Equilibrium constant defining

It should finally be noted that the amount of the neutral and zweitterionic forms of a compound in solution is determined by its tatuomeric equilibrium constant, defined as Kz = cz/cn. Therefore, the neutral species and the zwitterion coexist around the isoelectric pH, and membrane permeation is conditioned by Kx and by the partition coefficient values of both tautomers. 

The distribution coefficients are independent of the concentration of suspended solids in water, which can vary over a wide range they thus give a better picture than the fraction of metal ions in solution. Such distribution coefficients can be predicted on the basis of the equilibrium constants defining the complexation of metals by surfaces and their complexation by solutes (Table 11.1). 

The previous summary of activities and their relation to equilibrium constants is not intended to replace lengthier discussions [1,18,25,51], Yet it is important to emphasize some points that unfortunately are often forgotten in the chemical literature. One is that the equilibrium constants, defined by equation 2.63, are dimensionless quantities. The second is that most of the reported equilibrium constants are only approximations of the true quantities because they are calculated by assuming the ideal solution model and are defined in terms of concentrations instead of molalities or mole fractions. Consider, for example, the reaction in solution ... 

C-t, which means, of course, that the ideal solution model is adopted, no matter the nature or the concentrations of the solutes and the nature of the solvent. There is no way of assessing the validity of this assumption besides chemical intuition. Even if the activity coefficients could be determined for the reactants, we would still have to estimate the activity coefficient for the activated complex, which is impossible at present. Another, less serious problem is that the appropriate quantity to be related with the activation parameters should be the equilibrium constant defined in terms of the molalities of A, B, and C. As discussed after equation 2.67, A will be affected by this correction more than A f//" (see also the following discussion). 

Although molalities are simple experimental quantities (recall that the molality of a solute is given by the amount of substance dissolved in 1 kg of solvent) and have the additional advantage of being temperature-independent, most second law thermochemical data reported in the literature rely on equilibrium concentrations. This often stems from the fact that many analytical methods use laws that relate the measured physical parameters with concentrations, rather than molalities, as for example the Lambert-Beer law (see following discussion). As explained in section 2.9, the equilibrium constant defined in terms of concentrations (Kc) is related to Km by equation 14.3, which assumes that the solutes are present in very small amounts, so their concentrations (q) are proportional to their molalities nr, = q/p (p is the density of the solution). 

These experiments indicated (a) that profilin-actin-ATP can participate in actin filament, (b) that the derived rate and equilibrium constants define a model which satisfies a closed thermodynamic cycle, and (c) that contrary to earlier suggestions, there is no absolutely need to invoke any special property of profilin in promoting irreversible ATP hydrolysis during actin polymerization. 

The equilibrium constant defined by eqn. (26) can be used to calculate the equilibrium conversion of reactants to products under specified conditions of temperature and pressure. The activity of a component X in a mixture of ideal gases, Ox, is given by... 

Chromatography and thermodynamics. Thermodynamic relationships can be applied to the distribution equilibria defined in chromatography. /C(= Cs/Cm), the equilibrium constant defining the concentration C of analyte in the mobile phase (M) and stationary phase (S) can be determined from chromatographic experiments. If the temperature of the experiment is known, it is possible to determine the variation of the standard free energy AG° for this transformation ... 

For the equilibrium constants defined above, the activity of the ions in question has been used. The activity of a species a, is related to the total concentration [Q] via the activity coefficient y which is expressed in the following equation ... 

In these relations the primes on the multiplication symbols explicitly designate the fact that pure materials are to be excluded from the product. This is accomplished by dropping such factor of unity out from Eq. (3.9.5) before taking the next step of converting (3.9.5) into (3.9.6). The quantities K, Kc, Kj, correspond to the three equilibrium constants defined in Section 2.11. 

In equation (49), which is the van t Hoff equation, —dH/de may be replaced by — AH, since these two quantities are equal for ideal-gas reactions. Relationships analogous to equation (49) may be derived for each of the equilibrium constants defined in Section A. 3, but for reactions in systems other than ideal-gas mixtures, — AH and — dH/de may not, in general, be equated in these expressions. Heats of reaction can be determined directly either by spectroscopic measurements followed by the application of statistical mechanics (for ideal-gas reactions) or by calorimetric measurements of Q (for arbitrary reactions). Since the measurement of equilibrium compositions may be simpler than either of the above procedures, in practice equation (49) is often used to obtain heats of reaction from experimental values of Kp at neighboring temperatures. 

Aqueous electrolytes and the equilibrium constants that define various reactions in low-temperature geochemistry are inexorably linked with the problem of activity coefficients, or the problem of nonideality for aqueous electrolyte solutions. Thermodynamic equilibrium constants, defined by an extrapolation to infinite dilution for the standard state condition (not the only standard state), require the use of activity coefficients. Unfortunately, there is neither a simple nor universal nonideality method that works for all electrolytes under all conditions. This section provides a brief overview of a major subject still undergoing research and development but for... 

As before, the log species concentrations and equilibrium constants, defined by the horizontal rows, can be read as follows ... 

Table 7.2. Equilibrium Constants Defining the Solubility of Carbonates...

With the equilibrium constants defined for a given/ 02 the ratio Fe /... 

The dimensionless quantity K is the thermodynamic equilibrium constant, which Section 14.3 shows can be calculated from tabulated data on the products and reactants, even if the empirical equilibrium constant defined in Equation 14.1b is not known. Therefore, K is the preferred tool for analyzing reaction equilibria in general. The informal argument by which we replaced ICp with K is made rigorous... 

In many cases, the equilibrium between the concentrations in the solids and liquid is constant throughout the range of interest, and the equilibrium curve is a straight line. The slope of the equilibrium line is related to the equilibrium constant defined in Equation 11.1 and the amount of liquid the marc retains by the following relationship ... 

The rationale for such a representation is that the ionic product of water is a function of the temperature and the equilibrium constant defined by Eq. (3,44) expresses the distance between PZC and neutral pH at given T. Indeed, pH 7 which is neutral at 25°C becomes basic at elevated T and acidic at T < 25°C. It can be easily shown that at 25°C... 

For example, the concept of Kj, (Eq. (4.9)) corresponds to Henry adsorption isotherm (adsorption is proportional to the equilibrium concentration/pressure of the adsorbate), which can be derived from the adsorption reaction 4.1, whose equilibrium constant defined by Eq. (4.2) depends only on the nature of the adsorbent and the adsorbate, but it is independent of the experimental conditions (over certain limited range). It is well known that in principle Kjy is variable, e.g. the effect of the pH on is demonstrated in Figs. 4.28-4.63. These figures show that the pH is an important but not unique factor affecting the distribution of the adsorbate, e.g. the usually decreases when the concentration of the adsorbate increases at constant pH. However, a few cases of constant over a broad range of concentrations of the adsorbate are also reported in Tables 4.1 and 4.2. 

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 equilibrium constant defined by Eq. (5.24) can be determined directly from experimental c7o(pH) curves obtained at different ionic strengths as their CIP, but Eq. (5.24) is not sufficient to calculate the cro(pH) curves when only the pHo is known, namely, some model assumption is necessary to calculate 0 beyond the pHo. Generally the surface potential makes the changes in uq with pH less steep than they would be (assuming a fixed iVg value) without the exponential term in Eq. (5.24). It was already discussed above (Eq. (5.21)) that the Nernstian 0 leads to constant [=AI0H2 ]/[=A10H ], and consequently constant (tq over the entire pH range, and this is in conflict with experimental facts. 

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