Reductant:

If the metal ion (oxidant) is reduced to metal (reductant), most of the reductant will form amalgam with the dropping mercury electrode, and then the concentration of the metal in the amalgam is also directly proportional to the current on the wave. Therefore, the concentration of reductant formed is proportional to the observed current, so

i = K₂[Red]o

where K ₂ = 607 n_red D_re  ^1/2 m^2/3t^1/6

If the reductant is soluble in water, it will diffuse from the surface of the electrode to the bulk of the solution. So, the concentration of [ R e d ] o  at the surface at any value of 'i' will be proportional to the rate of diffusion of the reductant from the surface of the electrode to the solution (under the concentration gradient [ R ed ] o ) and hence the same Eq. (8.10) also holds good.

Substituting these in Eq. (1)

E = E⁰ - 0.059/n log K₁/K₂ - 0.059/n log i/i_d-i

when the potential of the dropping electrode is equal to the half- wave potential, E^1/2 where i = i_d/2 the last term in the Eq. (1) then becomes zero and we have,

 E = E _1/2= E⁰- (0.059/n) log (K₁/K₂             )

Eq. (8.11) may now be written as,

E = E _1/2-( 0.059/n) log(i/((i_d  - i))

This equation is termed as "Equation of the Polarographic Wave" and represents the potential as a function of current at any point on the polarographic wave.  The theoretical treatment for anodic waves is similar to the above.