The Correction in Calculating the Mass of the Pre-cipitation on a Solid Electrode According to Fara-day’s Law

Aleksandr Guntsov, Department of General and Physical Chemistry, Tyumen Industrial University, Tyumen, Russia (av.guntsov@gmail.com)

Faraday's law is the basic law of electrochemistry. One of the most important tasks of practical electrochemistry is the problem of calculating the mass of the precipitate according to the Faraday’s law m=k*Q, where k is a constant and Q is the total charge.

We propose the derivation of Faraday's law theoretically based on the equation of mass balance at the phase boundary of the electrolyte deposit. The mass balance equation is used to solve the Stefan problem on the growth of a thin deposit film on a solid electrode.

The grows of the sediment may be described by the mass balance condition on the surface, where the phase transition occurs:

( C_T-C_S(t) )* dh /dt = D* dC(t)/dx  = I/(z*F*S)   (1)

Where C_T is a constant representing the effective concentration of the sediment at the surface; Cs(t) is the time varying concentration of ions in the solution adjacent to the surface; x is the distance from the electrode surface; And  D, z, F, S are constants.

By integrating and rearranging, we get the correction to Faraday’s law

                        m – Δm = k*Q                                  (2)

Δm = MS*int( Cs(t)dh )  Int() represents integration over dh.

Where Δm is the correction term, M is the molar mass and S is the surface area of the film.

The correction term is due to the non-zero concentration at the surface of the film, in contrast to what is a priory assumed in the original Faraday’s law. This correction theoretically may reach about 2% of the total mass of the sediment, which may be significant in practical usage.