Henderson equation, liquid-junction potentials

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) ... 

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. 

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

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.)... 

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

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. 

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)...

Use the Henderson equation to estimate the liquid junction potentials for the following systems assume that the limiting molar conductivities given in table 6.2 can be used to calculate the ionic mobility. 

This result is at variance with the accepted values of the second dissociation constants of the acids. Reference [92GRE/FUG] selects log K° = - 1.80 for selenic and log,o K2 = -. 98 for sulphuric acid. The expected potential difference would therefore be about 1 to 2 mV from these data if the liquid junction potential ( ,) is ignored, and not a few tenths of a millivolt. The contradiction can probably be traced to the neglect of An estimate of Ej by the Henderson equation indicates that the first term in the above expression for E is largely cancelled by the second term. The same... 

The Integration of the Differential Equation for Liquid Junction Potential. To account for the results of such measurements as have been described in the previous section there have been a number of integrations of the fundamental differential equation (3). Of these the following will deal only with the integrations by Henderson and by Planck. In addition a graphical integration method devised by Maclnnes and Longsworth will be discussed. 

Equation or Method 26b Author Henderson o Planck Cell Potential millivolts E Liquid Junction Potential, millivolts Eh 26.85... 

At a diaphragm two solutions are separated from each other. When these two solutions consist of different electrolytes or electrolytes in different concentrations, a diffusion of the constituent of the solutions occurs. This leads to a potential difference, which is called a liquid-junction potential, the magnitude of which depends strongly on the composition of the solutions. Ideally, this liquid-junction potential should be very small and constant to minimise errors. To estimate liquid-junction potentials, the Henderson equation is applicable [23] ... 

Between two dissimilar electrolyte solutions a potential difference is created, just like between a metal and an electrolytic solution. By Brownian motion, the ions randomly walk with a velocity proportional to the Boltzmann factor kT. The corresponding E-field will have a direction to slow down the rapid ions and accelerate the slow ones in the interface zone. The resulting potential difference is called the liquid junction potential and follows a variant of the Nemst equation called the Henderson equation ... 

In a series of papers, Hurlen (13,14) has reported convenient" single ion activities derived from cells with transference. The liquid-junction potentials involved were estimated by the Henderson equation. In addition, Shatkay s ion-selective electrode measurements of the activities of Na" " and Ca2+ ions in NaCl and CaCl2 solutions, based on the Henderson equation, appear eminently reasonable in comparison with other estimates (15,16). 

Both internal and external reference electrodes possess an interface between the internal solution and the external environment. This interfaee is eommonly established within a porous junction and is designed to permit electrolytic communication while preventing flow. In any event, the junction gives rise to the isothermal liquid junetion potential (ILJP), Ed(T2), which develops, because some ions diffuse faster than others, thereby generating an eleetrie field that opposes the proeess. Integration of the electric field across the junetion yields the isothermal liquid junction potential. Bard and Faulkner provide a detailed discussion of the thermodynamics of the isothermal liquid junction. For dilute solutions, the potential ean be ealeulated from Henderson s equation. In the ease of Thermoeell I, the isothermal liquid junetion potential is expressed by ... 

Fig. 9.12 Calculated liquid junction potentials according to the Henderson equation for a 3 M KCI bridge electrolyte and various sample concentrations. The counterion in the sample is chloride...

Commercial pH electrodes are typically purchased as the so-called combination electrode where the reference electrode is integrated into the pH electrode body. A liquid junction potential develops in the contact zone between the sample solution and the reference electrolyte. If one considers a typical reference electrolyte of 3 M KCl in contact with a sample containing 10 mM KCl with varying concentrations of HCl or KOH, one obtains the liquid junction potentials from the Henderson equation as presented in Fig. 9.15. 

In the derivation of the formula for calculating the liquid junction potential, the electric work done in separating the charges is set equal to the work of diffusion that is, the change in chemical potential arising from the diffusion of the ions. Only after making certain approximations can one arrive at the so-called Henderson solution [56] of the Nernst-Planck equation [57] ... 

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... 

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

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