rate of formation, \(\nu _{n\text{,y}}\), \(\nu_{\text{c,y}}\)

https://doi.org/10.1351/goldbook.R05152
Like the @[email protected], the rate of formation of a specified product may be defined in two ways:
  1. As the time derivative of the amount of a product. Thus for a product Y, present at any time in amount \(n_{\text{Y}}\). the rate of its formation may be given by: \[\nu (n_{\text{Y}}) = \frac{\text{d}n_{\text{Y}}}{\text{d}t}\] This definition is particularly appropriate for open systems.
  2. For kinetics in closed systems it is more usual to define a rate of formation per unit volume, denoted \(\nu (c_{\text{Y}}) \): \[\nu (c_{\text{Y}}) = \frac{1}{V}\frac{\text{d}n_{\text{Y}}}{\text{d}t}\] When the volume is constant this reduces to: \[\nu (c_{\text{Y}}) = \frac{1}{V}\frac{\text{d}n_{\text{Y}}}{\text{d}t} = \frac{\text{d[Y]}}{\text{d}t}\] When the volume is not constant the relationship \(n_{\text{Y}} = [\text{Y}]V\) may be differentiated to give: \[{\text{d}}n_{\text{Y}} = V\text{d[Y]} + \text{[Y]d}V\] and the rate of formation becomes: \[\nu (c_{\text{Y}}) = \frac{\text{d[Y]}}{\text{d}t} + \frac{\text{[Y]}}{V}\frac{\text{d}V}{\text{d}t}\] A rate of formation may be specified even for a reaction of time dependent @[email protected] or of unknown @[email protected]
Source:
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 181 [Terms] [Paper]