transformed per unit time. The sum of all the chemical fluxes leading to destruction of B is designated the 'total chemical flux out of B' (symbol \(\sum \varphi _{-\text{B}}\)); the corresponding formation of B by concurrent elementary reactions is the 'total chemical flux into B or A' (symbol \(\sum \varphi _{\text{B}}\)). For the mechanism:
the total chemical flux into C is caused by the single reaction (1): \[\sum \varphi _{\text{C}}=\varphi _{1}\] whereas the chemical flux out of C is a sum over all reactions that remove C: \[\sum \varphi _{-\text{C}} = \varphi _{-1}+\varphi _{2}\] where \(\varphi _{-1}\) is the 'chemical flux out of C into B (and/or A)' and \(\varphi _{2}\) is the 'chemical flux out of C into E'. The @[email protected] of C is then given by: \[\frac{\text{d}\left[\text{C}\right]}{\text{d}t} = \sum \varphi _{\text{C}} - \sum \varphi _{-\text{C}}\] In this system \(\varphi _{1}\) (or \(\sum \varphi _{-\text{A}}\)) can be regarded as the hypothetical rate of decrease in the concentration of A due to the single (unidirectional) reaction (1) proceeding in the assumed absence of all other reactions. For a non-reversible reaction: \[\text{A}\overset{1}{\rightarrow }\text{P}\] \[-\frac{\text{d}\left[\text{A}\right]}{\text{d}t} = \varphi _{1}\] If two substances A and P are in @[email protected]: \[\text{A}\rightleftarrows \text{P}\] then: \[\sum \varphi _{\text{A}}=\sum \varphi _{-\text{A}}=\sum \varphi _{\text{P}}=\sum \varphi _{-\text{P}}\] and \[-\frac{\text{d}\left[\text{A}\right]}{\text{d}t} = \frac{\text{d}\left[\text{P}\right]}{\text{d}t}=0\]
See also:
order of reaction
rate-limiting step
steady state
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1095 [Terms] [Paper]