Bulk composition calculation

The penetration theory has been used to calculate the rate of mass transfer across an interface for conditions where the concentration CAi of solute A in the interfacial layers (y = 0) remained constant throughout the process. When there is no resistance to mass transfer in the other phase, for instance when this consists of pure solute A, there will be no concentration gradient in that phase and the composition at the interface will therefore at all Limes lie the same as the bulk composition. Since the composition of the interfacial layers of the penetration phase is determined by the phase equilibrium relationship, it, too. will remain constant anil the conditions necessary for the penetration theory to apply will hold. If, however, the other phase offers a significant resistance to transfer this condition will not, in general, be fulfilled. 

For the a-Pt02 system, we find that above an electrode potential of 1.2 V, the (001) surface with bulk composition is most stable and shows only minor relaxation effects (denoted as (OOl)-O in Fig. 5.11a). This surface structure corresponds to experimental UHV measurements of surface oxides on Pt(llO), supported by DFT calculations [Li et al., 2004]. In the case of a very thin surface layer, the layer composition might even be PtO. Increasing the electrode potential above 2.0 V would cause stronger interactions with the surrounding water dipoles and lead to a o -PtO2(011) surface with an enrichment of oxygen (as 0 ) on the surface. 

We assume that a constant mass fraction fr remains in the mantle wedge after melt extraction. As in Section A2 of the Appendix, the ratio of slab mass to wedge mass is assumed to be equal to 1 but more complex models are also possible. The bulk composition of the mantle wedge after melt extraction is calculated with the following equation after each extraction increment ... 

For the calculation of AhP we must count contacts within the surface layer, and between the surface layer and the neighbouring layer (which has bulk composition). This calculation is simplified very much if we assume that at the critical point the surface is almost saturated with displacer (i.e. g 1), since not only the polymer, but also the still more weakly adsorbing solvent will have been almost completely displaced. Before exchange, we have a displacer molecule at the surface, and a segment in the solution, giving contributions to the mixing energy h = X Jx 0 and ... 

Garrels and Thompson s calculation, computed by hand, is the basis for a class of geochemical models that predict species distributions, mineral saturation states, and gas fugacities from chemical analyses. This class of models stems from the distinction between a chemical analysis, which reflects a solution s bulk composition, and the actual distribution of species in a solution. Such equilibrium models have become widely applied, thanks in part to the dissemination of reliable computer programs such as SOLMNEQ (Kharaka and Barnes, 1973) and WATEQ (Truesdell and Jones, 1974). 

In solving the equations, we can consider the set of bulk compositions (Mw, Mi, Mfc) to be the boundary conditions from which we determine the system s equilibrium state. The result is given in terms of the values of (nw, mi, n ). Once these values are known, the dependent variables mj can be set immediately using Equation 3.27. Note that we have demonstrated the conjecture of the first chapter that the equilibrium state of any system at known temperature and pressure can be calculated once the system s bulk composition is known. 

The remaining step is to compute the system s bulk composition, if it is not fully known, according to the mass balance equations. The mole numbers Mw, Mi, and are not known when the modeler has constrained the corresponding variable nw, mt, or tig. In these cases, the mole numbers are determined directly from Equations 4.3 1.5. Where gases appear in the basis, the mole numbers Mm of gas components are similarly calculated from Equation 4.6. 

The program produces in its output dataset a block of results that shows the concentration, activity coefficient, and activity calculated for each aqueous species (Table 6.4), the saturation state of each mineral that can be formed from the basis, the fugacity of each such gas, and the system s bulk composition. The extent of the system is 1 kg of solvent water and the solutes dissolved in it the solution mass is 1.0364 kg. 

In the calculation results, we can quickly identify the input constraints the fugacities of CC>2(g) and 02(g) and the bulk composition expressed in terms of components Cl-, Ca++, and so on. Note that the free species concentrations do not satisfy the input constraints, which are bulk or total values. The free concentration of the species Ca++, in other words, accounts for just part of the solution s calcium content. 

Once a substitution of constraints is accomplished, the calculation consists of incrementally changing the system s bulk composition as a function of reaction progress and, after each increment, recalculating the equilibrium state. The bulk composition is given from the component masses (M°, Mf, and Mp present at... 

Fig. 24.2. Calculated effects of evaporation at 25 °C on the chemistry of Sierra Nevada spring water. Top figures show how pH and ionic strength vary over the reaction path in Figure 24.1 bottom figure shows variation in the fluid s bulk composition.

Fig. 24.8. Evolution of fluid chemistry during the simulated evaporation of seawater as an equilibrium system at 25 °C, calculated using the Harvie-Mpller-Weare activity model. Upper figures show variation in salinity, water activity (aw), and ionic strength (/) over the reaction path in Figure 24.7 bottom figure shows how the fluid s bulk composition varies.

Given or temperature, the calculation of equilibrium concentrations from initial concentrations or from bulk compositions, which is prerequisite for any kinetic calculation, is shown in Box 2-2. 

Consider first the CAIs. In general, their bulk compositions are consistent with those calculated for the first 5% of condensable matter (Davis and Richter, 2004). Moreover, many of the minerals that comprise CAIs (hibonite, perovskite, spinel, melilite, diopside, anor-thite) are predicted to have been the earliest condensed phases. However, not all CAIs are... 

In estimating the bulk compositions of the other terrestrial planets, there are not nearly so many constraints. Determination of a planet s mass (obtained from its gravitational effect on the orbits of moons or nearby spacecraft) and volume (calculated from its diameter as measured by telescopes) enables the calculation of its mean density. A meaningful comparison of planet mean densities requires that we correct for the effects of self-compression due... 

Mg which is calculated as octahedral ions. It is nevertheless quite possible that the analyses of the fully expandable montmorillonites do show a valid chemical variation and not just analytical error of one sort or another. A remarkable point, in comparing the mixed layered and fully expandable bulk compositions is that the former defines two compositional series while the latter is found just between these two series. If indeed, this is the result of not only analytical errors, the relations would suggest that the fully expandable series are mixtures of the two extreme compositional types beidellite and montmorillonite. Since neither these nor the two forms are found alone, one would suspect the above deduction to be true. The possibility of the coexistence of two fully expanding phases has important implications in the phase relations as we will see. 

Equation (IS) provides the zeolite chemist with a powerful quantitative method for the determination of framework composition of zeolites. By comparing (Si/A1)NMR values with the results of chemical analysis, which gives bulk composition, the amount of nonframework (six-coordinated) aluminum can be calculated. This is of particular value in the study of chemically modified zeolites (see Sections III,J-III,M). 

Caggiano, Calculation of TNT Air-Blast Equivalences for Surface Blasts , PATR 4567 (1973) 19) R.S. Kukuvka K. Gandhi, Propagation Tests of 55Pound Boxes of Bulk TNT and 60-Pound Boxes of Bulk Composition B , PATR 4622 (1973) (Limited distrib) 20) J. Edel-maier, Makeshift Processing of Trinitrotoluene ,... 

The experimentally-determined effectiveness factor is determined as the ratio of the experimental macro reaction rate to the intrinsic reaction rate under the same interface (bulk) composition and temperature. Based on the experimental conditions of the macrokinetics, the predicted effectiveness factors of the methanation reaction and the WGSR are obtained by solving the above non-isothermal one-dimensional and two-dimensional reaction-diffusion models for the key components. Table 1 shows the calculated effectiveness factors and the experimental values. By... 

The process of condensation of minerals in the early solar nebula has long been invoked to explain the chemistry and mineralogy of primitive chondritic meteorites (e.g. Cameron 1963). Their observed bulk compositions show volatile-element depletions that are clearly smooth functions of calculated condensation temperature in a gas of solar composition (Davis 2006). Despite this success in explaining the bulk composition of chondrites, the diverse mineralogy of these bodies is not reproduced well in the condensation sequence calculations. To date, there is no incontrovertible evidence for direct condensation of rocky meteoritic material in the... 

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