EXPERIMENTAL DETERMINATION OF EQUILIBRIUM CONSTANTS

This chapter will be devoted mainly to describe two experimental approaches for the determination of equilibrium constants potentiometric and spectrophotometric. The two approaches are interrelated a spectropho-tometric method developed at the University of Arizona that provides significantly enhanced pH accuracy also impacts positively on the reliability of potentiometric pH measurements. A number of other methods including heterogeneous equilibria such as solvent extraction and ion exchange will be mentioned briefly. 

Experiments designed for determination of equilibrium constant naturally include means of obtaining a significant number of replicate measurements. This can involve a series of independent single runs. It is more desirable, whenever possible, to obtain data points in the context of a titration because the medium (i.e., the solution being titrated) is changing both slowly and 

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The following experiments involve the experimental determination of equilibrium constants and, in some cases, demonstrate the importance of activity effects. 

Both the second and third law methods rely on the experimental determination of equilibrium constants. As shown in section 2.9, the equilibrium constant (K) of a reaction is defined in terms of the activities (ar) of reactants and products ... 

Association reactions can be characterized by equilibrium constants. Experimental determination of equilibrium constants for each step in an association reaction provides vital information about the properties of the associating system. In particular, the mode of association (e.g., monomer-dimer, monomer-tetramer, indefinite), and the strength of the association (that is, the degree to which various oligomers can exist at various total concentrations) can be obtained. The evaluation of equilibrium constants over a range of solution conditions (such as salt concentration and temperature) can be used to obtain information on the enthalpy and entropy of the various steps in the association and the types of bonds involved in the assembly process. Note that this information can be obtained in the complete absence of structural information, although, of course, any available structural information can be used to aid in the interpretation of the thermodynamic data. 

Table 18 gives an example for the calculation of an equilibrium constant from the free energy. Due to the relatively big error for the determination of the free energy, it is not advisable to perform such conversions unless unavoidable. Direct experimental determination of equilibrium constants is often more reliable. 

L Determination of Standard Free Energies.—Three main procedures have been used for the evaluation of standard free energies of reactions. The first is based on the experimental determination of equilibrium constants, and their combination in the manner indicated above. By the procedure described in 33i, an expression can then be obtained for AF as a function of temperature, so that the value at any particular temperature can be evaluated. 

The majority of equilibrium constants (including those given in Tables I-III) have been determined in solutions containing high (usually >1 M) and constant concentration of an inert electrolyte (e.g., alkali perchlorate). In this way the variation of the activity coefficients of the studied species (kept below 0.1 M) is so small that no correction factors have to be applied. The equilibrium constants, however, are strictly valid only in the ionic medium in which they have been determined. In order to avoid the burden of experimental determination of equilibrium constants in each ionic medium encountered, semi-empirical methods have been developed to recalculate the constants from one ionic medium to another. One such method is the specific interaction theory (SIT), developed by Guggenheim il55) and Scatchard (156,157) on the basis... 

Extensive tabulations on experimentally determined surface equilibrium constants (Schindler and Stumm, 1987 Dzombak and Morel, 1990) reflecting the acid-base characteristic of surface hydroxyl groups and the stability of surface metal com-... 

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. 

Activity coefficients and concentration equilibrium constants. Strictly speaking, Eq. 6-31 applies only to thermodynamic equilibrium constants -that is, to constants that employ activities rather than concentrations. The experimental determination of such constants requires measurements of the apparent equilibrium constant or concentration equilibrium constant21 Kc at a series of different concentrations and extrapolation to infinite dilution (Eq. 6-32). 

These are now probably the most widely used methods in kinetic and mechanistic studies, and include a wide range of spectral frequencies radio frequencies (NMR, ESR), IR and UV-vis. Appropriate instrumentation which is easily adapted for kinetics is readily available in most research laboratories it is usually easy to use, and the output easily interpreted. Spectrophotometric methods are also widely used for the determination of equilibrium constants [25]. However, before deciding upon a spectrophotometric technique, the following experimental aspects must be considered carefully. 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

Finally, concordant results have been obtained from a kinetic study of the iodination of acetophenone and acetone at very low iodine concentration (Verny-Doussin, 1979). The procedure used is similar to that followed for the determination of equilibrium constants for enol formation by the kinetic-halogenation method, i.e. second-order rate constants were measured under conditions such that halogen additions to enol and enolate are rate-limiting (43). Under these conditions, the experimental kn-values can be expressed by... 

Because the measured potential of an electrochemical cell provides a very sensitive method for the experimental determination of equilibrium concentrations, the values of equilibrium constants are often determined from electrochemical measurements. 

Because of the importance that potentiometric methods have in the determination of equilibrium constants in aqueous solutions, a short discussion on the definition of pH and a simplified description of the experimental techniques used to measure pH will be given here. 

The determination of equilibrium constants for heterogeneous isotope-exchange reactions involving isotope-exchange between pure phases and solution phases yields partition-function ratios for the isotopic, solution-phase species. In favorable cases a comparison of calculated values for the solute partition-function ratio with the experimental value allows one to distinguish between possible solute models. 

Our comments on the stability of metal complexes have evolved from the study of stability constant data. The experimental determination of stability constants is an important but often difiBcult task. Perhaps the greatest problem in equilibrium measurements is to determine which species are actually present in solution. EquiUbriinn constants have been measured by many different methods. Usually a solution of the metal ion and ligand is prepared, sufficient time is allowed for the system to come to equilibrium, and the concentrations of the species in solution are then measured. From these equilibrium concentrations one can calculate the equilibrium constant using an expression such as equation (18). 

Acid-base properties determined for gas-phase molecular interactions are based on experimental measurements of equilibrium constants in proton transfer reactions between two gaseous bases ... 

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