https://doi.org/10.1351/goldbook.09139
Equation relating electric current at a dropping mercury electrode under purely diffusional control, \(I_{{\rm{d,}}t}\), the amount concentration of an electroactive substance at the drop surface \(c\), and the concentration in bulk solution \(c_{\rm{0}}\), \[I_{{\rm{d}},t} = -k\,z\,F\,D^{1/2}q_{\rm{m}}^{2/3} t^{1/6}(c - c_{0})\] where \(k\) is a numerical constant, $z$ the electron number of an electrochemical reaction, \(F\) the Faraday constant, \(D\) the diffusion coefficient of the electroactive substance, \(q_{\rm{m}}\) the mass flux of mercury at the dropping electrode, and \(t\) the time elapsed from the beginning of the drop.
Notes:
- At sufficiently large overpotentials, the surface concentration \(c\) will fall to zero, giving a limiting diffusion current. \[I_{\rm{d,lim}} = k\,z\,F\,D^{1/2} q_{\rm{m}}^{2/3} t^{1/6} c_{0}\] Mostly, the average current (averaged over drop time and thus drop size) is calculated, when \(t\) becomes the drop time \(t_{\rm{d}}\).
- The value of \(k\) depends on the units used for quantities in the equation (\(D\), \(q_{\rm{m}}\), \(t\), \(c\)), and whether the limiting current or the current averaged over the life of a drop is calculated. For \(D\) in \(\pu{cm2 s-1}\), \(q_{\rm{m}}\) in \(\pu{g s-1}\), \(t\) in \(s\), and \(c\) in \(\pu{mol cm-3}\), the constant \(k\) is 708 (limiting current in \(\pu{A}\)) and 607 (average current in \(\pu{A}\)).