The Thermodynamic Equilibrium Constant

Several features of equation 6.50 deserve mention. First, as the ionic strength approaches zero, the activity coefficient approaches a value of one. Thus, in a solution where the ionic strength is zero, an ion s activity and concentration are identical. We can take advantage of this fact to determine a reaction s thermodynamic equilibrium constant. The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolated... 

S. Adair, H. S. Sinuns, K. Linderstrom-Lang, and, especially, J. Wyman. These treatments, however, were empirical or thermodynamic in content, that is, expressed from the outset in terms of thermodynamic equilibrium constants. The advantage of the explicit use of the actual grand partition function is that it is more general it includes everything in the empirical or thermodynamic approach, plus providing, when needed, the background molecular theory (as statistical mechanics always does). 

From the thermodynamic equilibrium constant, the estimate of the standard molar free energy of ion-pair formation is sanctioned by the well known relationship ... 

Using AG = —RT In K, where K is the conventional thermodynamic equilibrium constant, the variation of K with pressure is obtained ... 

Reversible reactions Reactions that do not go to completion and occur in both the forward and reverse directions. Thermodynamic equilibrium constant The equilibrium constant defined in terms of activities of the products and reactants. 

This chapter discusses the thermodynamics of mixing processes and processes described by reaction equations (chemical equations). It introduces the important concepts of molar mixing and reaction quantities, advancement, and the thermodynamic equilibrium constant. The focus is on chemical processes that take place in closed systems at constant pressure, with no work other than expansion work. Under these conditions, the enthalpy change is equal to the heat (Eq. 5.3.7). The processes either take place at constant temperature, or have initial and final states of the same temperature. 

The lUPAC Green Book gives as an alternative symbol for the thermodynamic equilibrium constant, the appended superscript denoting standard. An lUPAC Commission on Thermodynamics has furthermore recommended the name standard equilibrium constant, apparently because its value depends on the choice of standard states. Using this alternative symbol and name could cause confusion, since the quantity defined by Eq. 11.8.9 does not refer to reactants and products in their standard states but rather to reactants and products in an equilibrium state. 

The reverse reaction rates are determined through the use of the thermodynamic equilibrium constant. The thermochemical data base36 is a modification of that used by Gordon and McBride in the NASA Chemical Equilibrium program. The thermochemical data is stored as polynomial fits for the specific heat Cp, enthalpy H°, and entropy S°, given by... 

In terms of the thermodynamic equilibrium constant, the activity of H2O is nearly constant and essentially 1, so it does not appear explicitly in the equilibrium constant. 

It is important to keep in mind that the hydrogenation of aromatics is thermodynamically limited it is favoured by high hydrogen pressure and low temperature. Moreover, the heavier the molecule, the more unfavourable is the thermodynamic equilibrium constant. The kinetics of hydrogenation depends on the type of molecule. Polyaromatic structures are more easily hydrogenated than light ones, if the Aermodynamic conditions are satisfied. 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

The true thermodynamic equilibrium constant, Ksp, for the solubility of AglOa, therefore, is... 

Finally, a consideration of equilibrium chemistry can only help us decide what reactions are favorable. Knowing that a reaction is favorable does not guarantee that the reaction will occur. How fast a reaction approaches its equilibrium position does not depend on the magnitude of the equilibrium constant. The rate of a chemical reaction is a kinetic, not a thermodynamic, phenomenon. Kinetic effects and their application in analytical chemistry are discussed in Chapter 13. 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

In this experiment the equilibrium constant for the dissociation of bromocresol green is measured at several ionic strengths. Results are extrapolated to zero ionic strength to find the thermodynamic equilibrium constant. Equilibrium Constants for Calcium lodate Solubility and Iodic Acid Dissociation. In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. 

From a general point of view, the tautomeric studies can be divided into 12 areas (Figure 20) depending on the migrating entity (proton or other groups, alkyl, acyl, metals. ..), the physical state of the study (solid, solution or gas phase) and the thermodynamic (equilibrium constants) or the kinetic (isomerization rates) approach. 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

Classical thermodynamics gives an expression that relates the equilibrium constant (the distribution coefficient (K)) to the change in free energy of a solute when transferring from one phase to the other. The derivation of this relationship is fairly straightforward, but will not be given here, as it is well explained in virtually all books on classical physical chemistry [1,2]. 

Equations (9.7) and (9.8) define K, the equilibrium constant for the reaction.b It is sometimes referred to as the thermodynamic equilibrium constant. As we shall see, this ratio of activities can be related to ratios of pressure or concentration which, themselves, are sometimes called equilibrium constants. But K, as defined in equations (9.7) and (9.8), is the fundamental form that is directly related to the free energy change of the reaction. 

It is important to note that, for any given temperature, the [thermodynamic] equilibrium constant is directly related to the standard change in free energy. Since, at any given temperature, the free energy in the standard state for each reactant and product, G°, is independent of the pressure, it follows that the standard change in free energy for the reaction, AfG°, is independent of the pressure.g Therefore, at constant temperature, the equilibrium constant K. .. is also independent of the pressure. That is,... 

The ambiguity results from the failure to recognize that the Rossini statement applies to the thermodynamic equilibrium constant, As we have already noted, the other forms that we have derived do depend upon the pressure. For example, for a gas phase reaction, Kp is related to K by equation (9.11)... 

Figure 9.1 is a graph of equation (9.52) showing how K varies with pressure at 298.15 K. We see that it increases by a factor of approximately 2 as the pressure increases by a factor of 1000. The increase is due to the change in the activity of the water rather than to a change in the thermodynamic equilibrium constant with pressure. 

The reactant mixture may be so nonideal that Equation (7.28) is inadequate. The rigorous thermodynamic approach is to replace the concentrations in Equation (7.28) with chemical activities. This leads to the thermodynamic equilibrium constant. 

As previously noted, the equilibrium constant is independent of pressure as is AG. Equation (7.33) applies to ideal solutions of incompressible materials and has no pressure dependence. Equation (7.31) applies to ideal gas mixtures and has the explicit pressure dependence of the F/Fq term when there is a change in the number of moles upon reaction, v / 0. The temperature dependence of the thermodynamic equilibrium constant is given by... 

For nonideal solutions, the thermodynamic equilibrium constant, as given by Equation (7.29), is fundamental and Ei mettc should be reconciled to it even though the exponents in Equation (7.28) may be different than the stoichiometric coefficients. As a practical matter, the equilibrium composition of nonideal solutions is usually found by running reactions to completion rather than by thermodynamic calculations, but they can also be predicted using generalized correlations. 

Suppose the numerical value of the thermodynamic equilibrium constant is known, say from the free energy of formation. Then Equation (7.40) is substituted into Equation (7.31) and the result is solved for s. 

Examples 7.12 and 7.13 treated the case where the kinetic equilibrium constant had been determined experimentally. The next two examples illustrate the case where the thermodynamic equilibrium constant is estimated from tabulated data. 

The kinetic equilibrium constant is estimated from the thermodynamic equilibrium constant using Equation (7.36). The reaction rate is calculated and compositions are marched ahead by one time step. The energy balance is then used to march enthalpy ahead by one step. The energy balance in Chapter 5 used a mass basis for heat capacities and enthalpies. A molar basis is more suitable for the current problem. The molar counterpart of Equation (5.18) is... 

Consequences of the Snyder and Soczewinski model are manifold, and their praetieal importance is very signifieant. The most speetaeular conclusions of this model are (1) a possibility to quantify adsorbents ehromatographic activity and (2) a possibility to dehne and quantify chromatographic polarity of solvents (known as the solvents elution strength). These two conclusions could only be drawn on the assumption as to the displacement mechanism of solute retention. An obvious necessity was to quantify the effect of displacement, which resulted in the following relationship for the thermodynamic equilibrium constant of adsorption, K,, in the case of an active chromatographic adsorbent and of the monocomponent eluent ... 

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