Potential graphical comparison

Figure 16.3 Graphical comparison of potential environmental impact of waste.

Chan (Chapter 6) presents a simple graphical method for estimating the free energy of EDL formation at the oxide-water interface with an amphoteric model for the acidity of surface groups. Subject to the assumptions of the EDL model, the graphical method allows a comparison of the magnitudes of the chemical and coulombic components of surface reactions. The analysis also illustrates the relationship between model parameter values and the deviation of surface potential from the Nernst equation. 

A very powerful tool of visualizing three-dimensional molecular properties, including potential surfaces, is computer graphics.(32) Computer graphics is particularly useful in the qualitative comparison of two or more molecules. 

In addition, in the graphical presentation of data, different conventions are used, giving rise to problems in the interpretation and comparison of results. However, a good convention will not cause any problems. In this book (Fig. 1.2) positive potentials are directed to the right of the origin, and anodic (oxidation) currents are taken as positive (directed upward from the... 

The value of the fugacity of a gas in a given state must be calculated by means of an equation of state, either algebraic or graphic it is not determined directly by experimental means. An expression for the fugacity of the fcth substance in a gas mixture can be obtained by comparison of Equations (7.67) and (7.77). These equations give two different ways of expressing the chemical potential, and consequently the two expressions must be equal. Thus,... 

The box plot has proved to be a popular graphical method for displaying and summarizing univariate data, to compare parallel batches of data, and to supplement more complex displays with univariate information. Its appeal is due to the simplicity of the graphical construction (based on quartiles) and the many features that it displays (location, spread, skewness, and potential outliers). Box plots are useful for summarizing distributions of treatment outcomes. A good example would be the comparison of the distribution of response to treatment at different dose levels or exposure (as measured by area under the plasma concentration-time curve) as in Figure 37.3. 

Given the appropriate potential energy diagrams from the DLVO theory, the stability ratio may be calculated by graphical or numerical integration and then compared with experimental values of W=kyk, the ratio of the experimental rate constants for rapid and slow flocculation. Such a comparison is a severe test of the applicability of theory to experiment, and the observed deviations, although often not appreciable, reflect the assumptions and approximations which are necessary in the calculation of the potential energy terms. An advanced treatment of these issues will be found in Russel et al.- . 

The thermodynamic relationship between standard state chemical potential differences and the position of chemical equihbrium can be shown graphically. Figure 3.2 illustrates what happens to the Gibbs free energy G when the solute is partitioned between an aqueous phase in contact with an immiscible organic phase, diethyl ether in this example. The hypothetical plots of G versus the mole fraction, denoted by X, of solute i dissolved in the ether phase are superimposed for comparison. When there is no solute in the ether phase, a standard state chemical potential, can be realized. In the other extreme, when 100% of all of the mass of solute is in the ether phase... 

Introduction To begin, let us consider as a typical example the change with temperature in the chemical potential of table salt /t(NaCl) (Fig. 5.1). For comparison, the graphic also shows the temperature dependence of the chemical drive of table salt to decompose into the elements j (NaCl —> Na + 2 2)-... 

Fig. 13.5 The (average) chemical potential as a function of the composition of a heterogeneous mixture (solid line) (For comparison, the dotted curve for a homogeneous mixture is also included in the graphic.).

To make comparisons with the above salt effects, however, accurate values of An from acid-base titrations and correction of concentrations to activities should be considered. At this time, however, several different graphical representations of relative efficiencies are possible. These include comparison of the relative effectiveness of changes in chemical potential, Ap, to drive T, from just above to below the operating temperature, comparison of the relative ApAn areas determined from acid-base titration curves, and comparison of the significance of different degrees of positive cooperativity, that is, the impact of changes in the Hill coefficient. 

The interpretation problems outlined previously and the so far unexplained effects of particle size, make comparisons of the performance of various potential flame retardant fillers reported in the literature very questionable. This is graphically illustrated by the case of MCS referred to earlier (Section 6.4.2). 

A simple graphics program for PC compatibles (CGA, VGA, and Hercules graphics) is provided for the simultaneous examination of two data sets. It is intended primarily for comparison of experimental and simulated data. The input is quite simple initial potential, final potential (V), current scale ( A), and the names of the two data files are requested. Default values are provided. If only one data file is to be examined, a blank file named tdata.pas should be created. Movement of a crosshair cursor is controlled with the arrow keys, and potential-current values are displayed at the top of the screen. A sample CVGRAF display is shown in Figures 5-4. 

This chapter is intended to provide a unified view of selected aspects of the physical, chemical, and biological properties of the actinide elements. The f block elements have many unique features, and a comparison of the lanthanide and actinide transition series provides valuable insights into the properties of both. Comparative data are presented on the electronic configurations, oxidation states, redox potentials, thermochemical data, crystal structures, and ionic radii of the actinide elements, together with a miscellany of topics related to their environmental and health aspects. Much of this material is assembled in tabular and graphical form to facilitate rapid access. Many of the topics covered in this chapter, and some that are not discussed here, are the subjects of subsequent chapters of this work, and these may be consulted for more comprehensive treatments. This chapter provides a welcome opportunity to discuss the biological and environmental aspects of the actinide elements, subjects that were barely mentioned in the first edition of this work but have assumed great importance in recent times. 

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