CHEM-E4185 - Electrochemical Kinetics, 25.02.2019-29.05.2019

The assumption up until now in this chapter has been that there is a heterogeneous equilibrium on each phase boundary. A cell reaction will proceed reversibly in both directions if the equilibrium is disturbed slightly. If liquid junctions are present in the cell, they cause a particular, non-measurable potential loss in the cell. A typical case where this kind of potential losses is found is a cell in which two solutions with different compositions are in direct contact with each other. Concentration gradients will force the different species in the system to transfer from one phase to another. If these species involve ions, a diffusion potential is formed between the solution phases. If a diaphragm or a membrane separates the phases, ionic transport creates a membrane potential between the phases. In practice, the cells in Figures 4.2 and 4.3 contain liquid junctions. In chapters 4.3-4.4 this potential loss was assumed to be insignificant and, therefore, was not taken into account. In those exemplary cells, the liquid junctions would form over the diaphragm in Figure 4.2 and the porous diaphragm of the Ag/AgCl electrode structure in Figure 4.3.

4.4.1 Liquid junctions

A liquid junction potential between two solutions is formed when:

·         solutions are in direct contact

·         solutions contain different ions at different concentrations

·         ions have different mobilities

A very common example of a liquid junction is the calomel (or the Ag/AgCl) electrode. It is used as a ‘universal’ reference electrode as it can be immersed in almost any aqueous solution. In many cases, no reference electrode is truly fully reversible with respect to the ion/s present in the solution. Furthermore, reference electrodes are often either also prone to interference by other ions or do not work reliably in concentrated solutions – a fact that often limits the use of ion-selective electrodes.

When a calomel electrode is immersed in, for example, a phosphate buffer solution at pH 7, a liquid junction is formed across the glass frit of the electrode. Inside the electrode there are K⁺ and Cl⁻ ions, whilst H⁺, H₂PO₄⁻   and HPO₄^{2  −} ions are present in the measurement solution. In the frit, there is a mixture of all these ions and their concentrations will vary as a function of position in an unknown manner. In principle, the solution of the liquid junction potential follows equation (3.49) there is no electric current present, i.e. i = 0. Since the transport numbers are functions of the ionic concentrations, there is no exact solution of the problem in a multi-ionic system as the exact concentration profiles are unknown. Assuming that all the ions have a similar concentration profile across the glass frit, namely

where g(x) is an undetermined function that has the property g(0) = 0 and g(h) = 1 (h is the frit thickness), the integration of equation (3.49) leads to the following useful form:          

 Equation (4.38b) is known as the Henderson equation. Let us assume that the inner solution is 1 M KCl and the outer (measurement) solution is a 0.1 M phosphate buffer at pH 7 with the following ionic concentration (in mol/dm³): H⁺, 10⁻⁷; Na⁺, 0.158; H₂PO₄⁻   0.042; HPO₄^{2  −} 0.058. The contribution of H⁺ can be omitted, as its concentration is orders of magnitude lower than that of the other ions. By using the diffusion coefficient values given in Appendix 2 and presuming that the diffusion coefficients of the phosphate species are approximately 10⁻⁵ cm²/s, equation (4.38b) gives \Delta f ≈ −2 mV. This calculation shows that junction potentials are very small and are, therefore, usually omitted from the cell potential. Although, there are more elaborate treatises of the junction potential in essence they do not change the overall picture, except in some special cases.

4.4.2 Concentration cells

A concentration cell has identical electrodes and electrode reactions. In principle, if two identical electrodes are immersed in the same solution, the cell potential will be zero (equation 4.4). However, if the electrodes are immersed in solutions which differ only in their concentrations, a cell potential will form. The solutions have to include an ion with respect to which the electrode is reversible.

          Let us consider a cell that has two identical Ag/AgCl electrodes immersed in KCl solutions of different concentrations:

 The cell potential is formed as the sum of the galvanic potential differences between the phases:

 In equation (4.40), (\( \phi_\text{Ag/AgCl'}-\phi_\text{KCl(II)} \)) and (\( \phi_\text{KCl(I)}-\phi_\text{Ag/AgCl} \)) are the electrode potentials and (\( \phi_\text{KCl(II)}-\phi_\text{KCl(I)} \)) is the potential difference between solution phases I and II. The electrodes are reversible with respect to the chloride ion. Electrochemical equilibrium gives:

 Taking into account the similarity of the electrodes, which makes the chemical potential of chloride ion equal in both electrodes, gives:

 Potential difference between KCl solutions of different concentrations is calculated using the equation of diffusion potential, Equation (3.49). This gives in a one-dimensional case, which when added up over all the ions in the solution is:

 The cell potential is obtained by inserting (4.44) into (4.43):

 Because transport numbers are constants in a binary solution, equation (4.45) can be integrated to give

 where the relation \( t_{\text{K}^+}+t_{\text{Cl}^-}=1 \) and equation (2.20) have been applied.