Referenced calculations

NHg, NH+, and NHj. The radical NHa was the first polyatomic free radical to be observed experimentally, and it has since been extensively studied spectroscopically. Bender and Schaefer 458 have referenced calculations on NHa prior to 1970, and have presented results for the most accurate calculations yet carried out, to which we return below. However, del Bene,459 at about the same time, reported the results of an SCF study, using small (STO-3G) or (ST04-31G) basis sets. The predicted zBi ground state of the radical has 0 = 108°, J (N—H) = 1.01 A, and for the Mi state 0 = 144°, 7 (N—H) = 0.98 A. 

When procedures require calculations, the calculations must be clear and understandable. In order to ensure accuracy for complicated or critical calculations, a formula or table Is Included In the procedure or on a referenced calculation sheet. 

Referenced Calculations. Exposure assessment involves numerous calculations, covering both cross-media transfers of chemicals and the derivation of exposures from concentrations and scenario-specific parameters. In general terms, such calculations can be viewed as the limiting case (in simplicity) of either theoretical or empirical models. All calculations in Risk Assistant for deriving exposures from concentrations in an appropriate medium (e.g. inhalation exposures from air concentrations) are obtained from the Exposure Factors Handbook (4). Equations for evaluating cross-media transfer for particular exposure scenarios (e.g. volatilization from domestic water to household air) are obtained from literature sources. For such equations, the original reference is provided for the user. 

It is possible to specify a ring system by specifying the atoms sequentially. Each atom can be referenced to the previous atom. In this case, a small change in angle between, say, the 3rd and 4th atoms specified would result in a significant change in the distance between the first and last atoms specified. This makes the calculation run inefficiently if it is successful at all. 

III some cases, Ihe calculated values reported in this table are nol explicitly given in the referenced paper they were calculated by this author on Ihe basis of the published data. 

Estimates of Composition. The best approach toward estimating the chemistry of most contaminant species is to assume chemical equiHbrium. Computer programs and databases (qv) for calculating chemical equiHbria are widely available (47). Care must be taken that all species of concern are in the database referenced by the program being used, and if necessary, important species must be added in order to get the complete picture. 

Approximate prediction of flow pattern may be quickly done using flow pattern maps, an example of which is shown in Fig. 6-2.5 (Baker, Oil Gas]., 53[12], 185-190, 192-195 [1954]). The Baker chart remains widely used however, for critical calculations the mechanistic model methods referenced previously are generally preferred for their greater accuracy, especially for large pipe diameters and fluids with ysical properties different from air/water at atmospheric pressure. In the chart. 

The Excel spreadsheet is constructed so that on page one, the referenced properties are listed in Column C, and the same with conversion factors to SI units in Column D. Conversion formulas and values calculated in SI Units are in Column E. Column F is a duplicate of Column E, and this can be used for additional calculation by changing to other conditions or to an entirely new case. It is recommended toleave Column E alone for a comparison case and to copy Column F to another page to execute calculations. 

Equation (16) was first developed by Purnell [3] in 1959 and is extremely important. It can be used to calculate the efficiency required to separate a given pair of solutes from the capacity factor of the first eluted peak and their separation ratio. It is particularly important in the theory and practice of column design. In the particular derivation given here, the resolution is referenced to (Ra) the capacity ratio of the first... 

P" = maximum header exit pressure into seal, psig p = density of seal liquid, Ib/cu ft Calculate the cross section of the drum volume for vapor above the liquid level, establishing the level referenced to h), plus clearance to drum bottom, hi, normally... 

Ward and Sommerfeld [130] present an equation based on the curves shown in Figure 9-21C, D and referenced to Eckert [125] and Leva [43] for calculating the gas and liquid flooding rates. There have been numerous other equations targeted for this pmpose, but many are too awkward for easy general use. The proposed equations have been tested by the authors. 

Select end of chapter Questions and Problems may be assigned in OWL and are cross-referenced in the Key Concepts list 1. Deduce the sign of AS for a process from randomness considerations. (Example 17.1 Problems 7-14) Questions and Problems assignable in OWL 6,8,10,16 2. Calculate AS° for a reaction, using Table 17.1. (Example 17.2 Problems 17-22) 20... 

Table II shows, as an example, the combinations of low and high levels for three factors selected by a design team for an accelerated test Involving photovoltaic solar cells. In column 2 the three factors are seen to be temperature T (50 C, 95 C), relative humidity RH (60%, 85%), and ultraviolet radiation UV (five suns, 15 suns). The eight combinations of the high and low levels are shown, together with the predicted months to failure for each combination. In this example the documentation to support each prediction is symbolically referenced as shown in the last column. The documentation includes assumptions, calculations, references to the literature, laboratory data, computer simulation results, and other related material. Such a factorial table is first completed by each scientist independently. Subsequently, the team alms to generate a single consensus factorial table has the same form as that shown in Table II.

Figure 5.8 Calculated y versus electrode potential A< sce (referenced to an SCE) curves for Au(lOO) in 0.01 M HCIO4. The crossing between the curves indicates the electrode potential at which the surface reconstruction is lifted [Au(100)-hex Au(100)-(1 x 1)].

Fig. 3.23 Left-. Calculated relationship between the thickness of an alteration rind and/or dust coating on a rock and the amount of 15.0-keV radiation absorbed in the rind/coating for densities of 0.4, 2.4, and 4.0 g cm [57]. The bulk chemical composition of basaltic rock was used in the calculations, and the 15.0 keV energy is approximately the energy of the 14.4 keV y-ray used in the Mossbauer experiment. The stippled area between densities of 2.4 and 4.0 g cm is the region for dry bulk densities of terrestrial andesitic and basaltic rocks [58]. The stippled area between densities of 0.1 and 0.4 g cm approximates the range of densities possible for Martian dust. The density of 0.1 g cm is the density of basaltic dust deposited by air fall in laboratory experiments [59]. Right Measured spectra obtained on layered laboratory samples and the corresponding simulated spectra, from top to bottom 14.4 keV measured (m) 14.4 keV simulated (s) 6.4 keV measured (m) and 6.4 keV simulated (s). All measurements were performed at room temperature. Zero velocity is referenced with respect to metallic iron foil. Simulation was performed using a Monte Carlo-based program (see [56])...

The solvent triangle classification method of Snyder Is the most cosDBon approach to solvent characterization used by chromatographers (510,517). The solvent polarity index, P, and solvent selectivity factors, X), which characterize the relative importemce of orientation and proton donor/acceptor interactions to the total polarity, were based on Rohrscbneider s compilation of experimental gas-liquid distribution constants for a number of test solutes in 75 common, volatile solvents. Snyder chose the solutes nitromethane, ethanol and dloxane as probes for a solvent s capacity for orientation, proton acceptor and proton donor capacity, respectively. The influence of solute molecular size, solute/solvent dispersion interactions, and solute/solvent induction interactions as a result of solvent polarizability were subtracted from the experimental distribution constants first multiplying the experimental distribution constant by the solvent molar volume and thm referencing this quantity to the value calculated for a hypothetical n-alkane with a molar volume identical to the test solute. Each value was then corrected empirically to give a value of zero for the polar distribution constant of the test solutes for saturated hydrocarbon solvents. These residual, values were supposed to arise from inductive and... 

At this point we should mention that today spectra are often referenced to a frequency which is calculated from the deuterium reference of the solvent... 

The major sources of uncertainty relating to the method should be identified. Those contributions not used in the final calculation, because they are considered insignificant, should be mentioned. The overall uncertainty should be listed, together with an explanation of how it was derived. A more detailed treatment may be in a cross-referenced hie. 

Amy Berger helped me write Chapter 10 (Surface Complexation), and Chapter 31 (Acid Drainage) is derived in part from her work. Edward Warren and Richard Worden of British Petroleum s Sunbury lab contributed data for calculating scaling in North Sea oil fields, Richard Wendlandt first modeled the effects of alkali floods on clastic reservoirs, and Kenneth Sorbie helped write Chapter 30 (Petroleum Reservoirs). I borrowed from Elisabeth Rowan s study of the genesis of fluorite ores at the Albigeois district, Wendy Harrison s study of the Gippsland basin, and a number of other published studies, as referenced in the text. 

---