Rearrangement defined

It is unusual for a Dimroth rearrangement (defined in Section III,D) to occur during formylation, but the following example is cautionary. 5-Aminomethyl-3-benzyl-4-methylaminotriazole and acetic formic anhydride, stirred in pyridine, gave 4-benzylamino-5-formamidomethyl-3-methyltriazole (23°C, 15 hr, 84%). Most likely, the use of pyridine determined this outcome [81JCS(P1)2344]. 

Two possible rearrangement pathways have been proposed for the rearrangement from the pentagonal bipyramid to the capped trigonal prism [49], one of which retains a 2-fold axis during the rearrangement, defined by the bisector of the angle formed by atoms 5,7 and the central atom, while the other retains a mirror plane, defined by atoms 1, 5 and 7. 

Rearrangement defines the "distribution coefficient ( equilibrium constant ) Kf, giving... 

The breaking of a strategic bond and the generation of synthesis precursors defines a synthesis reaction. In the simplest case, the reaction is already known from literature. In most cases, however, the rcaaion step obtained has to be generalised in order to find any similar and successfully performed reactions with a similar substituent pattern or with a similar rearrangement of bonds. One way of generalizing a reaction is to identify the reaction center and the reaction substructure of the reaction. This defines a reaction type. 

Rearranging equation 32 and defining the ratio h -a/iky-ci-Cf ) as r, the psychrometric ratio, give... 

The covalent compounds of graphite differ markedly from the crystal compounds. They are white or lightly colored electrical insulators, have Hi-defined formulas and occur in but one form, unlike the series typical of the crystal compounds. In the covalent compounds, the carbon network is deformed and the carbon atoms rearrange tetrahedraHy as in diamond. Often they are formed with explosive violence. 

Complexes involving larger metal clusters, eg, Au or Au2Rh, also undergo piezochromic rearrangements with rather dramatic changes in the absorption spectmm, and well-defined changes in molecular stmcture (6,7). 

The basic chemical description of rare events can be written in terms of a set of phenomenological equations of motion for the time dependence of the populations of the reactant and product species [6-9]. Suppose that we are interested in the dynamics of a conformational rearrangement in a small peptide. The concentration of reactant states at time t is N-n(t), and the concentration of product states is N-pU). We assume that we can define the reactants and products as distinct macrostates that are separated by a transition state dividing surface. The transition state surface is typically the location of a significant energy barrier (see Fig. 1). 

When the cake structure is composed of particles that are readily deformed or become rearranged under pressure, the resulting cake is characterized as being compressible. Those that are not readily deformed are referred to as sem-compressible, and those that deform only slightly are considered incompressible. Porosity (defined as the ratio of pore volume to the volume of cake) does not decrease with increasing pressure drop. The porosity of a compressible cake decreases under pressure, and its hydraulic resistance to the flow of the liquid phase increases with an increase in the pressure differential across the filter media. 

In practice, the scope of the benzilic rearrangement as a tool for the ring contraction of steroids is defined by the availability of a-diketones, or the corresponding diosphenols. 

From this expression, it is obvious that the rate is proportional to the concentration of A, and k is the proportionality constant, or rate constant, k has the units of (time) usually sec is a function of [A] to the first power, or, in the terminology of kinetics, v is first-order with respect to A. For an elementary reaction, the order for any reactant is given by its exponent in the rate equation. The number of molecules that must simultaneously interact is defined as the molecularity of the reaction. Thus, the simple elementary reaction of A P is a first-order reaction. Figure 14.4 portrays the course of a first-order reaction as a function of time. The rate of decay of a radioactive isotope, like or is a first-order reaction, as is an intramolecular rearrangement, such as A P. Both are unimolecular reactions (the molecularity equals 1). 

Apnular tautomerism has been defined as the class of tautomeric rearrangements in which only annular nitrogen or carbon atoms are involved [76AHC(S1), p. 266], In azoles, the latter case is frequently energetically un-... 

Sulfur and selenium analogues of 91 are also susceptible of this type of rearrangement. Its rate is defined by the strength of the C-chalcogen bonds in 91 and analogues and was found to increase in the order of S < Se < Te (94MI1). 

Defining pB as [B]/([B] + KB), substituting this into Equation 6.46, and rearranging yields... 

Defining [A ]/[A] as DR (the ratio of equiactive doses) and rearranging yield... 

Defining % as z /z and rearranging, Equation 10.34 The resulting equilibrium equations are... 

Geometrically defined a/ -epoxysilanes have been shown (6) to undergo a highly stereoselective rearrangement to silyl enol ethers (see also Chapter 15). This rearrangement is catalysed by boron trifluoride etherate, and seems to involved-opening of the epoxysilane, as shown ... 

Smith and Stirton applied this mechanism to the sulfonation of long-chain fatty acid esters [31]. Instead of forming the well-defined mixed anhydride during the reaction of fatty acids with S03, the acid esters form a complex less defined in structure and composition. In this complex the a-hydrogen is activated, so that a second molecule of S03 can react. These two addition steps are fast. The final step is again a slow rearrangement of the intermediate with a loss of one molecule of S03. 

Step 1 Calculate the amount of solute molecules, wso ule, present in a given mass of solvent, mio vent, by rearranging the equation defining molality (Eq. 3) into... 

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