Stoichiometric equilibrium

From changes in free energy in standard reference conditions it is possible to calculate equilibrium constants for reactions involving several reactants and products. Consider, for example, the chemical reaction aA + bB = cC + dD at equilibrium in solution. For this reaction we can define a stoichiometric equilibrium constant in terms of the concentrations of the reactants and products as... 

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

The activity coefficients can be used to compute a stoichiometric equilibrium... 

Table 15.1 Solubility as (S = 35) Stoichiometric Equilibrium Constants (-logKip) for a Function of Temperature and Pressure Where K p Calcite and Aragonite Has Units of (mol/kg) ...

In theory, it should be possible to deal with all carbonate geochemistry in seawater simply by knowing what the appropriate activity coefficients are and how salinity, temperature, and pressure affect them. In practice, we are only now beginning to approach the treatment of activity coefficients under this varying set of conditions with sufficient accuracy to be useful for most problems of interest. That is why "apparent" and stoichiometric equilibrium constants, which do not involve the use of activity coefficients, have been in widespread use in the study of marine carbonate chemistry for over 20 years. The stoichiometric constants, usually designated as K. involve only the use of concentrations, whereas expressions for apparent equilibrium constants contain both concentrations and aH+ derived from "apparent pH". These constants are usually designated as K Examples of these different types of constants are ... 

As an example, it appears still uncertain whether the high temperature conductivity of very pure magnesium oxide, and the way it varies with the ambient oxygen pressure, involves any measure of nonstoichiometry, or whether it is wholly attributable to residual impurities [Mitoff, 1959 (29)]. At very high temperatures the conductivity of refractory oxides may be intrinsic, and may mask any displacement of stoichiometric equilibrium. 

Equilibria and Equilibrium Constants. Many of the important reactions involving solutes in freshwaters can be described by equilibria. This approach means that an equilibrium constant, K, relating the activities of the solutes, can be defined for each stoichiometric equilibrium expression. 

Electrodes sensitive to one of the ion-pair partners in the so-called constant ionic strength cell [95] proved to be valuable to measure the free ion concentration and to determine the stoichiometric equilibrium constant. The latter has a clear thermodynamic meaning if the ionic strength of the medium is indicated, since in this approach, the reference standard state is not the usual infinite dilution of all species dissolved in the solvent (y-> 1, as c -> 0), but is the infinite dilution of the reacting species in the constant ionic medium (7—> 1, as c 0 at 1 = constant) [7]. Even if the constant ionic strength attenuates the variation of liquid junction potentials, the lower the association constant, the lower the consistency of the obtained constant. 

E. The equilibrium constants for these equilibria are, respectively, Kle, Km, Keh, Kleh, and Kle/Klh- These models are termed stoichiometric because they use stoichiometric equilibrium constants instead of thermodynamic constants (see below) to describe the ion association process. 

Apparent or stoichiometric equilibrium constants expressed as concentration quotients and valid for a medium of given ionic strength. 

These models, although of practical and intuitive value, are not well founded in physical chemistry. The pioneeristic, even if qualitative, work of Bidlingmayer demonstrated that IIRs adsorb onto the stationary phase. It follows that stoichiometric equilibrium constants, which depend on the change in free energy of adsorption of the analyte, cannot be considered constant if the IIR concentration in the mobile phase increases, because the stationary phase surface properties (including its charge density) are modified. The multibody interactions and long-term forces involved in IIC can better be described by a thermodynamic approach. 

FIGURE 1.18 Available heat vs. oxidizer preheat temperature for stoichiometric, equilibrium air/CTf, and 02/CH4 flames at an exhaust gas temperature of 2500°F (1644 K). 

Hegenauer, J., Saltman, P., and George, N. (1979). Iron(in)-phosphoprotein chelates stoichiometric equilibrium constant for interaction of iron(lll) and phosphorylserine residues of phosvitin and casein. Biochemistry. 18, 3865-3879. 

Masuoka J, Hegenauer J, Van Dyke BR, Saltman P (1993) Intrinsic stoichiometric equilibrium constants for the binding of zincfll) and copper(B) to the high affinity site of serum albumin. J Biol Chem 268 21533-21537... 

Figure 8.58 Schematic illustration of reaction coordinate diagram of Triose Phosphate Isomerase (TIM) enzyme illustrating near perfect energy landscape pathway allowing for near perfect 1 1 1 stoichiometric equilibrium between all enzyme-bound species optimal for flux through from one enzyme-bound species to another. Enzyme turnover rate kobs is at the diffusion limit, the rate determining step is the association of dihydroxy acetone phosphate (DHAP) with the TIM catalytic site, see Fig. 8.1, hence chemistry is not rate limiting. Therefore, TIM is considered a perfect enzyme For TIM enzyme assay see Fig. 8.17 for TIM enzyme mechanism see Fig. 8.49 (illustration adapted from Knowles, 1991, Fig. 2).

Consider a mixture of compounds (A, B) in stoichiometric equilibrium with each other ... 

Table 3a Stoichiometric Equilibrium Constants in the Extraction of Zn(II), Cu(II), and Cd(ll) from 0.1 M NaNO with DEHPA in Amberlite XAD2 and in Organic Solvents at...

Equivalent fractions of ion j in the solution phase Equivalent fractions of ion j in the resin phase Stoichiometric equilibrium constant for the extraction reaction... 

It is safe to check at this point whether the back pressure of CO2 above the liquid is negligible. This requires data on the stoichiometric equilibrium constant (kmol/m ) of the reaction ... 

Our approach is to treat solvation as a stoichiometric equilibrium process. Let W symbolize water, M an organic cosolvent, and R the solute. Then we postulate the 2-step (3-state) system shown below. 

The fixed groups in the membrane phase can also assume to receive charge by absorption or chelation of electrolyte cations penetrating from the diffiise electrical double layer. The absorption or chelation reaction can be described by the following stoichiometric equilibrium [68] ... 

If Equation 8.35 is rewritten as x. - x = x. exp[-(k+ + kjt], it follows that a unimo-lecular reaction approaches equilibrium as a first-order reaction with the rate constant k = k+ -I- k. If we determine x for the reaction (8.30) at a number of times and furthermore measure x at equilibrium, we may determine k+ -i- k. The separate rate constants k+ and k may be obtained subsequently by using the stoichiometric equilibrium constant and Equation 8.31 ... 

According to Equation 8.36, the stoichiometric equilibrium constant for a reversible, unimolecular reaction is given by the quotient between the rate constants for the forward reaction and the back reaction. The results are general. 

Table II. Rate constants and stoichiometric equilibrium constants for the Na salts investigates in DMA at 25 C...

It is sometimes sufficient to generate alkoxides in less than stoichiometric equilibrium concentrations. For this purpose, we may add an alkali metal hydroxide to the alcohol. 

The very general success of the phenomenological theory in quantitatively describing the composition dependence of many chemical and physical processes arises from the treatment of solvation effects by a stoichiometric equilibrium model. It is this model that pro-... 

---