Thermodynamic equilibrium constant definition

This distribution law applies only to the distribution of a definite chemical species, as does Henry s law. The distribution constant is not a true thermodynamic equilibrium constant, since it involves concentrations rather than activities. Thus it may vary slightly with the concentration of the solute (particularly because of the relatively high concentration of I2 in the CCI4 phase) it is therefore advantageous to determine 1 at a number of concentrations. It can be determined directly by titration of both phases with standard thiosulfate solution when I2 is distributed between CCI4 and pure water. Once k is known, (I2) in an aqueous phase containing I3 can be obtained by means of a titration of the I2 in a CCI4 layer that has been equilibrated with this phase. The use of a distribution constant in this manner depends upon the assumption that its value is unaffected by the presence of ions in the aqueous phase. 

In spite of the outlined above formulation of chemical equilibrium problem in terms of rigorous thermodynamics (equilibrium constants defined as quotients of activities) which is well known and does not pose any special difficulty when it is compared with formulation in terms of conditional equilibrium constants (defined as quotients of concentrations), the former approach is not very popular, and many equilibrium constants of surface reactions reported in published papers were defined in terms of concentrations. Even praise of use of concentrations rather than activities in modeling of adsorption can be found in recent literature. Many publications do not address this question explicit, and then it is difficult to figure out how the equilibrium constants of surface species were defined K, or Accordingly, the equilibrium constants of surface species reported in tables of Chapter 4 constitute a mixture of constants defined in different ways (K, or The details regarding the definition of equilibrium constants can be found (but not always) in the original publications. 

The value of 0rxn under equihbrium conditions is the thermodynamic equilibrium constant, K. The general definition of K is... 

The definition of the thermodynamic equilibrium constant of a reaction or other chemical process is given by Eq. 11.8.9 ... 

Equilibrium constants do not have units because in the strict thermodynamic definition of the equilibrium constant, the activity of a component is used, not its concentration. The activity of a species in an ideal mixture is the ratio of its concentration or partial pressure to a standard concentration (1 M) or pressure (1 atm). Because activity is a ratio, it is unitless and the equilibrium constant involving activities is also unitless. 

It is useful to keep in mind that the equilibrium constant is defined in terms of the difference in standard state free energies between products and reactants. Thus, for the reaction written in Equation 4.36 we obtained Equation 4.50, essentially by thermodynamic definition,... 

The p/<, of a base is actually that of its conjugate acid. As the numeric value of the dissociation constant increases (i.e., pKa decreases), the acid strength increases. Conversely, as the acid dissociation constant of a base (that of its conjugate acid) increases, the strength of the base decreases. For a more accurate definition of dissociation constants, each concentration term must be replaced by thermodynamic activity. In dilute solutions, concentration of each species is taken to be equal to activity. Activity-based dissociation constants are true equilibrium constants and depend only on temperature. Dissociation constants measured by spectroscopy are concentration dissociation constants." Most piCa values in the pharmaceutical literature are measured by ignoring activity effects and therefore are actually concentration dissociation constants or apparent dissociation constants. It is customary to report dissociation constant values at 25°C. 

The overall effect of the preceding chemical reaction on the voltammetric response of a reversible electrode reaction is determined by the thermodynamic parameter K and the dimensionless kinetic parameter . The equilibrium constant K controls mainly the amonnt of the electroactive reactant R produced prior to the voltammetric experiment. K also controls the prodnction of R during the experiment when the preceding chemical reaction is sufficiently fast to permit the chemical equilibrium to be achieved on a time scale of the potential pulses. The dimensionless kinetic parameter is a measure for the production of R in the course of the voltammetric experiment. The dimensionless chemical kinetic parameter can be also understood as a quantitative measure for the rate of reestablishing the chemical equilibrium (2.29) that is misbalanced by proceeding of the electrode reaction. From the definition of follows that the kinetic affect of the preceding chemical reaction depends on the rate of the chemical reaction and duration of the potential pulses. 

Thus we see that the pseudo-steady-state approximation gives orders of the reaction as the thermodynamic equilibrium approximation, the only difference being the definition of the rate constant... 

Equation (4.87) was obtained under the assumption of strict thermodynamic equilibrium between the particle and the surrounding radiation field that is, the particle at temperature T is embedded in a radiation field characterized by the same temperature. However, we are almost invariably interested in applying (4.87) to particles that are not in thermodynamic equilibrium with the surrounding radiation. For example, if the only mechanisms for energy transfer are radiative, then a particle illuminated by the sun or another star will come to constant temperature when emission balances absorption but the particle s steady temperature will not, in general, be the same as that of the star. The validity of Kirchhoff s law for a body in a nonequilibrium environment has been the subject of some controversy. However, from the review by Baltes (1976) and the papers cited therein, it appears that questions about the validity of Kirchhoff s law are merely the result of different definitions of emission and absorption, and we are justified in using (4.87) for particles under arbitrary illumination. 

Note that reactions 2.14, 2.15, and 2.23 involve fractional stoichiometric coefficients on the left-hand sides. This is because we wanted to define conventional enthalpies of formation (etc.) of one mole of each of the respective products. However, if we are not concerned about the conventional thermodynamic quantities of formation, we can get rid of fractional coefficients by multiplying throughout by the appropriate factor. For example, reaction 2.14 could be doubled, whereupon AG° becomes 2AG, AH° = 2AH , and AS° = 2ASf, and the right-hand sides of Eqs. 2.21 and 2.22 must be squared so that the new equilibrium constant K = K2 = 1.23 x 1083 bar-3. Thus, whenever we give a numerical value for an equilibrium constant or an associated thermodynamic quantity, we must make clear how we chose to define the equilibrium. The concentrations we calculate from an equilibrium constant will, of course, be the same, no matter how it was defined. Sometimes, as in Eq. 2.22, the units given for K will imply the definition, but in certain cases such as reaction 2.23 K is dimensionless. 

Equations 27 and 28 permit a simple comparison to be made between the actual composition of a chemical system in a given state (degree of advancement) and the composition at the equilibrium state. If Q K, the affinity has a positive or negative value, indicating a thermodynamic tendency for spontaneous chemical reaction. Identifying conditions for spontaneous reaction and direction of a chemical reaction under given conditions is, of course, quite commonly applied to chemical thermodynamic principle (the inequality of the second law) in analytical chemistry, natural water chemistry, and chemical industry. Equality of Q and K indicates that the reaction is at chemical equilibrium. For each of several chemical reactions in a closed system there is a corresponding equilibrium constant, K, and reaction quotient, Q. The status of each of the independent reactions is subject to definition by Equations 26-28. 

The derivation of the law of mass action from the second law of thermodynamics defines equilibrium constants K° in terms of activities. For dilute solutions and low ionic strengths, the numerical values of the molar concentration quotients of the solutes, if necessary amended by activity coefficients, are acceptable approximations to K° [Equation (3)]. However, there exists no justification for using the numerical value of a solvent s molar concentration as an approximation for the pure solvent s activity, which is unity by definition.76,77... 

In the previous sections concerning reference and standard states we have developed expressions for the thermodynamic functions in terms of the components of the solution. The equations derived and the definitions of the reference and standard states for components are the same in terms of species when reactions take place in the system so that other species, in addition to the components, are present. Experimental studies of such systems and the thermodynamic treatment of the data in terms of the components yield the values of the excess thermodynamic quantities as functions of the temperature, pressure, and composition variables. However, no information is obtained concerning the equilibrium constants for the chemical reactions, and no correlations of the observed quantities with theoretical concepts are possible. Such information can be obtained and correlations made when the thermodynamic functions are expressed in terms of the species actually present or assumed to be present. The methods that are used are discussed in Chapter 11. Here, general relations concerning the expressions for the thermodynamic functions in terms of species and certain problems concerning the reference states are discussed. 

The thermodynamic information is normally summarized in a Pourbaix diagram7. These diagrams are constructed from the relevant standard electrode potential values and equilibrium constants and show, for a given metal and as a function of pH, which is the most stable species at a particular potential and pH value. The ionic activity in solution affects the position of the boundaries between immunity, corrosion, and passivation zones. Normally ionic activity values of 10 6 are employed for boundary definition above this value corrosion is assumed to occur. Pourbaix diagrams for many metals are to be found in Ref. 7. 

There is no thermodynamic equilibrium between the ideally polarizable electrode (more exactly the metal phase) and the solution phase because there is no common component capable of changing its charge and being transferred between the phases, conditions necessary for equilibrium. The state of an ideally polarizable electrode is well defined only if an external source is used to maintain a constant polarization potential, i.e., the double-layer capacitor charged with a definite charge. The polarization potential is an independent parameter of the system. 

Since AF° has a definite constant value for the system, F is also a constant for that system. We refer to as the equilibrium constant. Readers may note that this relationship for is analogous to the classical postulates of equilibrium constant where it is defined as the ratio of the products of concentrations of reaction products and reactants. Only concentration terms have been replaced by activity terms. Here the science of thermodynamics has provided us with a correction for the classical postulate. 

Equation (7.8) offers a clear separation of inner-shell and outer-shell contributions so that different physical approximations might be used in these different regions, and then matched. The description of inner-shell interactions will depend on access to the equilibrium constants K. These are well defined, observationally and computationally (see Eq. (7.10)), and so might be the subject of either experiments or statistical thermodynamic computations. Eor simple solutes, such as the Li ion, ab initio calculations can be carried out to obtain approximately the Kn (Pratt and Rempe, 1999 Rempe et al, 2000 Rempe and Pratt, 2001), on the basis of Eq. (2.8), p. 25. With definite quantitative values for these coefficients, the inner-shell contribution in Eq. (7.8) appears just as a function involving the composition of the defined inner shell. We note that the net result of dividing the excess chemical potential in Eq. (7.8) into inner-shell and outer-shell contributions should not depend on the specifics of that division. This requirement can provide a variational check that the accumulated approximations are well matched. 

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