## rate of formation, $$\nu _{n\text{,y}}$$, $$\nu_{\text{c,y}}$$

https://doi.org/10.1351/goldbook.R05152
Like the rate of consumption, 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 nY. 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 v(cY): $\nu (c_{\text{Y}}) = \frac{1}{V}\frac{\text{d}n_{\text{Y}}}{\text{d}t}$ 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 nY = [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 stoichiometry or of unknown stoichiometry.
Source:
PAC, 1996, 68, 149. 'A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)' on page 181 (https://doi.org/10.1351/pac199668010149)