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

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.
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)