APPLICATIONS OF EQUILIBRIUM CONSTANTS

We have seen that the magnitude of K indicates the extent to which a reaction proceeds. If K is very large, the equilibrium mixture contains mostly substances on the product side of the equation for the reaction. (That is, the reaction proceeds far to the right.) If K is very small (that is, much less than 1), the equilibrium mixture contains mainly substances on the reactant side of the equation. The equilibrium constant also allows us to (1) predict the direction in which a reaction mixture achieves equilibrium and (2) calculate equilibrium concentrations of reactants and products. 

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APPLICATIONS OF EQUILIBRIUM CONSTANTS We also see that equilibrium constants can be used to predict equilibrium concentrations of reactants and products and to... 

In the previous chapter the necessary conditions for equilibrium were introduced in terms of the chemical potentials of the constituent species in the various phases. In this chapter we will relate these chemical potentials to a more convenient form, that of the equilibrium constant. Furthermore, we will discuss the application of equilibrium constants to the three types of equilibria which occur in our overall vapor-liquid-solid model ... 

The application of equilibrium constant in predicting the stability of a specified oxide refractory under a designated atmosphere has been illustrated in Example 5.A. Example 5.B illustrates how the value of the equilibrium... 

Equilibrium Constants Another application of acid-base titrimetry is the determination of equilibrium constants. Consider, for example, the titration of a weak acid, HA, with a strong base. The dissociation constant for the weak acid is... 

Determination of Equilibrium Constants Another important application of molecular absorption is the determination of equilibrium constants. Let s consider, as a simple example, an acid-base reaction of the general form... 

Determining Equilibrium Constants for Coupled Chemical Reactions Another important application of voltammetry is the determination of equilibrium constants for solution reactions that are coupled to a redox reaction occurring at the electrode. The presence of the solution reaction affects the ease of electron transfer, shifting the potential to more negative or more positive potentials. Consider, for example, the reduction of O to R... 

Some further uses of kinetics, less sweeping in their scope than the preceding applications, are for the testing of rate theories the measurement of equilibrium constants the analysis of solutions, including mixtures of solutes and the measurement of solvent properties that depend upon rates. Some of these applications are treated later in the book. 

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. 

Having introduced matters pertaining to the electrochemical series earlier, it is only relevant that an appraisal is given on some of its applications. The coverage hereunder describes different examples which include aspects of spontaneity of a galvanic cell reaction, feasibility of different species for reaction, criterion of choice of electrodes to form galvanic cells, sacrificial protection, cementation, concentration and tempera lure effects on emf of electrochemical cells, clues on chemical reaction, caution notes on the use of electrochemical series, and finally determination of equilibrium constants and solubility products. 

Problems are encountered in practice in the application of this procedure. The data in the literature for both V o/pH and error bounds for the resulting set of equilibrium constants are quite large. Also, it is difficult to evaluate to which extent... 

E D. J. Eatough, R. M. Izatt, J. J. Christensen. Determination of Equilibrium Constants by Titration Calorimetry Part III, Application of the Method to Several Chemical Systems. Thermochim. Acta 1972, 3, 233-246. 

Titrations are veiy powerful techniques that contain two very different kinds of information and thus serve two different purposes (a) titrations are used for quantitative analytical applications, e.g. the determination of the concentration of an acid by an acid-base titration or the determination of a metal ion by a complexometric titration (b) titrations serve also as a method for the determination of equilibrium constants, e.g. the determination of the strength of the interaction between a metal ion and a ligand. Naturally, both objectives can be combined and the analysis of one titration can deliver both types of information. 

Marshall s extensive review (16) concentrates mainly on conductance and solubility studies of simple (non-transition metal) electrolytes and the application of extended Debye-Huckel equations in describing the ionic strength dependence of equilibrium constants. The conductance studies covered conditions to 4 kbar and 800 C while the solubility studies were mostly at SVP up to 350 C. In the latter studies above 300°C deviations from Debye-Huckel behaviour were found. This is not surprising since the Debye-Huckel theory treats the solvent as incompressible and, as seen in Fig. 3, water rapidly becomes more compressible above 300 C. Until a theory which accounts for electrostriction in a compressible fluid becomes available, extrapolation to infinite dilution at temperatures much above 300 C must be considered untrustworthy. Since water becomes infinitely compressible at the critical point, the standard entropy of an ion becomes infinitely negative, so that the concept of a standard ionic free energy becomes meaningless. 

An accurate knowledge of the thermochemical properties of species, i.e., AHf(To), S Tq), and c T), is essential for the development of detailed chemical kinetic models. For example, the determination of heat release and removal rates by chemical reaction and the resulting changes in temperature in the mixture requires an accurate knowledge of AH and Cp for each species. In addition, reverse rates of elementary reactions are frequently determined by the application of the principle of microscopic reversibility, i.e., through the use of equilibrium constants, Clearly, to determine the knowledge of AH[ and S for all the species appearing in the reaction mechanism would be necessary. 

Since all electrophoretic mobility values are proportional to the reciprocal viscosity of the buffer, as derived in Chapter 1, the experimental mobility values n must be normalized to the same buffer viscosity to eliminate all other influences on the experimental data besides the association equilibrium. Some commercial capillary zone electrophoresis (CZE) instruments allow the application of a constant pressure to the capillary. With such an instrument the viscosity of the buffer can be determined by injecting a neutral marker into the buffer and then calculating the viscosity from the time that the marker needs to travel through the capillary at a set pressure. During this experiment the high voltage is switched off. 

Another application in the first category is for experimentalists investigating equilibrium processes (such as the determination of equilibrium constants) to evaluate whether equilibrium is reached. The experimental duration must be long enough to reach equilibrium. To estimate the required experimental duration to insure that equilibrium is reached, one needs to have a rough idea of the kinetics of the reaction to be studied. Or experiments of various durations can be conducted to evaluate the attainment of equilibrium. 

One of these applications of NMR is in the non-invasive determination of equilibrium constants. These are usually most easily carried out for unimolecular... 

This expression, known as Sand s equation, gives the variation of the interfacial concentration of M"+ with time after application of a constant current density. But one seeks also to know the time variation of the potential difference across the interface at which the electronation reaction M"+ + ne — M is occurring. To obtain this information, one recalls that the charge-transfer reaction across the interface is assumed in the present treatment to be virtually in equilibrium and therefore the Nenist equation (7.177) can be used to relate the potential difference to the concentration at the interface. That is, by substituting (7.181) in (7.177),... 

Equation 6-33 suggests that extrapolation of equilibrium constants to infinite dilution is done appropriately by plotting log Kc vs-01. For example, Fig. 6-1 shows plots of pK a for dissociation of H2P04-, AMP, and ADP2-, and ATP3 vs fp. The variation of pK a with- p at low concentrations (Eq. 6-35) is derived by application of the Debye-Huckel equation (Eq. 6-33) ... 

The rest of this chapter is a variation on a theme the use of equilibrium constants to calculate the equilibrium composition of solutions of acids and bases. We begin with solutions of acids, bases, and salts, explore the contribution of the autoprotolysis of the solvent to the pH, which is significant in very dilute solutions, and see how to handle the complications of acids that can donate more than one proton. Although the applications are varied, the techniques are all very similar and are based on the material in Chapter 9. 

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

Eq 18 is applicable to equilibrium constants in alternate form. For ideal gases the equilibrium constant Kp is expressed in terms of partial pressures (rather than fugacities) of products and reactants. Still another form of the equilibrium constant. JC. is exnressed in terms nf... 

Richard, the Marcus analysis, allied to the concept imbalance of bond making and charge development at the transition state, has provided an effective framework for tackling one of the outstanding problems for a general interpretation of reactivity. A reasonable conclusion might be that further measurements of equilibrium constants will be required to support and test the level of understanding achieved so far, and to probe more deeply the interpretation of hard and soft nucleophilicity in its application to reactions of electrophilic carbon atoms. 

Equation 2.16 shows that potentiometry is a valuable method for the determination of equilibrium constants, ffowever, it should be borne in mind that the system should be in equilibrium. Some other conditions, which are described below, also need to be fulhlled for use of potentiometry in any application. The basic measurement system must include an indicator electrode that is capable of monitoring the activity of the species of interest, and a reference electrode that gives a constant, known half-cell potential to which the measured indicator electrode potential can be referred. The voltage resulting from the combination of these two electrodes must be measured in a manner that minimises the amount of current drawn by the measuring system. This condition includes that the impedance of the measuring device should be much higher than that of the electrode. 

For simplicity, let us consider perfectly drained conditions (p = 0) and start from an equilibrium between solid and solute (xjrc — xj/x). The equilibrium is disturbed by application of a constant macroscopic stress X = <5 ( > 0). 

The application of equilibrium speciation models in aquatic systems works best when the oxidation state remains relatively constant and when complexes formed from solution or absorption are reversible (Tipping et al., 1998). For example, the application of such models to changing oxidation states, dissolution and/or formation of oxide precipitates, or formation of organometallic complexes will not prove useful because many of these... 

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