Ion transport number

Last updated

In chemistry, ion transport number, also called the transference number, is the fraction of the total electric current carried in an electrolyte by a given ionic species i: [1]

Contents

Differences in transport number arise from differences in electrical mobility. For example, in an aqueous solution of sodium chloride, less than half of the current is carried by the positively charged sodium ions (cations) and more than half is carried by the negatively charged chloride ions (anions) because the chloride ions are able to move faster, i.e., chloride ions have higher mobility than sodium ions. 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. [2] Liquid junction potential can arise from ions in a solution having different ion transport numbers.

At zero concentration, the limiting ion transport numbers may be expressed in terms of the limiting molar conductivities of the cation (), anion (), and electrolyte ():

and

where and are the numbers of cations and anions respectively per formula unit of electrolyte. [1] In practice the molar ionic conductivities are calculated from the measured ion transport numbers and the total molar conductivity. For the cation , and similarly for the anion. 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. [4] [3]

Experimental measurement

There are several experimental techniques for the determination of transport numbers. [3] The Hittorf method is based on measurements of ion concentration changes near the electrodes. The moving boundary method involves measuring the speed of displacement of the boundary between two solutions due to an electric current. [5]

Hittorf method

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. [6] The exact relationship depends on the nature of the reactions at the two electrodes. For the electrolysis of aqueous copper(II) sulfate (CuSO4) as an example, with Cu2+(aq) and SO2−4(aq) ions, the cathode reaction is the reduction Cu2+(aq) + 2 e → Cu(s) and the anode reaction is the corresponding oxidation of Cu to Cu2+. At the cathode, the passage of coulombs of electricity leads to the reduction of moles of Cu2+, where is the Faraday constant. Since the Cu2+ ions carry a fraction of the current, the quantity of Cu2+ flowing into the cathode compartment is 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]

Moving boundary method

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.

The cation of the indicator electrolyte should not move faster than the cation whose transport number is to be determined, and it should have same anion as the principle electrolyte. Besides the principal electrolyte (e.g., HCl) is kept light so that it floats on indicator electrolyte. 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. The anode reaction is Cd → Cd2+ + 2 e so that a cadmium chloride (CdCl2) solution is formed near the anode and moves toward the cathode during the experiment. An acid-base indicator such as bromophenol blue is added to make visible the boundary between the acidic HCl solution and the near-neutral CdCl2 solution. [8] The boundary tends to remain sharp since the leading solution HCl has a higher conductivity that the indicator solutionCdCl2, 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. [1]

Concentration cells

This quantity can be calculated from the slope of the function of two concentration cells, without or with ionic transport.

The EMF of transport concentration cell involves both the transport number of the cation and its activity coefficient:

where and are activities of HCl solutions of right and left hand electrodes, respectively, and is the transport number of Cl.

Electrophoretic magnetic resonance imaging method

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 [9]

See also

Notes

  1. 1 2 3 4 Peter Atkins and Julio de Paula, Physical Chemistry (8th ed. Oxford University Press, 2006) p.768-9 ISBN   0-7167-8759-8
  2. Pathways to Modern Chemical Physics by Salvatore Califano (Springer 2012) p.61 ISBN   9783642281808
  3. 1 2 3 http://lacey.se/science/transference/
  4. M. Doyle, T. F. Fuller and J. Newman, "The importance of the lithium ion transference number in lithium/polymer cells." Electrochim Acta, 39, 2073 (1994) 10.1016/0013-4686(94)85091-7
  5. 1 2 3 Laidler K.J. and Meiser J.H., Physical Chemistry (Benjamin/Cummings 1982) p.276-280 ISBN   0-8053-5682-7
  6. Electrochemistry Dictionary - H Corrosion Doctors.
  7. 1 2 Principles and Applications of Electrochemistry D.R.Crow (4th ed., CRC Press 1994) p.165-169 ISBN   0748743782
  8. Transport numbers and ionic mobilities by the moving boundary method, G. A. Lonergan and D. C. Pepper, J. Chem. Educ., 1965, 42 (2), p. 82. doi:10.1021/ed042p82
  9. Klett, Matilda; Giesecke, Marianne; Nyman, Andreas; Hallberg, Fredrik; Lindström, Rakel Wreland; Lindbergh, Göran; Furó, István (2012). "Quantifying Mass Transport during Polarization in a Li Ion Battery Electrolyte by in Situ 7Li NMR Imaging". Journal of the American Chemical Society. 134 (36): 14654–14657. doi:10.1021/ja305461j. PMID   22900791.

Related Research Articles

<span class="mw-page-title-main">Electrochemistry</span> Branch of chemistry

Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference and identifiable chemical change. These reactions involve electrons moving via an electronically-conducting phase between electrodes separated by an ionically conducting and electronically insulating electrolyte.

<span class="mw-page-title-main">Electrode</span> Electrical conductor used to make contact with nonmetallic parts of a circuit

An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit. Electrodes are essential parts of batteries that can consist of a variety of materials depending on the type of battery.

<span class="mw-page-title-main">Electrolysis</span> Technique in chemistry and manufacturing

In chemistry and manufacturing, electrolysis is a technique that uses direct electric current (DC) to drive an otherwise non-spontaneous chemical reaction. Electrolysis is commercially important as a stage in the separation of elements from naturally occurring sources such as ores using an electrolytic cell. The voltage that is needed for electrolysis to occur is called the decomposition potential. The word "lysis" means to separate or break, so in terms, electrolysis would mean "breakdown via electricity".

An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dissolving, the substance separates into cations and anions, which disperse uniformly throughout the solvent. Solid-state electrolytes also exist. In medicine and sometimes in chemistry, the term electrolyte refers to the substance that is dissolved.

<span class="mw-page-title-main">Galvanic cell</span> Electrochemical device

A galvanic cell or voltaic cell, named after the scientists Luigi Galvani and Alessandro Volta, respectively, is an electrochemical cell in which an electric current is generated from spontaneous oxidation–reduction reactions. A common apparatus generally consists of two different metals, each immersed in separate beakers containing their respective metal ions in solution that are connected by a salt bridge or separated by a porous membrane.

In electrochemistry, standard electrode potential, or , is a measure of the reducing power of any element or compound. The IUPAC "Gold Book" defines it as; "the value of the standard emf of a cell in which molecular hydrogen under standard pressure is oxidized to solvated protons at the left-hand electrode".

In electrochemistry, a half-cell is a structure that contains a conductive electrode and a surrounding conductive electrolyte separated by a naturally occurring Helmholtz double layer. Chemical reactions within this layer momentarily pump electric charges between the electrode and the electrolyte, resulting in a potential difference between the electrode and the electrolyte. The typical anode reaction involves a metal atom in the electrode being dissolved and transported as a positive ion across the double layer, causing the electrolyte to acquire a net positive charge while the electrode acquires a net negative charge. The growing potential difference creates an intense electric field within the double layer, and the potential rises in value until the field halts the net charge-pumping reactions. This self-limiting action occurs almost instantly in an isolated half-cell; in applications two dissimilar half-cells are appropriately connected to constitute a Galvanic cell.

<span class="mw-page-title-main">Solid oxide fuel cell</span> Fuel cell that produces electricity by oxidization

A solid oxide fuel cell is an electrochemical conversion device that produces electricity directly from oxidizing a fuel. Fuel cells are characterized by their electrolyte material; the SOFC has a solid oxide or ceramic electrolyte.

<span class="mw-page-title-main">Sodium chlorate</span> Chemical compound

Sodium chlorate is an inorganic compound with the chemical formula NaClO3. It is a white crystalline powder that is readily soluble in water. It is hygroscopic. It decomposes above 300 °C to release oxygen and leaves sodium chloride. Several hundred million tons are produced annually, mainly for applications in bleaching pulp to produce high brightness paper.

Electrical mobility is the ability of charged particles to move through a medium in response to an electric field that is pulling them. The separation of ions according to their mobility in gas phase is called ion mobility spectrometry, in liquid phase it is called electrophoresis.

A silver chloride electrode is a type of reference electrode, commonly used in electrochemical measurements. For environmental reasons it has widely replaced the saturated calomel electrode. For example, it is usually the internal reference electrode in pH meters and it is often used as reference in reduction potential measurements. As an example of the latter, the silver chloride electrode is the most commonly used reference electrode for testing cathodic protection corrosion control systems in sea water environments.

<span class="mw-page-title-main">Voltammetry</span> Method of analyzing electrochemical reactions

Voltammetry is a category of electroanalytical methods used in analytical chemistry and various industrial processes. In voltammetry, information about an analyte is obtained by measuring the current as the potential is varied. The analytical data for a voltammetric experiment comes in the form of a voltammogram, which plots the current produced by the analyte versus the potential of the working electrode.

<span class="mw-page-title-main">Electrodialysis</span> Applied electric potential transport of salt ions.

Electrodialysis (ED) is used to transport salt ions from one solution through ion-exchange membranes to another solution under the influence of an applied electric potential difference. This is done in a configuration called an electrodialysis cell. The cell consists of a feed (dilute) compartment and a concentrate (brine) compartment formed by an anion exchange membrane and a cation exchange membrane placed between two electrodes. In almost all practical electrodialysis processes, multiple electrodialysis cells are arranged into a configuration called an electrodialysis stack, with alternating anion and cation-exchange membranes forming the multiple electrodialysis cells. Electrodialysis processes are different from distillation techniques and other membrane based processes in that dissolved species are moved away from the feed stream, whereas other processes move away the water from the remaining substances. Because the quantity of dissolved species in the feed stream is far less than that of the fluid, electrodialysis offers the practical advantage of much higher feed recovery in many applications.

The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas. It is a linearized Poisson–Boltzmann model, which assumes an extremely simplified model of electrolyte solution but nevertheless gave accurate predictions of mean activity coefficients for ions in dilute solution. The Debye–Hückel equation provides a starting point for modern treatments of non-ideality of electrolyte solutions.

The molar conductivity of an electrolyte solution is defined as its conductivity divided by its molar concentration.

Liquid junction potential occurs when two solutions of electrolytes of different concentrations are in contact with each other. The more concentrated solution will have a tendency to diffuse into the comparatively less concentrated one. The rate of diffusion of each ion will be roughly proportional to its speed in an electric field, or their ion mobility. If the anions diffuse more rapidly than the cations, they will diffuse ahead into the dilute solution, leaving the latter negatively charged and the concentrated solution positively charged. This will result in an electrical double layer of positive and negative charges at the junction of the two solutions. Thus at the point of junction, a potential difference will develop because of the ionic transfer. This potential is called liquid junction potential or diffusion potential which is non-equilibrium potential. The magnitude of the potential depends on the relative speeds of the ions' movement.

<span class="mw-page-title-main">Solid state ionics</span>

Solid-state ionics is the study of ionic-electronic mixed conductor and fully ionic conductors and their uses. Some materials that fall into this category include inorganic crystalline and polycrystalline solids, ceramics, glasses, polymers, and composites. Solid-state ionic devices, such as solid oxide fuel cells, can be much more reliable and long-lasting, especially under harsh conditions, than comparable devices with fluid electrolytes.

<span class="mw-page-title-main">Conductivity (electrolytic)</span> Measure of the ability of a solution containing electrolytes to conduct electricity

Conductivity of an electrolyte solution is a measure of its ability to conduct electricity. The SI unit of conductivity is siemens per meter (S/m).

Pitzer equations are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. They were first described by physical chemist Kenneth Pitzer. The parameters of the Pitzer equations are linear combinations of parameters, of a virial expansion of the excess Gibbs free energy, which characterise interactions amongst ions and solvent. The derivation is thermodynamically rigorous at a given level of expansion. The parameters may be derived from various experimental data such as the osmotic coefficient, mixed ion activity coefficients, and salt solubility. They can be used to calculate mixed ion activity coefficients and water activities in solutions of high ionic strength for which the Debye–Hückel theory is no longer adequate. They are more rigorous than the equations of specific ion interaction theory, but Pitzer parameters are more difficult to determine experimentally than SIT parameters.

Aluminium-ion batteries are a class of rechargeable battery in which aluminium ions serve as charge carriers. Aluminium can exchange three electrons per ion. This means that insertion of one Al3+ is equivalent to three Li+ ions. Thus, since the ionic radii of Al3+ (0.54 Å) and Li+ (0.76 Å) are similar, significantly higher numbers of electrons and Al3+ ions can be accepted by cathodes with little damage. Al has 50 times (23.5 megawatt-hours m-3) the energy density of Li and is even higher than coal.