Nernst, equation

The Nemst equation solves the potential of an electrochanical cell containing a reversible system with fast kinetics and it is valid only at equilibrium and at the surface of the electrode  

The standard electrode potential for platinum is 1.188 V and the temperature is 25 °C. The voltage of this half-reaction is 1.1 V. 

The Nernst equation was named after the German chemist Walther Nernst who established very useful relations between the energy and the potential of a cell to the concentrations of participating ions and other chemical species. Equation (4.8) can be derived from the equation linking free energy changes to the reaction quotient 

The capital letters A, B,M, and N in Eq. (4.9) represent, respectively, the reactants and products of a given reaction while the small letters represent the coefficients required to balance the reaction. 

In the case of an electrochemical reaction, substitution of the relationships AG = -nFE and AG = - f into the expression of a reaction free energy and division of both sides by -nF gives the Nernst expression for an electrode reaction described in Eq. (4.11)  

Combining constants at 25°C (298.15 K) gives the simpler form of the Nernst equation for an electrode reaction at this temperature  

the electrode potential (E) would be the actual potential difference across a cell containing this electrode as a halfcell and a standard hydrogen electrode as the other half-cell. Alternatively, the relationship in Eq. (4.3) can be used to combine two Nernst equations corresponding to two half-cell reactions into the Nernst equation for a cell reaction  

By generalizing Equation 4.12, the key equation of equilibrium electrochemistry, the Nernst equation, can be written as follows  

Walther Hermann Nemst (1864-1941) was a German physical chemist who is known for his theories behind the calculation of chemical affinity as embodied in the third law of thermodynamics, for which he won the 1920 Nobel Prize in Chemistry. Nemst also made fundamental contributions to the theory of electrolyte solutions. He is most known for developing the Nernst equation, one of the most fundamental equations of equilibrium electrochemistry. 

Inzelt, and F. Scholz, Electrochemical Dictionary, Springer, BerUn, Germany, 2008. 

we provide a recipe to properly compose a Nemst equation for an electrochemical cell  

Write down the electrochanical half-reactions showing chemicals, stoichiometric coefficients (v, and phases of all chanical components (reactants and products). 

Thus far, all of our calculations have been based on the standard cell potential or standard halfcell potentials—that is, the standard state conditions that were defined previously. However, many times the cell is not at standard conditions—commonly the concentrations are not 1 M. The actual cell potential, E, can be calculated by the use of the Nemst equation  

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values, 

Let s practice. Calculate the potential of a half-cell containing 0.10 M K2Cr207(aq), 

Electrochemical experiments fall into two broad categories. Some experiments are concerned with standard cell voltages, while other experiments use the Nernst equation directly or indirectly. Experiment 21 in the Experimental chapter uses these concepts. 

Measurements of the cell potential are essential and require a voltmeter (potentiometer). These measurements may be taken from different combinations of half-cells, or from measurements before and after changes of some aspect of the cell were made. 

R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday s constant, and Q is the activity quotient. The second form, involving the log Q, is the more useful form. If you know the cell reaction, the concentrations of ions, and the E°ell, then you can calculate the actual cell potential. Another useful application of the Nernst equation is in the calculation of the concentration of one of the reactants from cell potential measurements. Knowing the actual cell potential and the E°ell, allows you to calculate Q, the activity quotient. Knowing Q and all but one of the concentrations, allows you to calculate the unknown concentration. Another application of the Nernst equation is concentration cells. A concentration cell is an electrochemical cell in which the same chemical species are used in both cell compartments, but differing in concentration. Because the half reactions are the same, the E°ell = 0.00 V. Then simply substituting the appropriate concentrations into the activity quotient allows calculation of the actual cell potential. 

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values and then apply the Nernst equation. If the Ecell turns out to be negative, it indicates that the reaction is not a spontaneous one (an electrolytic cell) or that the reaction is written backwards if it is supposed to be a galvanic cell. If it is supposed to be a galvanic cell, then all you need to 

We have seen how to use standard reduction potentials to calculate EP for cells. Real cells are usually not constructed at standard state conditions. In fact, it is almost impossible to make measurements at standard conditions because it is not reasonable to adjust concentrations and ionic strengths to give unit activity for solutes. We need to relate standard potentials to those measured for real cells. It has been found experimentally that certain variables affect the measured cell potential. These variables include the temperature, concentrations of the species in solution, and the number of electrons transferred. The relationship between these variables and the measured cell emf can be derived from simple thermodynamics (see any introductory general chemistry text). The relationship between the potential of an electrochemical cell and the concentration of reactants and products in a general redox reaction 

The logarithmic term has the same form as the equilibrium constant for the reaction. The term is called Q, the reaction quotient, when the concentrations (rigorously, the activities) are not the equilibrium values for the reaction. As in any equilibrium constant expression, pure liquids and pure solids have activities equal to 1, so they are omitted from the expression. If the values of R, T (25°C = 298 K), and F are inserted into the equation and the natural logarithm is converted to log to the base 10, the Nernst equation reduces to 

It should be noted that the square brackets literally mean the molar concentration of. For example, [Fe +] means the molar concentration of ferrous ion or moles of ferrous ion per liter 

Concentrations in molarity should really be the activities of the species, but we often do not know the activities. For that reason, we define the formal potential, E , as the measured potential of the cell when the species being oxidized and reduced are present at concentrations such that the ratio of the concentrations of oxidized to reduced species is unity and other components of the cell are present at designated concentrations. The use of the formal potential allows us to avoid activity coefficients, which are often unknown. This gives us 

The Nemst equation is also used to calculate the electrode potential for a given half-cell at nonstandard conditions. For example, for the half-cell Fe + e Fe that has an E° = 0.77 V and n = 1, the Nemst equation would be 

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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 change in the redox potential is given quantitatively by the Nernst equation ... 

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. 

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,... 

Adding together these two Nernst equations leaves us with 2 eq = + bce +/Ce3+ 0.05916 log... 

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... 

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

Making appropriate substitutions into the Nernst equation for the electrochemical cell (see Example 11.2)... 

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. 

To begin, we write Nernst equations for the two measured cell potentials. The cell potential for the sample is... 

Sensitivity The sensitivity of a potentiometric analysis is determined by the term RT/nF or RT/zF in the Nernst equation. Sensitivity is best for smaller values of n or z. 

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

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 shift in the voltammogram for a metal ion in the presence of a ligand may be used to determine both the metal-ligand complex s stoichiometry and its formation constant. To derive a relationship between the relevant variables we begin with two equations the Nernst equation for the reduction of O... 

In the absence of ligand the half-wave potential occurs when [R]x=o and [O] c=o are equal thus, from the Nernst equation we have... 

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)... 

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