Equilibrium constants from electromotive forces

Electrochemical Method.—In this the value of the equilibrium constant K is calculated from the maximum work measured by means of the electromotive force of a voltaic cell (cf. Chap. XVI.). 

The equilibrium constant for a redox reaction can be found from the standard electromotive force of a cell. 

The potential difference between the electrodes in a working electrochemical cell is called the cell potential. The cell potential is not a constant and changes with time as the cell reaction proceeds. Thus the cell potential is a potential difference measured under non-equilibrium conditions as electric current is drawn from the cell. Electromotive force is the zero-current cel potential and corresponds to the potential difference of the cell when the cell (not the cell reaction) is at equilibrium. Infinitesimally small changes from this equilibrium are reversible with constant concentration and, consequently, it is possible to relate emf to thermodynamic properties. 

The decrease in free energy of the system in a spontaneous redox reaction is equal to the electrical work done by the system on the surroundings, or AG = nFE. The equilibrium constant for a redox reaction can be found from the standard electromotive force of a cell. 10. The Nernst equation gives the relationship between the cell emf and the concentrations of the reactants and products under non-standard-state conditions. Batteries, which consist of one or more galvanic cells, are used widely as self-contained power sources. Some of the better-known batteries are the dry cell, such as the Leclanche cell, the mercury battery, and the lead storage battery used in automobiles. Fuel cells produce electrical energy from a continuous supply of reactants. 

Figure 2 shows data points from a long-term titration of a goethite suspension. One dataset represented by full squares results in an acceptable electromotive force (EMF) (Fig. 2a)/pH-value (Fig. 2b), the other (empty squares) not. The pH or log[H+] is nearly constant over the whole measurement period for the dataset represented by black squares the equilibrium criteria as imposed by the computer controlling the titration (i.e., drift of less than 0.05 mV in 90min) are fulfilled about 17 h after titrant addition. For the dataset represented by the empty squares, this is the case after about 35 h. Here, a constant drift to higher log[H+] values is noted (Fig. 2b), which becomes more obvious in the EMF readings with a drift over more than 10 mV (Fig. 2a). Nevertheless, the equilibrium criterion is finally fulfilled.

The most useful concept that biochemists have obtained from thermodynamics is that of free energy. By considering the free energy change one can tell whether a reaction may proceed spontaneously or whether it must be driven by other reactions. Further, one can calculate the amoimt of energy given off by a reaction or required by it, and this is a most important feature of many reactions. From free energy data one can easily calculate equilibrium constants and electromotive forces. 

Based on these ideas Marcus derived eq. (5.3.5), which is used for reactants and products of the same size and charge type. In this equation K12 is the equilibrium constant of the redox system, obtained from emf (electromotive force) measurements, and and 22 r te constants. 

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