The sum of the transport numbers for all of the ions in solution always equals unity: The concept and measurement of transport number were introduced by Johann Wilhelm Hittorf in the year 1853.
are the numbers of cations and anions respectively per formula unit of electrolyte.
In solutions, where ionic complexation or associaltion are important, two different transport/transference numbers can be defined.
[3] The practical importance of high (i.e. close to 1) transference numbers of the charge-shuttling ion (i.e. Li+ in lithium-ion batteries) is related to the fact, that in single-ion devices (such as lithium-ion batteries) electrolytes with the transfer number of the ion near 1, concentration gradients do not develop.
A constant electrolyte concentration is maintained during charge-discharge cycles.
In case of porous electrodes a more complete utilization of solid electroactive materials at high current densities is possible, even if the ionic conductivity of the electrolyte is reduced.
[3] The Hittorf method is based on measurements of ion concentration changes near the electrodes.
[5] This method was developed by German physicist Johann Wilhelm Hittorf in 1853.,[5] and is based on observations of the changes in concentration of an electrolyte solution in the vicinity of the electrodes.
In the Hittorf method, electrolysis is carried out in a cell with three compartments: anode, central, and cathode.
Measurement of the concentration changes in the anode and cathode compartments determines the transport numbers.
moles, so there is a net decrease of Cu2+ in the cathode compartment equal to
[7] This decrease may be measured by chemical analysis in order to evaluate the transport numbers.
Analysis of the anode compartment gives a second pair of values as a check, while there should be no change of concentrations in the central compartment unless diffusion of solutes has led to significant mixing during the time of the experiment and invalidated the results.
[7] This method was developed by British physicists Oliver Lodge in 1886 and William Cecil Dampier in 1893.
[5] It depends on the movement of the boundary between two adjacent electrolytes under the influence of an electric field.
If a colored solution is used and the interface stays reasonably sharp, the speed of the moving boundary can be measured and used to determine the ion transference numbers.
CdCl2 serves best because Cd2+ is less mobile than H+ and Cl− is common to both CdCl2 and the principal electrolyte HCl.
For example, the transport numbers of hydrochloric acid (HCl(aq)) may be determined by electrolysis between a cadmium anode and an Ag-AgCl cathode.
[8] The boundary tends to remain sharp since the leading solution HCl has a higher conductivity that the indicator solution CdCl2, and therefore a lower electric field to carry the same current.
If a more mobile H+ ion diffuses into the CdCl2 solution, it will rapidly be accelerated back to the boundary by the higher electric field; if a less mobile Cd2+ ion diffuses into the HCl solution it will decelerate in the lower electric field and return to the CdCl2 solution.
Also the apparatus is constructed with the anode below the cathode, so that the denser CdCl2 solution forms at the bottom.
[1] The cation transport number of the leading solution is then calculated as where
is the cation charge, c the concentration, L the distance moved by the boundary in time Δt, A the cross-sectional area, F the Faraday constant, and I the electric current.
are activities of HCl solutions of right and left hand electrodes, respectively, and
This method is based on magnetic resonance imaging of the distribution of ions comprising NMR-active nuclei (usually 1H, 19F, 7Li) in an electrochemical cells upon application of electric current.