Derivation from experimental data

The viscosity coefficient fjP can also be derived from experimental data. 

Parameters for elements (basis liinctions in ah miiw methods usually derived from experimental data and empirical parameters in semi-empirical methods nsually obtained from empirical data or ah initu> calcii la lion s) are in depen den t of th e ch em -leal environment, [n contrast, parameters used in molecular mechanics methods often depend on the chem ical en viron-ment. 

The one-center two-electron integrals in the MNDO method are derived from experimental data on isolated atoms. Most were obtained from Oleari s work L. Oleari, L. DiSipio, and G. DeMich-ells. Mol. Phys., 10, 97( 1977)1, but a few were obtained by IDewar using fits to molecular properties. 

The vapoi piessuie values have been calculated at the indicated tempeiatuies using the lelationship derived from experimental data at Pennsylvania State University, and a critical review of Hterature references (5). This study is a part of the effort by the American Institute of Chemical Engineers (AIChE) to obtain accurate data through their Design Institute for Physical Property Data (DIPPR). 

The generalized compressibility charts may be used with values obtained in the use of Equations 2.7 and 2.8 to determine the compressibility of a wide range of gases. The charts were derived from experimental data and are a good source of information for use in compressor calculations [1]. 

Semi-empirical methods, such as AMI, MINDO/3 and PM3, implemented in programs like MOPAC, AMPAC, HyperChem, and Gaussian, use parameters derived from experimental data to simplify the computation. They solve an approximate form of the Schrodinger equation that depends on having appropriate parameters available for the type of chemical system under investigation. Different semi-emipirical methods are largely characterized by their differing parameter sets. 

Semi-empirical methods are characterized by their use of parameters derived from experimental data in order to simplify the approximation to the Schrbdinger equation. As such, they are relatively inexpensive and can be practically applied to very, very large molecules. There are a variety of semi-empirical methods. Among the best known are AMI, PM3 and MNDO. Gaussian includes a variety of semi-empirical models, and they are also the central focus or present in many other programs including AMPAC, MOPAC, HyperChem and Spartan. 

The following equations were derived from experimental data [74] to calculate aggregation numbers of sodium alkane 1-sulfonates ... 

The calculated values are not exact, because they are derived from experimental data, which are subject to experimental error. 

The transport numbers thus depend on the mobilities of both the ions of the electrolyte (or of all the ions present). This quantity is therefore not a characteristic of an isolated ion, but of an ion in a given electrolyte. Table 2.2 lists examples of transport numbers. It can be seen from the table that the transport numbers also depend on the electrolyte concentration. The following rules can be derived from experimental data ... 

In a first attempt to derive characterization factors with QSARs, the entire dataset of plastics additives was included, and aquatic ecotoxicity was predicted for two different trophic levels. This generated characterization factors that did not correspond well with the ones derived from experimental data [30]. Hardly surprising, but a clear indication that two trophic levels are unsufficient. A second attempt to derive characterization factors with QSARs are currently being performed [31]. In this second attempt, substances that are difficult to model in QSAR models have been removed from the dataset and the ecotoxicity has been predicted for three different trophic levels instead of two. However, results have not yet been obtained from this second attempt. If the results show that it is possible to derive reliable characterization factors by the use of QSARs, the current data gap regarding characterization factors for human toxicity and ecotoxicity could be... 

Note The Slater-Condon parameters of Di Sipio et al. (75), derived from experimental data, lead to B values in reasonable agreement with those listed above for M+ and M2+ ions, but give appreciably larger values for M°. Fitting of the data of Table 22 on this basis would lead to appreciably smaller values of zeff than the listed values, especially where these are relatively low. 

In the early days, see, e.g., Bakker and Van den Akker (1994a), a black box representing the impeller swept volume was often used in RANS simulations, with boundary conditions in the outflow of the impeller which were derived from experimental data. The idea behind this approach was that such nearimpeller data are hardly affected by the rest of the vessel and therefore could be used throughout. Generally, this is not the case of course. Furthermore, this approach necessitates the availability of accurate experimental data, not only... 

SMD = 10-3 (7(6.1 l+0.32xl05FAfp 5 -e xlO APi 5 +1.89x1 0 6APL) Derived from experimental data for 25 different fuels using 6 different simplex nozzles of large Flow numbers Wef>10 Strong effect of t7 no effect of Pl Discrepant with other data Kennedy [445]... 

It is generally believed that it was Ingold [1] in the early 1930s who proposed the first global electrophilicity scale to describe electron-deficient (electrophile) and electron-rich (nucleophile) species based on the valence electron theory of Lewis. Much has been accomplished since then. One of the widely used electrophilicity scales derived from experimental data was proposed by Mayr et al. [5-12] ... 

Heat and mass balance equations are used in all aspects of process modelling however, what is key to this model is an understanding of the electrolytic process behind the cell. For example, the model must be able to predict current efficiency and k-factor if it is to predict electricity consumption. Most of these electrolytic parameters are calculated using empirical relationships derived from experimental data both from test cells and the full-scale plant. Considering k-factor, this is primarily a function of brine strength and temperature. Figure 20.5 illustrates the experimentally derived function used in the model. 

We can compare this to the expression derived from experimental data for transition in internal energy density. Good agreement between the empirical model and the experimentally derived curve is observed (Figure 5.15). 

The numerical values of the distribution coefficients X and D have been derived from experimental data for a large number of systems (e.g. (10, 11, 13). From the constancy of either X or D values it can be determined whether or not the system yielded homogeneous precipitates. In either case, the numerical value of X or D should be equal to ... 

Although the agreement between calculated and experimental correlation and total energies is reassuring, as chemists we are more interested in relative quantities. Let us therefore turn our attention to AEs. In Table 1.9, we compare the calculated all-electron CCSD(T) equilibrium AEs with the corresponding AEs derived from experimental data, see Ref. 9. 

The calculated AEs are very accurate, with typical errors of about 1 kJ/mol and errors larger than 2.3 kJ/mol occurring only for 03 (-10.7 kJ/mol) and HOF (-12.0 kJ/mol). For 03, the difference probably arises from an error in the calculation as the high accuracy of the CCSD(T) model does not extend to systems that are poorly represented by a single determinant. For the single-determinant HOF molecule, the discrepancy is most likely caused by an error in the tabulated value derived from experimental data. 

One other alternative for obtaming derivatives from experimental data is to fit the data to a function by the method of least squares, either linear or nonlinear, and then to obtain the derivative analytically. We carried out both procedures for Exercise 18.4(c), and the different procedures agreed very well. Another alternative is to use a software package for numerical differentiation that does not require equal intervals in the independent variable. In any case, it is preferable to use more than one method. 

Table 9 Total molecular electronic ener, Et, derived from experimental data, ondEq. (5) All energies in atomic units.

In the system Th(IV)-H20 three sets of thermodynamic quantities can be derived from experimental data (1) the hydrolysis constants l°gio j3° and log10 /34 of ThOH3+ and Th(OH)4(aq), respectively, have been determined potentiometrically by several authors over a wide range of ionic strength (for references see Hummel et al. 2002) (2) the thermodynamic properties of Th02(cr) have been determined by calorimetry, and thus a solubility product logio K°s 0 (cr) for... 

In the case of tin, no meaningful value for the Sn(IV)/Sn(II) redox equilibrium could be derived from experimental data and no estimate was possible. As a consequence,... 

This may be derived from experimental data by analyzing the first order inductive shift in non alternants and second order shift in alternants. Both substituent constants are therefore intimately related to substituent effects on the it - n dipole excited states. Figure 44 shows the correlation with the shake up intensities. The trends displayed are quite striking and leave little doubt that the satellites arise from it->it excitations. 

In the column infiltration experiments with strontium, the model predictions closely resemble the experimental curves for the four flow rates compared. The input parameters to the ARDISC model were derived from experimental data obtained in infiltration experiments. The model predictions were based on the assumptions that the rate for adsorption and the rate for desorption were equal and that the sorption reactions were both first order. 

Which thermodynamic function needs to be known for assessing the temperature dependence of equilibrium partitioning How can this function be derived from experimental data What caution is advised when extrapolating partition constants from one temperature to another temperature ... 

Write down the most common mathematical expressions used to describe sorption isotherms. Discuss the meaning of the various parameters and describe how they can be derived from experimental data. 

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