Standard Cell Potential and the Equilibrium Constant

As you know from Section 20.3, a spontaneous reaction has a negative free energy change (AG 0), and you ve just seen that a spontaneous electrochemical reaction has a positive cell potential (Eceii 0)- Note that the signs of AG and Eceii are opposite for a spontaneous reaction. These two indications of spontaneity are proportional to each other  

Let s determine this proportionality constant by focusing on the electrical work done (w, in joules), which is the product of the potential (Eceiu in volts) and the amount of charge that flows (in coulombs)  

The value used for Eceii is measured with no current flowing and, therefore, no energy lost to heating the cell. Thus, fceii is maximum voltage the cell can generate, that is, the maximum work the system can do on the surroundings. Recall from Chapter 20 that only a reversible process can do maximum work. For 

Wmiix = ceii charge = -AG or AG = - ceii X charge The charge that flows through the cell equals the number of moles of electrons (n) transferred times the charge of 1 mol of electrons (symbol F)  

The charge of 1 mol of electrons is the Faraday constant (F), named in honor of Michael Faraday, the 19 -century British scientist who pioneered the study of electrochemistry  

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Identity the relationships between standard Gibbs energy of reaction, standard cell potential, and the equilibrium constant K. 

The above important relationship now allows evaluation of the thermodynamic driving force of a redox reaction in terms of a measurable cell emf. Moreover, it is possible to utilize the relationship between the standard state potential and the standard state free energy to arrive at an expression for the equilibrium constant of a redox reaction in terms of the emf. Thus... 

Potentiometric transducers measure the potential under conditions of constant current. This device can be used to determine the analytical quantity of interest, generally the concentration of a certain analyte. The potential that develops in the electrochemical cell is the result of the free-energy change that would occur if the chemical phenomena were to proceed until the equilibrium condition is satisfied. For electrochemical cells containing an anode and a cathode, the potential difference between the cathode electrode potential and the anode electrode potential is the potential of the electrochemical cell. If the reaction is conducted under standard-state conditions, then this equation allows the calculation of the standard cell potential. When the reaction conditions are not standard state, however, one must use the Nernst equation to determine the cell potential. Physical phenomena that do not involve explicit redox reactions, but whose initial conditions have a non-zero free energy, also will generate a potential. An example of this would be ion-concentration gradients across a semi-permeable membrane this can also be a potentiometric phenomenon and is the basis of measurements that use ion-selective electrodes (ISEs). 

Relate the standard cell potential (E n) to the standard Gibbs free energy change (AG ) and the equilibrium constant (K)... 

Figure 21.10 summarizes the interconnections among the standard free energy change, the equilibrium constant, and the standard cell potential. The procedures... 

If you can build a galvanic cell with the tin as one half-cell and the N2O as the other half-cell, the measurement of the standard cell potential would provide the best means to determine the equilibrium constant. You could also calculate this standard cell potential if the necessary reduction potentials for the relevant half-reactions are available. 

We leam to determine the standard reduction potentials based on the standard hydrogen electrode reference and use them to calculate the emf of a cell and hence the spontaneity of a cell reaction. A relationship exists between a cell s emf, the change in the standard Gibbs free energy, and the equilibrium constant for the ceU reaction. (19.3 and 19.4)... 

Write down the expression for the copper-zinc electrochemical cell. Write the reducing reactions for the half-cells and the redox reaction for the whole cell. Assume that equilibrium has been reached and from the standard Cu /Cu and Zn" /Zn potentials calculate the equilibrium constant. 

Eigure 21.10 summarizes the interconnections among the standard free energy change, the equilibrium constant, and the standard cell potential. In Chapter 20, we determined K from AG°, which we found either from A//° and A5° values or from AGf values. Now, for redox reactions, we have a direct experimental method for determining K and AG° measure E eii-... 

We can derive a relationship between the standard cell potential (Sceii) and the equilibrium constant for the redox reaction occurring in the cell (K) by returning to the relationship between AG° and K that we learned in Chapter 17. Recall from Section 17.9 that ... 

The equilibrium constant of a reaction can be calculated from standard potentials by combining the equations for the balf-reactions to give the cell reaction of interest and determining the standard potential of the corresponding cell. 

Experiments involving the Nernst equation are primarily concerned with concentrations. One or more of the concentrations in the Q portion of the Nernst equation are calculated by measuring the nonstandard cell potential and comparing this to the standard cell potential. Remember, you calculate the concentration from a measured voltage. Once the concentration is determined, it may be combined with other concentrations and used to calculate an equilibrium constant. 

All species are aqueous unless otherwise indicated. The reference state for amalgams is an infinitely dilute solution of the element in Hg. The temperature coefficient, dE°/dT, allows us to calculate the standard potential, E°(T), at temperature T E°(T) — Ec + (dE°/dT)AT. where A T is T — 298.15 K. Note the units mVIK for dE°ldT. Once you know E° for a net cell reaction at temperature T, you can find the equilibrium constant, K, for the reaction from the formula K — lOnFE°,RTln w, where n is the number of electrons in each half-reaction, F is the Faraday constant, and R is the gas constant. 

FIGURE 18.7 The relationship between the equilibrium constant K for a redox reaction with n = 2 and the standard cell potential E°. Note that K is plotted on a logarithmic scale. 

The SOFC consists of cathode, electrolyte and anode collectively referred to as the PEN - positive electrode, electrolyte, negative electrode. A single cell operated with hydrogen and oxygen provides at equilibrium a theoretical reversible (Nernst) or open circuit voltage (OCV) of 1.229 V at standard conditions (STP, T = 273.15 K. i> = 1 atm). With the standard electrode potential E°, universal gas constant R. temperature T. Faraday s constant F, molar concentration x and pressure p, the OCV is given by... 

The quantity AG° is the free energy of the half-reaction when the activities of the reactant and product have values of unity and is directly proportional to the standard half-cell potential for the reaction as written. It also is a measure of the equilibrium constant for the half-reaction assuming the activity of electrons is unity ... 

Preliminary emf measurements were made on Cell I, and the standard potential of the Ag-AgBr electrode was determined as 0.07106 V from data taken in 0.01000 mol kg"1 hydrobromic acid. This value of Em° was identical with that given in the literature (20). The emf values were reproducible up to m = 1.0 mol kg"1. There was some evidence of irreversible behavior for m = 1.5 mol kg"1. In order to avoid this kind of drift in the emf values at the highest constant total molality tested, the cell with the hydrogen electrode was allowed to equilibrate for 45 min before the Ag-AgBr electrode (which was kept in a separate standard-joint test tube containing a solution of the same composition) was transferred to the electrode compartment. The equilibrium emf value was recorded every 5 min until no deviation was noticed. 

The third largest class of enzymes is the oxidoreductases, which transfer electrons. Oxidoreductase reactions are different from other reactions in that they can be divided into two or more half reactions. Usually there are only two half reactions, but the methane monooxygenase reaction can be divided into three "half reactions." Each chemical half reaction makes an independent contribution to the equilibrium constant E for a chemical redox reaction. For chemical reactions the standard reduction potentials ° can be determined for half reactions by using electrochemical cells, and these measurements have provided most of the information on standard chemical thermodynamic properties of ions. This research has been restricted to rather simple reactions for which electrode reactions are reversible on platinized platinum or other metal electrodes. 

Using (7) the cell emf method and (2) the electrode-potential method, calculate the equilibrium constants for the following chemical reactions. (Use the values for standard electrode potentials in Table 12-1.)... 

The graphing calculator can run a program that calculates the equilibrium constant for an electrochemical cell using an equation called the Nemst equation, given the standard potential and the number of electrons transferred. Given that the standard potential is 2.041 V and that two electrons are transferred, you will calculate the equilibrium constant. The program will be used to make the calculations. 

If the reactants and products are in their standard states, the resulting cell potential is called the standard cell potential. This latter quantity is related to the standard free-energy change for the reaction and thus to the equilibrium constant by... 

We will use standard electrode potentials throughout the rest of this text to calculate cell potentials and equilibrium constants for redox reactions as well as to calculate data for redox titration curves. You should be aware that such calculations sometimes lead to results that are significantly different from those you would obtain in the laboratory. There are two main sources of these differences (1) the necessity of using concentrations in place of activities in the Nernst equation and (2) failure to take into account other equilibria such as dissociation, association, complex formation, and solvolysis. Measurement of electrode potentials can allow us to investigate these equilibria and determine their equilibrium constants, however. 

F is the Faraday constant, K is the equilibrium constant of the reaction, R is the gas constant, and T is the thermodynamic temperature. However, E jj is not the standard potential of the electrode reaction (or sometimes called half-cell reaction), which is tabulated in the tables mentioned. It is the standard potential of the reaction in a chemical cell which is equal to the standard potential of an electrode reaction (abbreviated as standard electrode potential), E when the reaction involves the oxidation of molecular hydrogen to solvated protons... 

The changes in the equilibrium constants and cell potentials with the change in the standard state pressure follow from the expression for Gibbs energy changes, Eq.(11.48)... 

As will be shown later (Section 9.17 and Worked Problem 9.20), the standard electrode potential is related to the equilibrium constant for the cell reaction. This has proved extremely useful for determining equilibrium constants for the redox reactions of inorganic systems and for redox reactions occurring in biological systems. 

Further we looked at galvanic cells where it was possible to extract electrical energy from chemical reactions. We looked into cell potentials and standard reduction potentials which are both central and necessary for the electrochemical calculations. We also looked at concentration dependence of cell potentials and introduced the Nemst-equation stating the combination of the reaction fraction and cell potentials. The use of the Nemst equation was presented through examples where er also saw how the equation may be used to determine equilibrium constants. 

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