## chemical flux, $$\varphi$$

https://doi.org/10.1351/goldbook.C01024
A concept related to @R05156@, 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 @A00297@ 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:
C01024.png
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 @R05156@ 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 @C01023@: $\text{A}\rightleftarrows \text{P}$ then: $\sum \varphi _{\text{A}}=\sum \varphi _{-\text{A}}=\sum \varphi _{\text{P}}=\sum \varphi _{-\text{P}}$ and $-\frac{\text{d}\left[\text{A}\right]}{\text{d}t} = \frac{\text{d}\left[\text{P}\right]}{\text{d}t}=0$