Activity coefficients concentration cells

Basic equations for almost every subfield of electrochemistry from first principles, referring at all times to the soundest and most recent theories and results unusually useful as text or as reference. Covers coulometers and Faraday s Law, electrolytic conductance, the Debye-Hueckel method for the theoretical calculation of activity coefficients, concentration cells, standard electrode potentials, thermodynamic ionization constants, pH, potentiometric titrations, irreversible phenomena. Planck s equation, and much more, a indices. Appendix. 585-item bibliography. 197 figures. 94 tables, ii 4. 478pp. 5-% x 8. ... 

Because the ionic strength of a 1 1 electrolyte is equal to the concentration, copy the value 0.041 23 from cell B10 into cell B4. (To transfer a numerical value, rather than a formula, COPY cell B10 and then highlight cell B4. In the EDIT menu, select PASTE SPECIAL and then choose Value. The numerical value from B10 will be pasted into B4.) This procedure gives new activity coefficients in cells B6 and B8 and a new concentration in cell B10. Copy the new concentration from cell BIO into cell B4 and repeat this procedure several times until you have a constant answer. 

Activity Coefficients from Cells With Transference.—In order to set up a cell without transference it is necessary to have electrodes reversible with respect to each of the ions of the electrolyte this is not always possible or convenient, and hence the use of cells with transference, which require electrodes reversible with respect to one ion only, has obvious advantages. In order that such cells may be employed for the purpose of determining activity coefficients, however, it is necessary to have accurate transference number data for the electrolyte being studied. Such data have become available in recent years, and in the method described below it will be assumed that the transference numbers are known over a range of concentrations. ... 

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. 

The reduction potentials for the actinide elements ate shown in Figure 5 (12—14,17,20). These ate formal potentials, defined as the measured potentials corrected to unit concentration of the substances entering into the reactions they ate based on the hydrogen-ion-hydrogen couple taken as zero volts no corrections ate made for activity coefficients. The measured potentials were estabhshed by cell, equihbrium, and heat of reaction determinations. The potentials for acid solution were generally measured in 1 Af perchloric acid and for alkaline solution in 1 Af sodium hydroxide. Estimated values ate given in parentheses. 

To be preci.se in physical chemical terms, the activities of tire various components, not their molar concentration.s,. should be u.sed in the.se equations. The activity ( z) of a. solute component is defined as the product of its molar concentration, c, and an activity coefficient, 7 a = [c]y. Mo.st biochemical work involves dilute solutions, and die u.se of acdvides instead of molar concentration.s is usually neglected. However, the concentration of certain solutes may be very high in living cells. 

Direct measurements of solute activity are based on studies of the equilibria in which a given substance is involved. The parameters of these equilibria (the distribution coefficients, equilibrium constants, and EMF of galvanic cells) are determined at different concentrations. Then these data are extrapolated to very low concentrations, where the activity coincides with concentration and the activity coefficient becomes unity. 

The solubility of silver bromide is very low, and if no other ions are present in discernible amounts, the activity coefficients will be adequately close to unity to permit the activities to be displaced by concentrations. Again, at equilibrium the emf of the cell will be zero and... 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

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)... 

The second method of minimizing the junction potential is to employ a swamping electrolyte S. We saw in Section 4.1 how diffusion occurs in response to entropy effects, themselves due to differences in activity. Diffusion may be minimized by decreasing the differences in activity, achieved by adding a high concentration of ionic electrolyte to both half-cells. Such an addition increases their ionic strengths I, and decreases all activity coefficients y to quite a small value. 

Figure 13-3 puts everything together in a spreadsheet. Input values for FKH,P04, FNaiHPOj, pA i, pKn, pK3, and pA w are in the shaded cells. We guess a value for pH in cell H15 and write the initial ionic strength of 0 in cell Cl9. Cells A9 H10 compute activities with the Davies equation. With pi = 0, all activity coefficients are 1. Cells A13 H16 compute concentrations. [HT] in cell B13 is (10 PH)/yH = (10A-H15)/B9. Cell El 8 computes the sum of charges. 

Input values of concentration, volume, and moles are in cells B3 B6 in Figure 13-13. Cell B7 has the value 2 to indicate that glycine is a diprotic acid. Cell B8 has the activity coefficient of H+ computed with the Davies equation, 13-18. Cell B9 begins with the effec-... 

In addition to the foregoing, it is customary to include under electrochemistry (I) processes for which the net reaction is physical transfer, e g., concentration cells (2) electrokinetic phenomena, e.g.. electrophoresis. eleclroosmnsis, and streaming potential (3) properties ot electrolytic solutions, if they are determined by electrochemical or other means, e g.. activity coefficients and hydrogen ion concentration (4) processes in which electrical energy is first converted to heal, which in turn causes a chemical reaction that would not occur spontaneously at ordinary temperature. The... 

The left-hand side of this equation can be calculated from measurements of cell voltage as a function of concentration. The second term on the right-hand side becomes zero at infinite dilution. However, because no meaningful measurements can be made at zero concentration of reactants, we must extrapolate the equation to infinite dilution using the known concentration behavior of activity coefficients. In approaching infinite dilution, it is sufficient to use the Debye-Huckel... 

If the Nernst equation is applied to more concentrated solutions, the terms in the reaction quotient Q must be expressed in effective concentrations or activities of the electroactive ionic species. The activity coefficient y (gamma) relates the concentration of an ion to its activity a in a given solution through the relation a = yc Since electrode potentials measure activities directly, activity coefficients can be determined by carrying out appropriate EMF measurements on cells in which the concentration of the ion of interest is known. The resulting Es can then be used to convert concentrations into activities for use in other calculations involving equilibrium constants. 

In many situations, accurate determination of an ion concentration by direct measurement of a cell potential is impossible due to the presence of other ions and a lack of information about activity coefficients. In such cases it is often possible to determine the ion indirectly by titration with some other ion. For example, the initial concentration of an ion such as Fe2+ can be found by titrating with a strong oxidizing agent such as Ce4+. The titration is carried out in one side of a cell whose other half is a reference electrode ... 

The activity a2 of an electrolyte can be derived from the difference in behavior of real solutions and ideal solutions. For this purpose measurements are made of electromotive forces of cells, depression of freezing points, elevation of boiling points, solubility of electrolytes in mixed solutions and other characteristic properties of solutions. From the value of a2 thus determined the mean activity a+ is calculated using the equation (V-38) whereupon by application of the analytical concentration the activity coefficient is finally determined. The activity coefficients for sufficiently diluted solutions can also be calculated directly on the basis of the Debye-Hiickel theory, which will bo explained later on. 

When the activity of the cupric ions will drop to a value 1037 times smaller than the activity of zinc ions, the cell will cease to generate current. The same can be said about the concentration of cupric salt, because at such a great difference of activity the activity coefficients can be disregarded. The same equilibrium will be obtained by the precipitation of copper from a solution of its salts by metallic zinc, if the process of precipitation is carried out by a chemical method, i. e. by copper displacement (cementation). 

The values of the electrode standard potentials were obtained by measuring the EMF s of suitably arranged cells at varying concentrations and by extrapolating the found values into a state of infinitely diluted solutions in which the activity coefficients of electromotively active substances equal unity. To determine standard potentials is very laborious and requires considerable care. A detailed description of the working method and the method of results evaluation is beyond the limits of this book it is, therefore, necessary to refer to the pertinent technical literature" ... 

The -> concentration cells are used only for determination of -> transport (transference) numbers, - activity, and -> activity coefficients of electrolytes and other quantities. Their practical application is limited by the -> selfdischarge due to the spontaneous diffusion process. In concentration cells no chemical reactions occur, a physical process (the equalization of activities by diffusion) causes the potential difference and supplies the energy. 

Formal potential — Symbol Efr (SI Unit V), has been introduced in order to replace the standard potential of -> cell reaction when the values of - activity coefficients of the species involved in the cell reaction are unknown, and therefore concentrations used in the equation expressing the composition dependence of ceii instead of activities. It also involves the activity effect regarding the -+ standard hydrogen electrode, consequently in this way the formal electrode potential is also defined. Formal potentials are similar to conditional (apparent) equilibrium constants (-> equilibrium constant), in that, beside the effect of the activity coefficients, side reaction equilibria are also considered if those are not known or too complex to be taken into account. It follows that when the logarithmic term which contains the ratio of concentrations in the -> Nernst... 

Example 10.5 Diffusion cell and transference numbers The diffusion cell shown in Figure 10.2 has NaCl mixtures in the two chambers with concentrations c1A = lOOmmol/L and c1B = lOmmol/L. The mobilities of Na+ and Cl- ions are different and their ratio yields their transference numbers b+lb = t+/t = 0.39/0.61 (NaCl). The transference number t for an ion is the fraction of the total electric current carried by the ion when the mixture is subjected to an electric potential gradient. For monovalent ions, we have t+lt = 1. Estimate the diffusion potential of the cell at steady-state conditions at 298 K. Assume that activity coefficients are equal in the two reservoirs (Garby and Larsen, 1995). 

The electric potential difference between the interior and exterior of a cell is measured as 90 my with the cell interior negative, so that At/r = i/rB — i/rA = — 90 mV The cell s interior and exterior ions and their concentrations are shown in figure below. The activity coefficients for these ions are assumed to be the same in both phases. The temperature is uniform at 37°C. We want to estimate which of the three ions is closest to equilibrium. 

---