Stoichiometric constants

Evaluation of the consistency of relevant experimental results. Stoichiometric constant. Mass and energy balances. 

Cross-sectional area Volumetric flow rate Reaction rate Stoichiometric constant Molar flow rate Molar feed flow rate A Molar feed flow rate B Molar inert flow rate Pressure Gas constant Temperature Fraction conversion Mole fraction Length... 

Components are the most basic units (molecules or ions or atoms) that interact with each other. In the above example X, Y, and Z are components. All the resulting products of the interactions (molecules or ions or complexes) are called species. In the example, one of potentially many species is XxYyZz. To be consistent and to allow elegant and efficient notation and computer coding, the components themselves are also species. Their equilibrium constant is one. The equilibrium constants fixyz as defined in (3.22) are called formation constants. The composition of a particular species is defined by a set of three stoichiometric constants written as the indices x, y, and z. If a species is composed of only two components, the appropriate index is zero. 

This assumes H2O = 1, which is nearly true, even in seawater. For example, H2O = 0.98 at 35%o, 25°C, and 1 atm. As with other equilibrium expressions, and can be rewritten as stoichiometric constants that are specific for a particular temperature, pressure, and ionic strength. 

Often more complex situations arise in which additional tautomers or other forms arise via pH-independent reactions. These can all be related back to the reference ionic species by additional ratios R, which may describe equilibria for tautomerization, hydration, isomerization, etc. (Eq. 6-82).76 In the case illustrated, only one of the ratios, namely R2 or R3, is likely to be a tautomerization constant because, as a rule, H2P and P will not have tautomers. Equations analogous to Eqs. 6-76 to 6-82 can be written easily to derive Kc, K0 and any other microscopic constants desired from the stoichiometric constants plus the ratios R, to R4. While it is easy to describe tautomerism by equations such as Eqs. 6-76 and 6-82 it is often difficult... 

Concentration of A Arrhenius constants Arrhenius constant Constant in equation 5.82 Surface area per unit volume Parameter in equation 5.218 Cross-sectional area Concentration of B Stoichiometric constants Parameter in equation 5.218 Concentration of gas in liquid phase Saturation concentration of gas in liquid Concentration of G-mass Concentration of D-mass Dilution rate DamkOhler number Critical dilution rate for wash-out Effective diffusion coefficient Dilution rate for maximum biomass production Dilution rate for CSTF 1 Dilution rate for CSTF 2 Activation energy Enzyme concentration Concentration of active enzyme Active enzyme concentration at time t Initial active enzyme concentration Concentration of inactive enzyme Total enzyme concentration Concentration of enzyme-substrate complex with substance A... 

Determining solubility constants in aqueous solutions generally involves analytical work to determine concentrations [ ] or potentiometric measurements to obtain activities. The ratio of activity and concentration—i.e., the activity coefficient and its change with concentration— depends on the choice of the standard state. If pure water is chosen as a standard state, the activity coefficients approach unity only in dilute solutions. It is therefore necessary to express the so-called thermodynamic constants TK (48) in terms of activities. If, on the other hand, one chooses as reference an aqueous solution of comparatively high and constant ionic strength, the activity coefficients remain close to unity even at rather high concentrations of the reacting species. In this case, we may use stoichiometric constants K (48), expressed in molarities, M, and related to a particular ionic medium. 

Our calculation will be based on solubility data, mainly TK values, valid for 25 °C. and 1 atm. In a few cases stoichiometric constants for different media are available, but only two (for calcite and SrC03) refer to sea water. Furthermore, many of the given values are uncertain, and there are only a few systems where a complete and reliable set of solubility constants enables one to construct a solubility diagram. 

Knowing the stability constants (actually, molarity quotients or stoichiometric constants are more useful here), it is possible to say which... 

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 ... 

It should be noted that in seawater the molinity concentration scale (moles kg-1 of seawater) is often used, and care must be taken to make certain that stoichiometric and apparent constants are on the same concentration scale as the measured values. The ratios of thermodynamic constants to their apparent or stoichiometric constant are activity coefficients, for example ... 

The general equation determined by Millero (1979) for the influence of temperature and salinity on apparent or stoichiometric constants in seawater is ... 

The influence of pressure on the apparent or stoichiometric constants can be determined by using equations 1.43, 1.44, and 1.45 with the data in Table 1.10. It should be noted that the currently available information for V and K is restricted to S=35. A reasonable approximation of pressure effects at other salinities, however, can be made assuming a linear variation of V and K between pure water and S=35 seawater as a function of the square root of ionic strength. The variations of pK values with pressure at 0 and 25°C for S=35 seawater are presented in Figure 1.6. 

Table 14. Equilibria and their stoichiometric constants (K) involved in the synergistic extraction of Pu(IV) from nitric acid medium by solutions of HTTA and some neutral organophosphorous donors (B)24,25). Aqueous medium = 1.0M nitric acid diluent - benzene Temp. — 25°C... 

This ion interaction retention model of IPC emphasized the role played by the electrical double layer in enhancing analyte retention even if retention modeling was only qualitatively attempted. It was soon realized that the analyte transfer through an electrified interface could not be properly described without dealing with electrochemical potentials. An important drawback shared by all stoichiometric models was neglecting the establishment of the stationary phase electrostatic potential. It is important to note that not even the most recent stoichiometric comprehensive models for both classical [17] and neoteric [18] IPRs can give a true description of the retention mechanism because stoichiometric constants are not actually constant in the presence of a stationary phase-bulk eluent electrified interface [19,20], These observations led to the development of non-stoichiometric models of IPC. Since stoichiometric models are not well founded in physical chemistry, in the interest of brevity they will not be described in more depth. 

Cantwell and co-workers submitted the second genuine electrostatic model the theory is reviewed in Reference 29 and described as a surface adsorption, diffuse layer ion exchange double layer model. The description of the electrical double layer adopted the Stem-Gouy-Chapman (SGC) version of the theory [30]. The role of the diffuse part of the double layer in enhancing retention was emphasized by assigning a stoichiometric constant for the exchange of the solute ion between the bulk of the mobile phase and the diffuse layer. However, the impact of the diffuse layer on organic ion retention was danonstrated to be residual [19],... 

A simpler desaiption of the system is desired and it can be obtained using equilibrium constants that describe aU eqnilibria in the systan obviously only a thermodynamic equilibrium constant must be made use of since, as discussed above, at variance with stoichiometric constants, they account for all the molecular level interactions in a very simple way, and notably, their chromatographic and non-chromatographic estimates can be compared to validate the retention mechanism they describe. 

It must be emphasized that such stoichiometric stability constants are dependent, inter alia, upon the ionic strength of the solution, and, in reporting experimental results, the ionic strength of the experimental solutions should always be specified. Further, the numerical value of a stoichiometric constant will depend upon the units used, viz. mole fractions, molar, molal, millimole, and so on, and which is used should always be made clear. 

The interest in the carbonate system is related to attempts to understand the uptake of fossil fuel produced CO2 by the oceans. The carbonate system can be studied by measuring pH, total alkalinity (TA), total inorganic carbon (TCO2), and the fugacity of CO2 (fco )- At least two of these variables are needed (Park, 1969) to characterize the CO2 system in the oceans. Reliable stoichiometric constants (K ) for the carbonate system are needed to determine the concentration, mol (kg solution) of the components of the CO2 system ([HCOa"], [CO2], [COa ]) and the saturation state of CaCOa as a function of salinity, temperature, and pressure (Culberson and Pytkowicz, 1968 Ingle, 1975 Millero, 1995, 2001). This includes constants for the solubility of CO2 in seawater (Weiss, 1974)... 

Since the tautomeric ratio R equals [HP]g/ [HP], Eqs. 6-76 and 6-77 can be rearranged to Eqs. 6-78 to 6-81. These allow the evaluation of all of the microscopic constants from the two stoichiometric constants and K2 plus the tautomeric ratio R. 

Cantwell and co-workers proposed a surface adsorption, diffuse-layer ion-exchange double-layer model in which they underlined the role of the diffuse part of the double layer by assigning a stoichiometric constant for the exchange of ions. 

Normally, the feed composition will be given (the stoichiometric constants o p the thermostatic data 7, and the parameters of the kinetic expression are, of course, known), and as these two equations contain five variables, namely 7/, 7, and three variables must be chosen while the remaining... 

The stoichiometric dissociation constant and not the thermodynamic constant is calculated from the results of the kinetic method. The thermodynamic constant can then be computed from the stoichiometric constant by the method described in connection with the conductivity method (sub b). 

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