Standard potential equilibrium constant

These conventions are arbitrary, but you must use them if you wish to use tabulated values of equilibrium constants, standard reduction potentials, and free energies. 

In thermodynamic terms the equilibrium constant is related to the standard chemical potential by the equation... 

To proceed fiirther, to evaluate the standard free energy AG , we need infonnation (experimental or theoretical) about the particular reaction. One source of infonnation is the equilibrium constant for a chemical reaction involving gases. Previous sections have shown how the chemical potential for a species in a gaseous mixture or in a dilute solution (and the corresponding activities) can be defined and measured. Thus, if one can detennine (by some kind of analysis)... 

The standard-state electrochemical potential, E°, provides an alternative way of expressing the equilibrium constant for a redox reaction. Since a reaction at equilibrium has a AG of zero, the electrochemical potential, E, also must be zero. Substituting into equation 6.24 and rearranging shows that... 

Balance the following redox reactions, and calculate the standard-state potential and the equilibrium constant for each. Assume that the [H3O+] is 1 M for acidic solutions, and that the [OH ] is 1 M for basic solutions. 

Preparation and chemistry of chromium compounds can be found ia several standard reference books and advanced texts (7,11,12,14). Standard reduction potentials for select chromium species are given ia Table 2 whereas Table 3 is a summary of hydrolysis, complex formation, or other equilibrium constants for oxidation states II, III, and VI. 

The standard electrode potentials , or the standard chemical potentials /X , may be used to calculate the free energy decrease —AG and the equilibrium constant /T of a corrosion reaction (see Appendix 20.2). Any corrosion reaction in aqueous solution must involve oxidation of the metal and reduction of a species in solution (an electron acceptor) with consequent electron transfer between the two reactants. Thus the corrosion of zinc ( In +zzn = —0-76 V) in a reducing acid of pH = 4 (a = 10 ) may be represented by the reaction ... 

Thus the equilibrium constant K can be evaluated from standard electrode potential or from the standard chemical potentials x . 

This equation may be employed to calculate the equilibrium constant of any redox reaction, provided the two standard potentials Ef and Ef are known from the value of K thus obtained, the feasibility of the reaction in analysis may be ascertained. 

It is evident that the abrupt change of the potential in the neighbourhood of the equivalence point is dependent upon the standard potentials of the two oxidation-reduction systems that are involved, and therefore upon the equilibrium constant of the reaction it is independent of the concentrations unless these are extremely small. The change in redox potential for a number of typical oxidation-reduction systems is exhibited graphically in Fig. 10.15. For the MnO, Mn2+ system and others which are dependent upon the pH of the... 

One of the most useful applications of standard potentials is in the calculation of equilibrium constants from electrochemical data. The techniques that we develop here can be applied to any kind of reaction, including neutralization and precipitation reactions as well as redox reactions, provided that they can be expressed as the difference of two reduction half-reactions. 

The fact that we can calculate E° from standard potentials allows us to calculate equilibrium constants for any reaction that can be expressed as two half-reactions. The reaction does not need to be spontaneous nor does it have to be a redox reaction. Toolbox 12.3 summarizes the steps and Example 12.8 shows the steps in action. 

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. 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

In addition to defined standard conditions and a reference potential, tabulated half-reactions have a defined reference direction. As the double arrow in the previous equation indicates, E ° values for half-reactions refer to electrode equilibria. Just as the value of an equilibrium constant depends on the direction in which the equilibrium reaction is written, the values of S ° depend on whether electrons are reactants or products. For half-reactions, the conventional reference direction is reduction, with electrons always appearing as reactants. Thus, each tabulated E ° value for a half-reaction is a standard reduction potential. 

Equations and provide a method for calculating equilibrium constants from tables of standard reduction potentials. Example illustrates the technique. 

This is a quantitative calculation, so it is appropriate to use the seven-step problem-solving strategy. We are asked to determine an equilibrium constant from standard reduction potentials. Visualizing the problem involves breaking the redox reaction into its two half-reactions ... 

These equations show that whereas the kinetic coefficients of an individual reaction can assume any value, the coefficients of its forward and reverse process are always interrelated. The relation between the standard equilibrium potential EP and the rate constants and is analogous to the well-known physicochemical relation between equilibrium constant K and the rate constants of the forward and reverse process. 

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... 

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

Here, R is the gas constant, 7k is absolute temperature, and XB is the mole fraction of B in the solution phase. Using this equation, we can calculate the equilibrium point of reactions in ideal systems directly from tabulated values of standard potentials p°. 

From the measured electron-transfer equilibrium constant and the known standard potential for the reference D /D- couple it has been possible to determine E for the PhO /PhO- couple. The method, however, is non-trivial and does not lend itself to the rapid determination of standard potentials for a large series of related compounds. 

The equilibrium constant for the disproportionation reaction, KD, may be expressed as a function of the standard potentials of the two-electrode electron transfer reactions according to... 

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. 

Given the above standard reduction potentials, estimate the approximate value of the equilibrium constant for the following reaction ... 

The standard cell potential can also be used to calculate the equilibrium constant for a nE°... 

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