Hypothetical imagination

How can this trend in half-cell potentials and oxidizing abilities be explained Let us imagine that reaction (7), as an example, is carried out in a hypothetical series of... 

Figure Cl shows a hypothetical set of data before mean centering. Figure C2 shows the same data set after mean centering. We can imagine that this is a plot of the y data (let s call them concentration values) for a two component system. For each of the 15 samples in the data set, we plot the concentration of the first component along the x-axis and the concentration of the second...

This has just the A 2P form to which the earlier equations apply. Consider for a moment a hypothetical experiment (we shall shortly see the real one). Imagine that the dimer (= A), initially present alone, equilibrates in toluene, the reaction being followed by the increase of absorbance as Ph3C forms. 

In the second hypothetical step, we imagine the gaseous ions plunging into water and forming the final solution. The molar enthalpy of this step is called the enthalpy of hydration, AHhvd, of the compound (Table 8.7). Enthalpies of hydration are negative and comparable in value to the lattice enthalpies of the compounds. For sodium chloride, for instance, the enthalpy of hydration, the molar enthalpy change for the process... 

So each bond has a bond order of 1.5, which is consistent with the observed bond length. These two resonance structures are often called Kekule structures because they were first proposed in 1865 by Kekule, who imagined that the molecule converted very rapidly from one form to the other. This, however, is not the case the molecule never has either of the Kekule structures but only a single structure, which is intermediate between these two hypothetical structures and is approximately represented as follows ... 

The stated preference method is a direct approach and is used in order to value both use values and non-use values by using a hypothetical market. The choice experiment (CE) and the contingent valuation (CV) methods are the two most common examples of stated preference methods. In the CE method the respondents are asked to choose a level of environmental quality from a set of varying environmental qualities, called choice set. In the CV method the respondent is asked to imagine an environmental market situation and is then asked how she would act in that given situation. CE and CV attempts to find the WTP for a good or service by asking individuals direct questions about their preferences. Alternatively, researchers can ask the respondents for their WTA. 

Turning to macromolecular inorganic compounds, say ZnS, the two hypothetical ionic extremes are Zn2+S2- and Zn6-S6+ (an inverted, unusual formulation). We can imagine a continuous array of possible electron distributions between these extreme limits, one of which is the electron-pair covalent bonding state. The association of covalency with = Ay in Eqn. III.3 warrants non-polar formal MOs. However, a different situation arises when electrons are permitted to enter the empty MO skeleton. The electron-pair "covalent state corresponds to... 

To explain the Green function method for the formulation of Dx, D and D, of the fuzzy cylinder [19], we first consider the transverse diffusion process of a test fuzzy cylinder in the solution. As in the case of rodlike polymers [107], we imagine two hypothetical planes which are perpendicular to the axis of the cylinder and touch the bases of the cylinder (see Fig. 15a). The two planes move and rotate as the cylinder moves longitudinally and rotationally. Thus, we can consider the motion of the cylinder to be restricted to transverse diffusion inside the laminar region between the two planes. When some other fuzzy cylinders enter this laminar region, they may hinder the transverse diffusion of the test cylinder. When the test fuzzy cylinder and the portions of such other cylinders are projected onto one of the hypothetical planes, the transverse diffusion process of the test cylinder appears as a two-dimensional translational diffusion of a circle (the projection of the test cylinder) hindered by ribbon-like obstacles (cf. Fig. 15a). 

The rotational diffusion coefficient of the fuzzy cylinder can be formulated in a similar way. For the rotational diffusion process, it is convenient to imagine a hypothetical sphere which has the diameter equal to Lc, just encloses the test fuzzy cylinder, and moves with the translation of the fuzzy cylinder. If the test cylinder and the portions of surrounding fuzzy cylinders entering the sphere are projected onto the spherical surface as depicted in Fig. 15b (cf. [108]), the rotational diffusion process of the test cylinder can be treated as the translational diffusion process of a circle on the hypothetical spherical surface with ribbon-like obstacles. 

TTf course, this is a hypothetical state, but easy to imagine. It is necessary to have it stationary otherwise it would have translational entropy. The condition at infinity means that the electron in its reference state is too far away from anything to experience an energy of interaction. 

Why do we use the terms acid and base in this context Recall from Section J that acids and bases are normally discussed in terms of the behavior of a hydrogen ion, H+ (a proton), and that, in water, an acid such as HC1 donates its proton to a neighboring water molecule. We could imagine this reaction as taking place in two hypothetical steps first, an HC1 molecule releases a hydrogen ion as soon as it dissolves in water and then that hydrogen ion immediately bonds to a neighboring water molecule. The second step is... 

To understand the values in Table 8.6, we can think of dissolving as a two-step process (Fig. 8.23). In the first hypothetical step, we imagine the ions separating from the solid to form a gas of ions. The change in enthalpy accompanying this highly endothermic step is the lattice enthalpy, AHL, of the solid, which was introduced in Section 6.20 (see Table 6.3 for values). The lattice enthalpy of sodium chloride (787 kj-mol-1), for instance, is the molar enthalpy change for the process... 

Near a critical point, the parent p coexists with another phase that is only slightly different if, as we assume here, the free energy function is smooth, these two phases are separated—in p-space—by a hypothetical phase which has the same chemical potentials but is (locally) thermodynamically unstable. [This is geometrically obvious even in high dimensions between any two minima of f p)—p p, at given p, there must lie a maximum or a saddle point, which is the required unstable phase. ] Now imagine connecting these three phases by a smooth curve in density space p(e). At the critical point, all three phases collapse, and the variation of the chemical potential around p e = 0) = p must therefore obey... 

The actual reaction of sodium with chlorine occurs all at once rather than in a stepwise manner, but energy calculations can be made more easily if we imagine a series of hypothetical steps for which experimentally measured energy values can be obtained. There are five contributions that must be taken into account to calculate the overall energy change during the formation of solid NaCI from solid sodium metal and gaseous chlorine molecules ... 

Imagine a hypothetical process where biomass is transformed to CO and H2, by partial combustion. Assume that biomass is denoted by (CH20), and use the standard exergy value of 480kJ/mol for biomass. Assume that the standard exergy of C02 is 20, CO is 275, and H2 is 236 kj/mol. Assume that the dominant set of reactions can be simplified to... 

To better appreciate 102(g) and the possibilities presented by some different scenarios, let s consider a hypothetical example. Imagine that two chemists working... 

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