Activity coefficient potentiometric measurement

Two types of methods are used to measure activity coefficients. Potentiometric methods that measure the mean activity coefficient of the dissolved electrolyte directly will be described in Section 3.3.3. However, in galvanic cells with liquid junctions the electrodes respond to individual ion activities (Section 3.2). This is particularly true for pH measurement (Sections 3.3.2 and 6.3). In these cases, extrathermodynamical procedures defining individual ion activities must be employed. 

Quantitative Analysis Using the Method of Standard Additions Because of the difficulty of maintaining a constant matrix for samples and standards, many quantitative potentiometric methods use the method of standard additions. A sample of volume, Vx) and analyte concentration, Cx, is transferred to a sample cell, and the potential, (ficell)x) measured. A standard addition is made by adding a small volume, Vs) of a standard containing a known concentration of analyte, Cs, to the sample, and the potential, (ficell)s) measured. Provided that Vs is significantly smaller than Vx, the change in sample matrix is ignored, and the analyte s activity coefficient remains constant. Example 11.7 shows how a one-point standard addition can be used to determine the concentration of an analyte. 

Standard potentials Ee are evaluated with full regard to activity effects and with all ions present in simple form they are really limiting or ideal values and are rarely observed in a potentiometric measurement. In practice, the solutions may be quite concentrated and frequently contain other electrolytes under these conditions the activities of the pertinent species are much smaller than the concentrations, and consequently the use of the latter may lead to unreliable conclusions. Also, the actual active species present (see example below) may differ from those to which the ideal standard potentials apply. For these reasons formal potentials have been proposed to supplement standard potentials. The formal potential is the potential observed experimentally in a solution containing one mole each of the oxidised and reduced substances together with other specified substances at specified concentrations. It is found that formal potentials vary appreciably, for example, with the nature and concentration of the acid that is present. The formal potential incorporates in one value the effects resulting from variation of activity coefficients with ionic strength, acid-base dissociation, complexation, liquid-junction potentials, etc., and thus has a real practical value. Formal potentials do not have the theoretical significance of standard potentials, but they are observed values in actual potentiometric measurements. In dilute solutions they usually obey the Nernst equation fairly closely in the form ... 

However, under most conditions the activity coefficients cannot be neglected, certainly for a single redox couple where the ox/red concentration ratio cannot be simply calculated from the true standard potential and the potential directly observed. In order to overcome this difficulty the concept of the formal potential was introduced, which represents a formal standard potential E ° measured in an actual potentiometric calibration and obeying the Nernst equation, E = E ° + (0.05916/n) log ([ox]/[red]) at 25° C, E"0 must meet the conditions under which the analytical measurements have to be made. Sometimes the formal potential values are decisive for the direction of the reaction between two redox couples even when the E° values do not differ markedly10. 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

It would appear from Eq. (3.2.8) that the pH, i.e. the activity of a single type of ion, can be measured exactly. This is not, in reality, true even if the liquid junction potential is eliminated the value of Eref must be known. This value is always determined by assuming that the activity coefficients depend only on the overall ionic strength and not on the ionic species. Thus the mean activities and mean activity coefficients of the electrolyte must be employed. The use of this assumption in the determination of the value of Eref will, of course, also affect the pH value found from Eq. (3.2.8). Thus, the potentiometric determination of the pH is more difficult than would appear at first glance and will be considered in the special Section 3.3.2. 

Potentiometry is used in the determination of various physicochemical quantities and for quantitative analysis based on measurements of the EMF of galvanic cells. By means of the potentiometric method it is possible to determine activity coefficients, pH values, dissociation constants and solubility products, the standard affinities of chemical reactions, in simple cases transport numbers, etc. In analytical chemistry, potentiometry is used for titrations or for direct determination of ion activities. 

The potentiometric measurement of physicochemical quantities such as dissociation constants, activity coefficients and thus also pH is accompanied by a basic problem, leading to complications that can be solved only if certain assumptions are accepted. Potentiometric measurements in cells without liquid junctions lead to mean activity or mean activity coefficient values (of an electrolyte), rather than the individual ionic values. 

Mean activity coefficients can be measured potentiometrically, mostly in a concentration cell with or without transfer. Consider, for example, the cell (with a non-aqueous electrolyte solution)... 

So what do we do about the problem of activity coefficients - surely we can t just write off potentiometric measurements ... 

Determining solubility constants in aqueous solutions generally involves analytical work to determine concentrations [ ] or potentiometric measurements to obtain activities. The ratio of activity and concentration—i.e., the activity coefficient and its change with concentration— depends on the choice of the standard state. If pure water is chosen as a standard state, the activity coefficients approach unity only in dilute solutions. It is therefore necessary to express the so-called thermodynamic constants TK (48) in terms of activities. If, on the other hand, one chooses as reference an aqueous solution of comparatively high and constant ionic strength, the activity coefficients remain close to unity even at rather high concentrations of the reacting species. In this case, we may use stoichiometric constants K (48), expressed in molarities, M, and related to a particular ionic medium. 

Potentiometry has found extensive application over the past half-century as a means to evaluate various thermodynamic parameters. Although this is not the major application of the technique today, it still provides one of the most convenient and reliable approaches to the evaluation of thermodynamic quantities. In particular, the activity coefficients of electroactive species can be evaluated directly through the use of the Nemst equation (for species that give a reversible electrochemical response). Thus, if an electrochemical system is used without a junction potential and with a reference electrode that has a well-established potential, then potentiometric measurement of the constituent species at a known concentration provides a direct measure of its activity. This provides a direct means for evaluation of the activity coefficient (assuming that the standard potential is known accurately for the constituent half-reaction). If the standard half-reaction potential is not available, it must be evaluated under conditions where the activity coefficient can be determined by the Debye-Hiickel equation. 

Usually, the analytical chemist needs to determine the concentration of the ion of interest rather than its activity. The obvious approach to converting potentiometric measurements from activity to concentration is to make use of an empirical calibration curve, such as the one shown in Figure 5.3. Electrodes potentials of standard solutions are thus measured and plotted (on a semilog paper) versus the concentration. Since the ionic strength of the sample is seldom known, it is often useful to add a high concentration of an electrolyte to the standards and the sample to maintain approximately the same ionic strength (i.e., the same activity coefficient). The ionic strength adjustor is usually a buffer (since pH control is also desired for most ISEs). The empirical calibration plot thus yields results in terms of concentration. Theoretically,... 

If the paH scale is used the catalytic coefficients and fcoH must be referred to H + and OH" activities which are obtained from potentiometric measurements. These are different from the concentrations. 

Electrode response is related to analyte activity rather than analyte concentration. We are usually interested in concentration, however, and the determination of this quantity from a potentiometric measurement requires activity coefficient data. Activity coefficients are seldom available because the ionic strength of the solution either is unknown or else is so large that the Debye-Huckel equation is not applicable. 

Values of/x = Ac/A may be calculated from Kohlrausch s measurements of electrical conductivity of hydrochloric acid solutions. /h and fci can be evaluated from the potentiometric measurements on hydrochloric acid solutions performed by Scatchaed. These data are very reliable since the concentration chain was so arranged as to eliminate diffusion potentials. In this way, ScATCHARD determined the mean activity coefficient V/h/ci instead of the individual ion activities. If we assume that in a potassium chloride solution/ = /ci— which is plausible when we recall that both ions have the same structure—and that fci is the same in hydrochloric acid solutions and potassium chloride solutions of the same concentration, then we can calculate/h and fci in hydrochloric acid solutions. Naturally these values are not strictly correct since the effect of the potassium ions on the activity of the chloride ions probably is different from that of the hydrogen ions at the same ionic strength. In the succeeding table are given values of /x, /h, and fci calculated by the above method. 

The potentiometric titration method possesses some advantages characteristic of potentiometry. The measured e.m.f. values are dependent on the logarithm of the activity (concentration) of the potential-defining ion and this considerably widens the range of concentrations which can be detected. The experimental techniques and routine are rather simple and the obtained results are well reproducible. Owing to the stable activity coefficients of metal cations the measurements can be performed in sufficiently concentrated solutions of the corresponding metal halides. Performing the measurement does not imply any interference in the acid-base processes in the melt studied and the experiment is faster than the isothermal saturation technique discussed above. 

The calcium and sodium activity coefficients were determined at 25.0 - 0.1 C with an Orion electrode (model 92-32) and a Radiometer electrode (model G502 Na), respectively. A saturated calomel electrode was used as the reference. Calibration curves were obtained using CaCl or NaCl solutions before and after each measurement. The CaCl2 and NaCl concentrations were measured by potentiometric determinations of the chlorides with silver nitrate and with a silver electrode. 

Potentiometric electrodes measure activity rather than concentration, a unique feature, and we will use activities in this chapter in describing electrode potentials. An understanding of activity and the factors that affect it are important for direct potentiometric measurements, as in pH or ion-selective electrode measurements. You should, therefore, review the material on activity and activity coefficients in Chapter 6. 

Potentiometric measurements have been performed at 25, 35 and 45°C to determine thermodynamic parameters of the mono-thiocyanato complexes of five 3d metal ions, among them nickel(II). The activity coefficients of the different species were calculated by the Davies equation. Since the Davies equation is not compatible with the SIT, and no experimental data are provided, the reported thermodynamic functions were not considered in this review. 

The standard-addition method, described in Section lD-3, is equally applicable to potentiometric determinations. In this method, the potential of the electrode system is measured before and after addition of a small volume (or volumes) of a standard to a known volume of the sample. We assume that this addition does not change the ionic strength and thus the activity coefficient yx nf fhe analyte. We further assume that the added standard does not significantly alter the junction potential. 

Equations (3-6) for the potentiometric and spectrophotometric methods will provide thermodynamic pKa values. For the solubility-pH dependence method [Eqs. (7-8)], the values obtained are apparent values (pKg )/ which are relevant to the ionic strength (7) of the aqueous buffers used to fix the pH value for each solution. If the ionic strength of each buffer solution is controlled or assessed, then the apparent value can be corrected to a thermod)mamic value, using an activity coefficient from one of the Debye-Hiickel equations (Section 2.2.5). If the solubility-pH dependence is measured in several buffer systems, each with a different ionic strength, then the Guggenheim approach can be used to correct the result to zero ionic strength [Eq. (17)]. 

Reliability assessment (data quality) is based on information in the original source describing the method used (including evidence for calibration of pH meters exclusion of CO2 in determining pKg values above 6.5), whether pKa values for standard compounds were measured, presence of organic cosolvents, the presence or absence of corrections for [H" "], [OH ] in potentiometric titrations, and use of mean ionic activity coefficients in the calculations. Considerable effort has been made to locate the original source for each measured value. Where only secondary sources have been located, data reliability cannot be assessed with confidence. 

Potentiometric measurements for the evaluation of Na" activity coefficients were carried out using a Drion BD1 Analyser with a Orion IMa-electrode in conjunction with a reference calomel electrode and a water JacKeted titration cell. 

If the half-cell equation includes H, then pE will depend on pH. The formal potential, will also incorporate the aj values relating to the presence of complexing ligands and a, values if the ligand is affected by pH. Finally, activity coefficients must be included in order to relate to potentiometric measurement values which give p E . 

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