Concentration cells, cell potential

Individual ion activities may be obtained from electromotive force measurements using suitable concentration cells. The potential difference between an electrode and a solution containing ions of the electrode material is determined, according to the... 

In Chapter 20, we discussed the relationship of useful work, free energy, and the equilibrium constant. In this section, we examine this relationship in the context of electrochemical cells and see the effect of concentration on cell potential. 

Figure 15.15 Relationship between Ag concentration, the cell potential and the volume of Cl solution added.

Fig. 2.23 Plot of ZnCl2 concentrations vs. cell potential for the Zn corrosion cell.

The Nernst equation, expressing the effect of concentration on cell potential... 

In an operating sensor, which works as a concentration cell, the potential difference between a reference solution containing a known concentration of fluoride ion and the unknown fluoride concentration test solution is proportional to the logarithm of the ratio of the concentrations, as described by the Nemst equation. Interference from most anions is insignificant, except from hydroxide ions. The specifications for making the actual measurements are normally specified within a certain pH range, usually 5.5 to 6.0. 

Whenever you perform a calculation involving nonstandard cell concentrations, you can use Le Chatelier s principle to see if your answo- is reasonable. Recall that standard cell concentrations are equivalent and are 1.00 M. At standard concentrations the cell potential is 1.10 V. In this problem, the concentration of the product (Zn ) is 1.0 X 10 M, whereas the concentration of the reactant (Cu ) is O.KX) M. With these concentrations we would expect this spontaneous reaction to be shifted toward products, thereby resulting in a value of ceii greater than the standard value, which is what we observe. 

In fact, some care is needed with regard to this type of concentration cell, since the assumption implicit in the derivation of A2.4.126 that the potential in the solution is constant between the two electrodes, caimot be entirely correct. At the phase boundary between the two solutions, which is here a semi-pemieable membrane pemiitting the passage of water molecules but not ions between the two solutions, there will be a potential jump. This so-called liquid-junction potential will increase or decrease the measured EMF of the cell depending on its sign. Potential jumps at liquid-liquid junctions are in general rather small compared to nomial cell voltages, and can be minimized fiirther by suitable experimental modifications to the cell. 

For the equilibrium M(s) M (aq) + 2e, it might then be (correctly) assumed that the equilibrium for copper is further to the left than for zinc, i.e. copper has less tendency to form ions in solution than has zinc. The position of equilibrium (which depends also on temperature and concentration) is related to the relative reducing powers of the metals when two different metals in solutions of their ions are connected (as shown in Figure 4.1 for the copper-zinc cell) a potential difference is noted because of the differing equilibrium positions. 

In potentiometry the potential of an electrochemical cell is measured under static conditions. Because no current, or only a negligible current, flows while measuring a solution s potential, its composition remains unchanged. For this reason, potentiometry is a useful quantitative method. The first quantitative potentiometric applications appeared soon after the formulation, in 1889, of the Nernst equation relating an electrochemical cell s potential to the concentration of electroactive species in the cell. ... 

In potentiometry, the concentration of analyte in the cathodic half-cell is generally unknown, and the measured cell potential is used to determine its concentration. Thus, if the potential for the cell in Figure 11.5 is measured at -1-1.50 V, and the concentration of Zn + remains at 0.0167 M, then the concentration of Ag+ is determined by making appropriate substitutions to equation 11.3... 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

Plot of cell potential versus the log of the analyte s concentration In the presence of a fixed concentration of Interferent, showing the determination of the selectivity coefficient. 

The membrane also responds to the concentration of with the cell potential given as... 

If a mixture of an insoluble silver salt and Ag2S is used to make the membrane, then the membrane potential also responds to the concentration of the anion of the added silver salt. Thus, pellets made from a mixture of Ag2S and AgCl can serve as a Ck ion-selective electrode, with a cell potential of... 

Membranes fashioned from a mixture of Ag2S with CdS, CuS, or PbS are used to make ion-selective electrodes that respond to the concentration of Cd +, Cu +, or Pb +. In this case the cell potential is... 

The change in the concentration of H3O+ is monitored with a pH ion-selective electrode, for which the cell potential is given by equation 11.9. The relationship between the concentration of H3O+ and CO2 is given by rearranging the equilibrium constant expression for reaction 11.10 thus... 

The potentiometric determination of an analyte s concentration is one of the most common quantitative analytical techniques. Perhaps the most frequently employed, routine quantitative measurement is the potentiometric determination of a solution s pH, a technique considered in more detail in the following discussion. Other areas in which potentiometric applications are important include clinical chemistry, environmental chemistry, and potentiometric titrations. Before considering these applications, however, we must first examine more closely the relationship between cell potential and the analyte s concentration, as well as methods for standardizing potentiometric measurements. 

Activity Versus Concentration In describing metallic and membrane indicator electrodes, the Nernst equation relates the measured cell potential to the concentration of analyte. In writing the Nernst equation, we often ignore an important detail—the... 

The concentration of Ca + in a water sample was determined by the method of external standards. The ionic strength of the samples and standards was maintained at a nearly constant level by making each solution 0.5 M in KNO3. The measured cell potentials for the external standards are shown in the following table. 

Substituting the cell potential for the sample gives the concentration of Ca + as 2.17 X 10 M. Note that the slope of the calibration curve is slightly different from the ideal value of 0.05916/2 = 0.02958. 

The relative measurement error in concentration, therefore, is determined by the magnitude of the error in measuring the cell s potential and by the charge of the analyte. Representative values are shown in Table 11.7 for ions with charges of+1 and +2, at a temperature of 25 °C. Accuracies of 1-5% for monovalent ions and 2-10% for divalent ions are typical. Although equation 11.22 was developed for membrane electrodes, it also applies to metallic electrodes of the first and second kind when z is replaced by n. 

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

Calculate the molar concentration for the underlined component in the following cell if the cell potential is measured at +0.294 V... 

Ion-selective electrodes can be incorporated in flow cells to monitor the concentration of an analyte in standards and samples that are pumped through the flow cell. As the analyte passes through the cell, a potential spike is recorded instead of a steady-state potential. The concentration of K+ in serum has been determined in this fashion, using standards prepared in a matrix of 0.014 M NaCl. ... 

Ice formation is both beneficial and detrimental. Benefits, which include the strengthening of food stmctures and the removal of free moisture, are often outweighed by deleterious effects that ice crystal formation may have on plant cell walls in fmits and vegetable products preserved by freezing. Ice crystal formation can result in partial dehydration of the tissue surrounding the ice crystal and the freeze concentration of potential reactants. Ice crystals mechanically dismpt cell stmctures and increase the concentration of cell electrolytes which can result in the chemical denaturation of proteins. Other quaHty losses can also occur (12). 

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