Reactant Transfer in Electrolytes

Electrolytes are transported in electrolytic cells by three basic procedures, diffusion, convection, and by electrical migration. Convection does not contribute greatly to electrolyte transfer in normal cells although thermal and density gradients can contribute to some electrolyte transfer. If the electrode is rotated or the electrolyte stirred, convection can play a more significant part in the transfer process. Electrical migration will depend on the relative number of reactant ions to the total number of ions in the cell. By adding an inactive electrolyte to the cell at levels of 50 to 100 times greater concentration than that of the reactant, the contribution of electrical migration to the electrode reaction and consequently electrode current will be very small. Assuming an unstirred cell with a high concentration of inactive electrolyte, the reaction and the electrode current will depend almost exclusively on mass transfer by diffusion.

The electrode current (i) can be described by the following equation,

                                                                                     (26)

where is the rate of change of concentration with time at the electrode

                    surface,

             (n) is the number of electrons per mol of reactant involved in a half

                   reaction.

             (F) is Faraday’s Constant,

       and (i) is the electrode current.

Now if (F) is the surface area of the working electrode and (J) is the concentration flux (mols/s/cm2) leaving the electrode surface,

Then,                                                                                 (27)

To be precise           

Thus, from equations (26) and (27)                                (28)

As (J_(diffusion)) is the concentration flux due to diffusion alone it can also be described by the equation,

                                                                              (29)

where (D) is the diffusivity of the reactant in the electrolyte and is given in

                 units of (cm²/c)

Thus, the current is controlled by the total flux and the area of the electrode. It is also seen that the current will depend on the rate the reactant is brought to the surface of the electrode.

Consider the surface conditions depicted in figure 19.

Figure 19. Surface Conditions at a Working Electrode

When a current flows and a reduction/oxidation reaction takes place, the reactant is removed from the electrode surface. This produces a concentration difference between the electrode surface and the bulk electrolyte and so the reactant diffuses under the concentration gradient towards the electrode to replenish the loss. Thus, equilibrium is established between the electrode and the bulk electrolyte that is depicted in figure 19. It is seen that a diffusion band is formed where the concentration at the electrode, (x=0) is and at (x=δ) is ^.

It is also seen that the thickness of the layer is (δ), where (δd = x_d – x_o)

Thus ,                               

As the concentration gradient is linear,

                  and as  = 0      Then                          (30)

Consequently,

from equation, (28) 

And, thus,

                                                                             (31)

It is seen from equation (31) that the current will increase linearly with increase in reactant concentration and consequently, from the point of view of the analyst, is a means of measuring analyte concentration. However, the current is also inversely proportional to the thickness of the diffusion film and under quiet conditions, this layer extends over time and causes the limiting current to decrease slowly with time and eventually fall to zero. However, if forced convection is applied (i.e. the electrolyte is well stirred or the electrode rapidly rotated) the thickness of the diffusion layer, and consequently the limiting current, becomes constant.  Thus, if a constant potential is applied to the working electrode, the electrolyte stirred and the limiting current measured, the system can be used reliably for analytical purposes. This process is called DC amperometry or hydrodynamic voltammetry.