Henderson junction

That equation explicitly shows the dominating influence of the ion mobilities on the value of the liquid junction potential. Although its application is limited, the Henderson junction is a significant experimental achievement because it allows the measurement of one electrode against another with known contribution of the liquid junction potential. 

Here, x is the coordinate normal to the diaphragm, so that d — q—p. The liquid junction potential A0L is the diffusion potential difference between solutions 2 and 1. The liquid junction potential can be calculated for more complex systems than that leading to Eq. (2.5.31) by several methods. A general calculation of the integral in Eq. (2.5.30) is not possible and thus assumptions must be made for the dependence of the ion concentration on x in the liquid junction. The approximate calculation of L. J. Henderson is... 

Although the Henderson formula depends on a number of simplifications and also employs ion concentrations rather than activities, it can nonetheless be used for estimation of the liquid junction potential up to moderate electrolyte concentrations, apparently as a result of compensation of errors. 

Henderson or Plank formalisms. Mobilities for several ions can be seen in Table 18a. 1. Liquid junction potentials can become more problematic with voltammetric or amperometric measurements. For example, the redox potentials of a given analyte measured in different solvent systems cannot be directly compared, since the liquid junction potential will be different for each solvent system. However, the junction potential Ej can be constant and reproducible. It can also be very small (about 2-3 mV) if the anion and cation of the salt bridge have similar mobilities. As a result, for most practical measurements the liquid junction potential can be neglected [9]. 

In contrast to the Planck solution, the Henderson approximation enjoys considerable use [ 10,11 ]. Henderson s liquid-junction model is based on the assumption that the concentrations of the ions in the liquid junction change linearly withx between values corresponding to the edges of the liquid junction. This assumption is equivalent to the concept of a mixture of electrolytes changing unifonnly between the two edges of the liquid junction. Then... 

Another less precise but frequently used method employs a liquid bridge between the analysed solution and the reference electrode solution. This bridge is usually filled with a saturated or 3.5 m KCl solution. If the reference electrode is a saturated calomel electrode, no further liquid bridge is necessary. Use of this bridge is based on the fact that the mobilities of potassium and chloride ions are about the same so that, as follows from the Henderson equation, the liquid-junction potential with a dilute solution on the other side has a very low value. Only when the saturated KCl solution is in contact with a very concentrated electrolyte solution with very different cation and anion mobilities does the liquid junction potential attain larger values [2] for the liquid junction 3.5 M KCl II1 M NaOH, A0z, = 10.5 mV. 

Recently, Fuchs etal. [15], using the streaming mercury electrode and applying the Henderson equation, have determined the pzc value in the solutions of tetraethy-lammonium perchlorate in DMSO as —0.515 0.001 V (versus Ag/0.01 M Ag+ (DMSO) reference electrode). This value was corrected for the liquid junction potential and was independent of tetraethyl ammonium perchlorate (TEAR) concentration within the range 0.02 to 0.75 M. Using the same methodology, KiSova et al. 

In aqueous solutions, the method of measuring electrode potentials has been well established. The standard hydrogen electrode (SHE) is the primary reference electrode and its potential is defined as zero at all temperatures. Practical measurements employ reference electrodes that are easy to use, the most popular ones being a silver-silver chloride electrode and a saturated calomel electrode (Table 5.4). The magnitude of the liquid junction potential (LJP) between two aqueous electrolyte solutions can be estimated by the Henderson equation. However, it is usual to keep the LJP small either by adding the same indifferent electrolyte in the two solutions or by inserting an appropriate salt bridge between the two solutions. 

If two electrolyte solutions that are of different concentrations but in the same solvent contact each other at a junction, ion transfers occur across the junction (Fig. 6.3). If the rate of transfer of the cation differs from that of the anion, a charge separation occurs at the junction and a potential difference is generated. The potential difference tends to retard the ion of higher rate and accelerate the ion of lower rate. Eventually, the rates of both ions are balanced and the potential difference reaches a constant value. This potential difference is called the liquid junction potential (LJP) [10]. As for the LJP between aqueous solutions, the LJP between non-aqueous solutions can be estimated using the Henderson equation. Generally the LJP, Lj-, at the junction Ci MX(s) c2 NY(s) can be expressed by Eq. (6.1) ... 

The hydrated layer has finite thickness, therefore the exchanging ions can diffuse inside this layer, although their mobility is quite low compared to that in water (n 10-11cm2s-1 V-1). As we have seen in the liquid junction, diffusion of ions with different velocities results in charge separation and formation of the potential. In this case, the potential is called the diffusion potential and it is synonymous with the junction potential discussed earlier. It can be described by the equation developed for the linear diffusion gradient, that is, by the Henderson equation (6.24). Because we are dealing with uni-univalent electrolytes, the multiplier cancels out and this diffusion potential can be written as... 

To maintain the condition Eref+Ed = const, numerical corrections are possible, e.g., using the Henderson equation for liquid-junction potential. 

Correct measured values for liquid junction potentials using the Henderson formalism and calculate ion activities according to the Debye-Huckel approximation. 

Here it is not very correct to assume that the concentration gradients vary linearly through the junction, especially because the concentration profiles depend on the technique of junction formation. Assuming that activities are equal to concentrations and that there is, in fact, a linear transition, we obtain the Henderson equation... 

Electrolyte junction — A liquid junction is the region of contact of two different -> electrolyte solutions kept apart by a porous -> diaphragm, such as sintered glass or ceramic. At the contact a -> Galvani potential difference appears, which is called -> liquid junction potential (Ej). In the case of two solutions of the same electrolyte, but with different concentrations (c(a) and c(/S)), the potential Ej is defined by the equation Ej = (t+-t-) ln ry, where t+ and t are - transport numbers of the cation and anion, respectively. If the concentration of one of the ions is the same in both solutions, but the other ion differs (e.g., NaCl and KC1), the potential Ej is given by the Henderson equation, which is reduced to the Lewis-Sargent relation for a 1 1 electrolyte Ej = ln, where A (/3) and A (a) are molar conductivities of the electrolytes in the com-... 

Due to the different mobilities, concentration gradients and thus potential gradients will be established. In actual measurements these potentials will be added to the electrode potentials. A calculation of liquid junction potential is possible with the -> Henderson equation. As liquid junction potential is an undesired addition in most cases, methods to suppress liquid junction potential like -> salt bridge are employed. (See also -> diffusion potentials, -> electrolyte junction, -> flowing junctions, and -> Maclnnes.)... 

The solution is given for the case of a smeared-out boundary and linear spatial distributions of concentrations. Generally, Henderson and Planck equations yield similar results however, for junctions with a pronounced difference in ion mobilities (like HCl-LiCl), the deviation can reach about 10 mV. A specific feature of the Planck equation is the existence of two solutions, the firstbeing close to that of Henderson, and the second one being independent of the solution concentration and of no physical meaning [iv]. Two particular types of liquid junctions are (a) two solutions of the same electrolyte at different concentrations and (b) two solutions at the same concentration with different electrolytes having an ion in common. For type (b) junctions, the simplification of the Henderson model results in the Lewis-Sargent equation ... 

This is known as the Planck-Henderson equation for diffusion or liquid-junction potentials. 

P. Henderson, An Equation for the Calculation of Potential Difference at any Liquid Junction Boundary, Z. Phys. Chetn. (Leipzig) 59 118 (1907). 

III the two special cases considered above, first, two solutions of the same electrolyte at different concentrations, and second, two electrolytes with a common ion at the same concentration, the Planck equation reduces to the same form as does the Henderson equation, viz., equations (43) and (44), respectively. It appears, therefore, that in these particular instances the value of the liquid junction potential does not depend on the type of boundary connecting the two solutions. 

Marshall IG, Henderson F. Drug interactions at the neuromuscular junction. Clin Anaesthesiol 1985 3 261. 

When different electrolytes are present on either side of the boundary, the electrolyte distribution is time dependent. This means that an exact thermodynamic solution to the problem is not possible. The solution to the problem given here is a steady-state solution, that is, the solution appropriate to a system in which mass transfer is occurring but under conditions that the liquid junction potential is independent of time. The porous diaphragms described earlier are examples of junctions which meet this condition. There are two well-known solutions to equation (9.7.17), one by Planck [6] and the other by P. Henderson [7]. The latter solution is more often used in practice and therefore is presented here. 

There are three important assumptions made in obtaining the Henderson equation for the liquid junction potential. First of all, it is assumed that the concentration of each ion changes linearly from the value that it has in the solution on... 

The Henderson equation may also be used to illustrate the principle involved in keeping the liquid junction potential small. Consider the junction between a very concentrated or saturated electrolyte solution and a dilute electrolyte solution ... 

Table 9.5 Liquid Junction Potentials Between 4.2 M KCl (Solution 1) and More Dilute Solutions of HCl and KCl (Solution 2) Estimated by the Henderson Equation (9.7.32)...

It should be stressed that the Henderson model recognizes that the system is not at equilibrium, and instead assumes that it is in a steady state. In addition, it is not the only model which was developed to investigate liquid junctions. The design of the liquid junction is an important aspect of obtaining reproducible experimental results. More information about this aspect can be found in the monograph by Koryta and Stulik [8]. 

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