Concentration Nernst equation

The electrons flow in the direction that tends to equalize the concentrations Nernst equation... 

Nernst equation This equation relates the e.m.f. of a cell to the concentrations or, more accurately, the activities of the reactants and products of the cell reaction. For a reaction... 

The redox (electrode) potential for ion-ion redox systems at any concentration and temperature is given by the Nernst equation in the form... 

Thus under standard conditions chloride ions are not oxidised to chlorine by dichromate(Vr) ions. However, it is necessary to emphasise that changes in the concentration of the dichromate(VI) and chloride ions alters their redox potentials as indicated by the Nernst equation. Hence, when concentrated hydrochloric acid is added to solid potassium dichromate and the mixture warmed, chlorine is liberated. 

In a redox reaction, one of the reactants is oxidized while another reactant is reduced. Equilibrium constants are rarely used when characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products. 

You will recall from Chapter 6 that the Nernst equation relates the electrochemical potential to the concentrations of reactants and products participating in a redox reaction. Consider, for example, a titration in which the analyte in a reduced state, Ared) is titrated with a titrant in an oxidized state, Tox- The titration reaction is... 

Before the equivalence point the concentration of unreacted Fe + and the concentration of Fe + produced by reaction 9.16 are easy to calculate. For this reason we find the potential using the Nernst equation for the analyte s half-reaction... 

At the equivalence point, the moles of Fe + initially present and the moles of Ce + added are equal. Because the equilibrium constant for reaction 9.16 is large, the concentrations of Fe and Ce + are exceedingly small and difficult to calculate without resorting to a complex equilibrium problem. Consequently, we cannot calculate the potential at the equivalence point, E q, using just the Nernst equation for the analyte s half-reaction or the titrant s half-reaction. We can, however, calculate... 

After the equivalence point, the concentrations of Ce + and excess Ce + are easy to calculate. The potential, therefore, is best calculated using the Nernst equation for the titrant s half-reaction. 

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. ... 

Potential and Concentration—The Nernst Equation The potential of a potentio-metric electrochemical cell is given as... 

Despite the apparent ease of determining an analyte s concentration using the Nernst equation, several problems make this approach impractical. One problem is that standard-state potentials are temperature-dependent, and most values listed in reference tables are for a temperature of 25 °C. This difficulty can be overcome by maintaining the electrochemical cell at a temperature of 25 °C or by measuring the standard-state potential at the desired temperature. 

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). 

Since the junction potential is usually of unknown value, it is normally impossible to directly calculate the analyte s concentration using the Nernst equation. Quantitative analytical work is possible, however, using the standardization methods discussed in Chapter 5. 

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... 

Quantitative Analysis Using External Standards To determine the concentration of analyte in a sample, it is necessary to standardize the electrode. If the electrode s response obeys the Nernst equation. 

Influence of Applied Potential on the Faradaic Current As an example, let s consider the faradaic current when a solution of Fe(CN)6 is reduced to Fe(CN)6 at the working electrode. The relationship between the concentrations of Fe(CN)6 , Fe(CN)6 A and the potential of the working electrode is given by the Nernst equation thus... 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

When ligand is present we must account for its effect on the concentration of O. Solving equation 11.42 for [O] c=o and substituting into the Nernst equation gives... 

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. 

Nernst equation an equation relating electrochemical potential to the concentrations of products and reactants, (p. 146) neutron activation a means of inducing radioactivity in a nonradioactive sample by bombarding the sample with neutrons, (p. 645)... 

It must not be assumed that the protection potential is numerically equal to the equilibrium potential for the iron/ferrous-ion electrode (E ). The standard equilibrium potential (E ) for iron/ferrous-ion is -0-440V (vs. the standard hydrogen electrode). If the interfacial ferrous ion concentration when corrosion ceases is approximately 10 g ions/1 then, according to the Nernst equation, the equilibrium potential (E ) is given by ... 

A simple calculation based on the solubility product of ferrous hydroxide and assuming an interfacial pH of 9 (due to the alkalisation of the cathodic surface by reaction ) shows that, according to the Nernst equation, at -0-85 V (vs. CU/CUSO4) the ferrous ion concentration then present is sufficient to permit deposition hydroxide ion. It appears that the ferrous hydroxide formed may be protective and that the practical protection potential ( —0-85 V), as opposed to the theoretical protection potential (E, = -0-93 V), is governed by the thermodynamics of precipitation and not those of dissolution. 

The Nernst equation can also be used to determine the effect of changes in concentration on the voltage of an individual half-cell, E or Consider, for example, the half-reaction... 

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 ... 

The oxidation and reduction should be reversible. At a potential E the ratio of the concentrations of the two forms is given by the Nernst equation ... 

In the Nernst equation the term RT/nF involves known constants, and introducing the factor for converting natural logarithms to logarithms to base 10, the term has a value at a temperature of 25 °C of 0.0591 V when n is equal to 1. Hence, for an ion M+, a ten-fold change in ionic activity will alter the electrode potential by about 60 millivolts, whilst for an ion M2 +, a similar change in activity will alter the electrode potential by approximately 30 millivolts, and it follows that to achieve an accuracy of 1 per cent in the value determined for the ionic concentration by direct potentiometry, the electrode potential must be capable of measurement to within 0.26 mV for the ion M+, and to within 0.13 mV for the ion M2 +. ... 

As a consequence, the equilibrium potential of the single half-cell also depends on the concentrations of the compounds involved. The Nernst equation [Eq. (24)], which is one of the most important electrochemical relations, explains this context... 

Nernst equation for concentration cells, 467 theorem, 484, 489, 508, 531 theory of galvanic cells, 474... 

An important application of the Nernst equation is the measurement of concentration. In a concentration cell, the two electrodes are identical except for their concentrations. For such a cell, E° = 0 and at 25°C the potential corresponding to the cell reaction is related to Q by E = —(0.025693 V//z) In Q. For example, a concentration cell having two Ag+/Ag electrodes is... 

Provided that the pressure of hydrogen is 1 bar, we can write the reaction quotient as Q = [H "]2[C1 ]2. To find the concentration of hydrogen ions, we write the Nernst equation ... 

This standard potential is for an OH concentration of 1 mol-L 1, which corresponds to pH = 14, a strongly basic solution. However, from the Nernst equation, we can calculate that, at pH = 7, this couple has E = —0.42 V. Any metal with a standard potential more negative than —0.42 V can therefore reduce water at pH = 7 that is, at this pH, any such metal can be oxidized by water. Because E° = — 0.44 V for Fe2+(aq) 4- 2 e Fe(s), iron has only a very slight tendency to be oxidized by water at pH = 7. For this reason, iron can be used for pipes in water supply systems and can be stored in oxygen-free water without rusting (Fig. 12.17). 

Nernst equation The equation expressing the emf of an electrochemical cell in terms of the concentrations of the reagents taking part in the cell reaction E = E° - (RT/nF) In Q. 

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