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 \(\pu{A}\)).
Source:
PAC, 2020, 92, 641. 'Terminology of Electrochemical Methods of Analysis (IUPAC Recommendations 2019)' on page 674 (https://doi.org/10.1515/pac-2018-0109)