In depictions

Higher alkanes having unbranched carbon chains are like butane most stable m then-all anti conformations The energy difference between gauche and anti conformations is similar to that of butane and appreciable quantities of the gauche conformation are pres ent m liquid alkanes at 25°C In depicting the conformations of higher alkanes it is often more helpful to look at them from the side rather than end on as m a Newman projec tion Viewed from this perspective the most stable conformations of pentane and hexane... 

It is not possible to draw unambiguous Lewis structures for excited states of the sort that are so useful in depicting ground-state chemistry. Instead, it is common to asterisk the normal carbonyl structure and provide information about the nature and multiplicity of the excited state ... 

Note. These representations do not follow the recommendations for choice of main chain given in 2-Carb-37.3. Such deviations are common in depicting series of naturally occurring oligosaccharides where it is desirable to show homomorphic relationships. 

In chemical kinetics, one finds linked sets of differential equations expressing the rates of change of the interacting species. Overall, mathematical models have been exceedingly successfiil in depicting the broad outlines of an enormously diverse variety of phenomena in nature. Some scientists have even commented in surprise at how well mathematics works in describing nature. So successful have these mathematical models been that their use has spread from the hard sciences to areas as diverse as economics and the analysis of athletic performance [3]. 

Fig. 2.1-5. Formal description of the bonding in polyboranes, and various representations used in depicting formulae.

Fig. 10. Representative power Doppler US images from (A) tumors in the control group, (B) tumors treated with TNF, (C) tumors treated with radiation therapy, and (D) tumors receiving combined TNF and radiation therapy. Depicted blood vessels are greatest in the periphery of the tumors (arrowheads in A). Treatment with radiation alone or TNF alone results in a decrease in depicted blood vessels. Combined therapy results in a greater decrease in depicted blood vessels.

Haworth structures are easy to draw and unambiguous in depicting configurations,14 but they also do not show the spatial relationships of groups attached to other rings correctly. For this reason conformational formulas of the type described in Section 2 and shown in Fig. 4-4 are used most often in this book. 

Loss of the a-hydrogen (Group a). Dissociation of the a-hydrogen from the Schiff base leads to a quinonoid-carbanionic intermediate whose structure in depicted in Fig. 14-5. The name reflects the characteristics of the two resonance forms drawn. 

The three tartaric acids may be used to illustrate the method employed in depicting three-dimensional molecules in two-dimension projections. 

Haworth structures are unambiguous in depicting configurations, but even they do not show the true spatial relationship of groups attached to rings. The normal angle between the bonds formed by the saturated carbon atoms (109°) causes the pyranose molecule to pucker into either a chairlike or boatlike conformation. For glucose and most other pyranoses the chair form (fig. 12.6c) predominates. However, we usually display pyranoses by the Haworth projection because it is easier to draw. 

Fig. 2.16. Arrangement of the donor atoms in the equatorial plane of copper and of the copper dx2 v2 and sulfur p orbitals (A). The dihedral angle 0 between the Cu-S-C plane and one of the S-C-H planes in depicted in B [113].

Finally in this chapter, we consider the use of arrows (as opposed to straight lines) to denote coordinate (or dative) bonds in depicting the structures of coordination/organometallic compounds. The complex Be(NH3)2Cl2 could be represented by any of (i), (ii) or (iii) ... 

Steady state heat transfer refers to the condition where the rate of heat flowing into one face of an object is equal to that flowing out of the other. If, for example, a slab of metal were placed on a hot-plate, the heat flowing into the metal would initially contribute to a temperature rise in the material, until ultimately a linear temperature gradient formed between the hot and cold faces, wherein heat flowing in would equal heat flowing out and steady state heat transfer would be established. The time involved before steady state conditions axe encountered is dependent on the thermal requirements, that is, the total heat capacity of the material. A useful constant, therefore, in depicting transient, or non-steady state heat transfer is the thermal diffusivity ... 

Although space in depictions has long been used to convey concrete ideas, the use of space to convey abstract ideas is more recent. Early uses of space in depictions for the most part portrayed things that were inherently visualizable, such as objects, buildings, or environments, in picto-graphs, architectural plans, or maps. Maps appear in many forms, many taking liberty with spatial metrics, such as the T-0 maps popular in... 

Although both atomic orbitals and molecular orbitals are one-electron wave functions, the shape and symmetry of the molecular orbitals are different from those of the atomic orbitals of the isolated atom. The molecular orbitals extend over the entire molecule, and their spatial symmetry must conform to that of the molecular framework. Of course, the electron distribution is not uniform throughout the molecular orbital. In depicting these orbitals, usually only the portions with substantial electron density are emphasized. 

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