Simple correlation

There also exist relatively simple correlations between the heating value of motor fuels and certain characteristics such as density and composition by chemical family supplied by FIA analysis. Refer to Chapter 3. 

By use of Othmer plots of reference substances, large tables of thermodynamic data can be expressed as simple correlations which are extremely accurate and easy to use. The real power of these correlations is the abiUty to interpolate and extrapolate the correlations beyond the experimental values with considerable accuracy. Mathematically stated... 

Hayduk-Laudie They presented a simple correlation for the infinite dilution diffusion coefficients of nonelectrolytes in water. It has about the same accuracy as the Wilke-Chang equation (about 5.9 percent). There is no explicit temperature dependence, but the 1.14 exponent on I compensates for the absence of T in the numerator. That exponent was misprinted (as 1.4) in the original article and has been reproduced elsewhere erroneously. 

For the first time through a liqmd-liquid extrac tion problem, the right-triangular graphical method may be preferred because it is completely rigorous for a ternary system and reasonably easy to understand. However, the shortcut methods with the Bancroft coordinates and the Kremser equations become valuable time-savers for repetitive calculations and for data reduction from experimental runs. The calculation of pseudo inlet compositions and the use of the McCabe-Thiele type of stage calculations lend themselves readily to programmable calculator or computer routines with a simple correlation of equilibrium data. 

The phase rule is a mathematical expression that describes the behavior of chemical systems in equilibrium. A chemical system is any combination of chemical substances. The substances exist as gas, liquid, or solid phases. The phase rule applies only to systems, called heterogeneous systems, in which two or more distinct phases are in equilibrium. A system cannot contain more than one gas phase, but can contain any number of liquid and solid phases. An alloy of copper and nickel, for example, contains two solid phases. The rule makes possible the simple correlation of very large quantities of physical data and limited prediction of the behavior of chemical systems. It is used particularly in alloy preparation, in chemical engineering, and in geology. 

We consider first the Sn2 type of process. (In some important Sn2 reactions the solvent may function as the nucleophile. We will treat solvent nucleophilicity as a separate topic in Chapter 8.) Basicity toward the proton, that is, the pKa of the conjugate acid of the nucleophile, has been found to be less successful as a model property for reactions at saturated carbon than for nucleophilic acyl transfers, although basicity must have some relationship to nucleophilicity. Bordwell et al. have demonstrated very satisfactory Brjinsted-type plots for nucleophilic displacements at saturated carbon when the basicities and reactivities are measured in polar aprotic solvents like dimethylsulfoxide. The problem of establishing such simple correlations in hydroxylic solvents lies in the varying solvation stabilization within a reaction series in H-bond donor solvents. 

It is evident from the foregoing discussion that MW is the fundamental characteristic of polymer, controlling the performance properties. However, simple correlation of this molecular parameter can be misleading without taking the MWD into consideration. Control of MWD provides a proper balance of polymer performance characteristics. The effect of change in MWD on the properties of PEs is given in Table 6. 

The results show that it is possible to improve the Hartree-Fock energy —2.86167 at.u. considerably by means of a simple correlation factor, but also that it is essential to scale the total function W properly to fulfil the virial theorem. The parameters in the best function u of the form of Eq. III. 121 are further given below ... 

Because of the complex hydrodynamics associated with GPC systems, it is difficult to arrive at a simple correlation between GPC operational parameters and chain scission kinetics. At least five degradation mechanisms (given below with the associated flow field) may be operative in the different parts of the column, during a standard GPC analysis ... 

Carpenter and Colburn have put forward a simple correlation of their results for condensation at varying vapour velocities on the inner surface of a vertical tube which takes the form ... 

For Sn2 reactions, no such simple correlations are found. In this mechanism bond breaking is about as important as bond making in the ratedetermining step, and substituents have an effect on both processes, often in... 

The theory of radiation-induced grafting has received extensive treatment [21,131,132]. The typical steps involved in free-radical polymerization are also applicable to graft polymerization including initiation, propagation, and chain transfer [133]. However, the complicating role of diffusion prevents any simple correlation of individual rate constants to the overall reaction rates. Changes in temperamre, for example, increase the rate of monomer diffusion and monomer... 

After polymerization took place an additional EPR signal located at g = 2.002 was observed. This signal can be assigned to Ti + centers within an organic environment [142,143]. This result points towards a change of the chemical environment of the Ti center at the interface during polymerization. The signal intensity and width varies considerably from preparation to preparation, but there is no simple correlation of these quantities with the activity. 

Confined flows typically exhibit laminar-flow regimes, i.e. rely on a diffusion mixing mechanism, and consequently are only slowly mixed when the diffusion distance is set too large. For this reason, in view of the potential of microfabrication, many authors pointed to the enhancement of mass transfer that can be achieved on further decreasing the diffusional length scales. By simple correlations based on Fick s law, it is evident that short liquid mixing times in the order of milliseconds should result on decreasing the diffusion distance to a few micrometers. 

In detail, some of the trends within individual across-arc traverses are complicated. For example, within Kamchatka U/Th ratio increases with depth to the Benioff zone (Turner et al. 1998), although there is no simple correlation with (Fig. 20a). 

Bridgwater, IChemE (1988), gives a developed relatively simple correlation for plants that are predominantly liquid and/or solid phase handing processes. 

No simple correlation is available to predict the flooding velocities in extraction columns, and hence the column diameter needed. The more specialised texts should be consulted to obtain guidance on the appropriate method to use for a particular problem see Treybal (1980), Perry et al. (1997) and Humphrey and Keller (1997). 

Several studies have been attempted to make simple correlations between radon or radium concentrations in the soil and indoor radon concentrations.4344 No significant correlations were made between these variables. 

Hall, K.R., Yarborough, L. New Simple Correlation for Predicting Critical Volume, Chemical Engineering, Nov. 1, 1971, p. 76. 

Pachaiyappan, V., Ibrahim, S.H., Kuloor, N.R. Simple Correlation for Determining Viscosity of Organic Liquids, Chemical Engineering, May 22, 1967, p. 193. 

Figure 3.48 Comparison of potassium and sodium two-phase friction pressure drop data with Lock-hart-Martinelli correlation, and with a simple correlation [1/(1 - a)]. (From Fauskeand Grolmes, 1970. Copyright 1970 by American Society of Mechanical Engineers. Reprinted with permission.)...

Simple correlational analysis of the NHANES II data by Harlan (1988) and Harlan et al. (1985) revealed statistically significant associations between PbB levels and systolic and diastolic blood pressure for both men and women, aged 12-74 years. Statistical analyses controlling for a number of other potentially confounding factors (e.g., age, race, and body mass index), however, indicated significant associations between PbB level and blood pressure only for the men. Based on these analyses, the effect of PbB concentration on blood pressure was estimated to be an increase in blood pressure of 7 mm Hg at PbB levels between 14 and 30 pg/dL. 

The description of the degree of retention data correlation is more complicated than it appears. For example, the 2D retention maps cannot be characterized by a simple correlation coefficient (Slonecker et al., 1996) since it fails to describe the datasets with apparent clustering (Fig. 12.2f). Several mathematical approaches have been developed to define the data spread in 2D separation space (Gray et al., 2002 Liu et al., 1995 Slonecker et al., 1996), but they are nonintuitive, complex, and use multiple descriptors to define the degree of orthogonality. 

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