Nernst equation reactions

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... 

Ladder diagrams can also be used to evaluate equilibrium reactions in redox systems. Figure 6.9 shows a typical ladder diagram for two half-reactions in which the scale is the electrochemical potential, E. Areas of predominance are defined by the Nernst equation. Using the Fe +/Fe + half-reaction as an example, we write... 

Although this treatment of buffers was based on acid-base chemistry, the idea of a buffer is general and can be extended to equilibria involving complexation or redox reactions. For example, the Nernst equation for a solution containing Fe + and Fe + is similar in form to the Henderson-Hasselbalch equation. 

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 titration mixture consists of appreciable quantities of both the oxidized and reduced forms of the analyte, but very little unreacted titrant. The potential, therefore, is best calculated using the Nernst equation for the analyte s half-reaction... 

Although EXo /ATcd is standard-state potential for the analyte s half-reaction, a matrix-dependent formal potential is used in its place. After the equivalence point, the potential is easiest to calculate using the Nernst equation for the titrant s half-reaction, since significant quantities of its oxidized and reduced forms are present. 

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... 

Eeq by combining the two Nernst equations. To do so we recognize that the potentials for the two half-reactions are the same thus,... 

Note, again, that the Nernst equations for both E and Ta are written for reduction reactions. The cell potential, therefore, is... 

The difference between the potential actually required to initiate an oxidation or reduction reaction, and the potential predicted by the Nernst equation. 

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. 

Determining the Standard-State Potential To extract the standard-state potential, or formal potential, for reaction 11.34 from a voltammogram, it is necessary to rewrite the Nernst equation... 

The free energy changes of the outer shell upon reduction, AG° , are important, because the Nernst equation relates the redox potential to AG. Eree energy simulation methods are discussed in Chapter 9. Here, the free energy change of interest is for the reaction... 

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. 

These considerations show the essentially thermodynamic nature of and it follows that only those metals that form reversible -i-ze = A/systems, and that are immersed in solutions containing their cations, take up potentials that conform to the thermodynamic Nernst equation. It is evident, therefore, that the e.m.f. series of metals has little relevance in relation to the actual potential of a metal in a practical environment, and although metals such as silver, mercury, copper, tin, cadmium, zinc, etc. when immersed in solutions of their cations do form reversible systems, they are unlikely to be in contact with environments containing unit activities of their cations. Furthermore, although silver when immersed in a solution of Ag ions will take up the reversible potential of the Ag /Ag equilibrium, similar considerations do not apply to the NaVNa equilibrium since in this case the sodium will react with the water with the evolution of hydrogen gas, i.e. two exchange processes will occur, resulting in an extreme case of a corrosion reaction. 

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... 

Electrical units 503, 519 Electrification due to wiping 77 Electro-analysis see Electrolysis and Electrogravimetry Electrochemical series 63 Electro-deposition completeness of, 507 Electrode potentials 60 change of during titration, 360 Nernst equation of, 60 reversible, 63 standard 60, (T) 62 Electrode reactions 505 Electrodeless discharge lamps 790 Electrodes antimony, 555 auxiliary, 538, 545 bimetallic, 575... 

STRATEGY First, write the balanced equation for the cell reaction and the corresponding expression for Q, and note the value of n. Then determine E° from the standard potentials in Table 12.1 or Appendix 2B. Determine the value of Q for the stated conditions. Calculate the emf by substituting these values into the Nernst equation, Eq. 6. At 25.00°C, RT/1 = 0.025 693 V. 

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 ... 

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. 

Since the electrolyte membrane only allows the conduction of ions, the electrons are forced through an exterior circuit, creating an electromotive force. The voltage generated by such a cell is given by the Nernst equation. For the hydrogen-oxygen reaction we can write ... 

The rates of the transfer reactions of all relevant species across the O/W interface are sufficiently large [13] in comparison with the corresponding diffusion rates, so that the following Nernst equations are valid for the transfer of relevant species, as expressed by Eqs. (l)-(3), at x = 0 and t > 0 ... 

As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance. Ref. 230 232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak may then be expressed as a function of the interfacial area A, of the potential scan rate v, of the bulk concentration of the ion under study Cj and of its diffusion coefficient D". This leads to the Randles Sevcik equation [233] ... 

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. 

In the practice of potentiometric titration there are two aspects to be dealt with first the shape of the titration curve, i.e., its qualitative aspect, and second the titration end-point, i.e., its quantitative aspect. In relation to these aspects, an answer should also be given to the questions of analogy and/or mutual differences between the potentiometric curves of the acid-base, precipitation, complex-formation and redox reactions during titration. Excellent guidance is given by the Nernst equation, while the acid-base titration may serve as a basic model. Further, for convenience we start from the following fairly approximate assumptions (1) as titrations usually take place in dilute (0.1 M) solutions we use ion concentrations in the Nernst equation, etc., instead of ion activities and (2) during titration the volume of the reaction solution is considered to remain constant. 

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). 

A chemical reaction subsequent to a fast (reversible) electrode reaction (Eq. 5.6.1, case b) can consume the product of the electrode reaction, whose concentration in solution thus decreases. This decreases the overpotential of the overall electrode process. This mechanism was proposed by R. Brdicka and D. H. M. Kern for the oxidation of ascorbic acid, converted by a fast electrode reaction at the mercury electrode to form dehydro-ascorbic acid. An equilibrium described by the Nernst equation is established at the electrode between the initial substance and this intermediate product. Dehydroascorbic acid is then deactivated by a fast chemical reaction with water to form diketogulonic acid, which is electroinactive. 

Ans. In a reaction at equilibrium, the ratio can have only one value at any given temperature. In the Nernst equation, the value can change, since the reaction can be stopped short of equilibrium simply by disconnecting a wire or the salt bridge. 

For very many systems for which E° is well defined, the expected current behaviour is not described in any way by the Nernst equation (1.18). The current shows no marked rise as the potential is changed from ° and when the potential is raised or lowered sufficiently for electron transfer to take place the resulting electrochemical reactions arc often complex. 

Many natural waters, including most waters at low temperature, do not achieve redox equilibrium (e.g., Lindberg and Runnells, 1984 see Chapter 7). In this case, no single value of pe or Eh can be used to represent the redox state. Instead, there is a distinct value for each redox couple in the system. Applying the Nernst equation to Reaction 3.46 gives a pe or Eh representing the hydrolysis of water. Under disequilibrium conditions, this value differs from those calculated from reactions such as,... 

Electrode and therefore cell potentials are very important analytically as their magnitudes are determined by the activities of the reactants and products involved in the electrode reactions. The relation between such activities and the electrode potential is given by the Nernst equation. For a general half-cell reaction written as a reduction, i.e. aA + bB +. .. ne = xX + yY +. . ., the equation is of the form... 

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