Order relative

Symbols show the variations of bond order relative to unsubstituted thiazole — AfJ<... 

Ckimpounds Rate constants of pseudo first order Relative rate... 

Fiery1 252-254) studied only the last stage of the reactions, i.e. when the concentration of reactive end groups has been greatly decreased and when the dielectric properties of the medium (ester or polyester) no longer change with conversion. Under these conditions, he showed that the overall reaction order relative to various model esterifications and polyesterifications is 3. As a general rule, it is accepted that the order with respect to acid is two which means that the add behaves both as reactant and as catalyst. However, the only way to determine experimentally reaction orders with respect to add and alcohol would be to carry out kinetic studies on non-stoichiometric systems. 

Kemkes256 assumes that the overall order relative to the esterification of terephthalic acid by 1,2-ethanediol in oligo(l,2-ethanediyl terephthalate) is two no mechanism has however been suggested. Mares257 considers that during the esterification of terephthalic acid with 1,2-ethanediol, two parallel kinetic paths take place, one corresponding to a reaction catalyzed by non-dissociated add and the other to a non-catalyzed process. In fact, Mares257 is reserved about the existence of protonic catalysis. Some other orders were found for the system terephthalic atid/l,2-ethanediol 0 (overall)318 2 (add) andO (alcohol)203 1 (add) and 1 (alcohol)181 1 (add)194 . These contradictory results could be partly due to the low solubility of terephthalic acid in 1,2-ethanediol. 

If an order of n with respect to total add is obtained experimentally, it is out of the question to consider it as an nth order relative to free add. Unfortunately, this assumption has been made and it can be said that relative studies are a priori erroneous. 

Studying the reaction of carboxylic oligoesters with monohydric alcohols, Sorokina and Barshtein2231 found the reaction orders 1 and 0.5 with respect to acid and alcohol. However, they did not determine the reaction order relative to catalyst. According to these authors, the most important steps are ... 

The oxidations of toluene, diphenylmethane and triphenylmethane are second order , relative rates at 22 °C being... 

The kinetics of the reaction was measured by NMR studies and the reaction was found to be first order relative to borane-dimethyl sulfide and to the substrate (Figure 5.3). This result was consistent with a bimolecular reaction in the rate-limiting step. 

The order of the reaction, n, can be defined as n = a + b. Extended to the general case, the order of a reaction is the numerical sum of the exponents of the concentration terms in the rate expression. Thus if a = b = 1, the reaction just described is said to be second-order overall, first-order relative to A, and first-order relative to B. In principle, the numerical value of a or b can be integral or fractional. 

A note is in order relative to the exit loss coefficient, which is listed in Table 7-5 as equal to 1.0. Actually, if the fluid exits the pipe into unconfined space, the loss coefficient is zero, because the velocity of a fluid exiting the pipe (in a free jet) is the same as that of the fluid inside the pipe (and the... 

The next column reports the mean residue level found in conventional samples and the last column shows the ratio of the residue level in the organic sample compared to the mean of the residues in conventional samples. Residues in this table are ranked in descending order relative to this last column. Any value over about 0.5 in this last column suggests mislabeling, since the residue level in the organic sample was no less than one-half the mean level in all-positive conventional samples. Half to two-thirds of the residues in Table 14.5 are likely reflect mislabeling, while perhaps one-third are likely to be cases of inadvertent drift or cross-contamination. 

Formate First order Relative site Relative rate Relative rate based... 

The molecular transport term vV2(m m ) is closed, but negligible (order ReL 1) in high-Reynolds-number turbulent flows. The production term... 

Equation (5.46) shows a further difference relative to Eq. (5.34). Equation (5.46) indicates a zero reaction order relative to [BH] in the forward extraction rate, reflecting the complete saturation of the interface with the extracting reagent. 

The Pariser-Parr-Pople semiempirical method has been applied to dibenzothiophene to predict bond orders, relative electro-... 

In this section we examine the higher orders beyond the linear noise approximation. They add terms to the fluctuations that are of order relative to the macroscopic quantities, i.e., of the order of a single particle. They also modify the macroscopic equation by terms of that same order, as has been anticipated in (V.8.12) and (4.8). These effects are obviously unimportant for most practical noise problems, but cannot be ignored in two cases. First, they tell us how equilibrium fluctuations are affected by the presence of nonlinear terms in the macroscopic equation, in particular how... 

The last two terms in U can be used as a reference energy—the total internal energy of a system of composition XB that is divided into pure A and pure B portions. The change in internal energy due to mixing and ordering relative to this reference state is... 

The quality of the information potentially available through x-ray diffraction depends on the degree or extent of order of the protein molecules in a given sample. A sample under investigation usually consists of a hydrated purified protein. If the individual protein molecules are packed in a random order relative to one another, the distances between atoms or groups of atoms can be derived, but we cannot tell how these spacings are ordered in three dimensions. 

Refs 51, 53 58) reviewed the data of Warren gt oi (Ref 37) and observed that a few nonrigid generalizations could be made. Although the materials can be ordered relative to decompn. a variation in kinetics as shown by the calcns for the activation energies and temp coefficients of evaluation as follows ... 

As the reader can see, a rule bears a close resemblance to an if-then-else statement, but unlike an if-then-else statement, it stands alone and does not fire in any predetermined order relative to other if-then-else statements. 

The bulk of our knowledge regarding thermal oxidation has been derived from studies with model systems of fatty acids and their derivatives, or with individual natural oils (2,3,6,12,13,14,15,16). However, in biological systems as complex as food, lipids usually exist in a complicated environment markedly different from that of the single phase model system. In cell membranes, for example, the lipid molecules are highly ordered, relatively restricted in distance and mobility, and closely associated with different neighboring molecules, e.g., other lipids, protein, cholesterol, water, pro- and antioxidants. What influence does such an environment have on the oxidation of the lipids at elevated temperature Even in less organized systems, e.g., depot fat from animal or plant, the lipids... 

Interpretation of two-dimensional images of sheet silicates has previously been addressed. Computer-simulated images of chlorite (22) and biotite and muscovite (2A) show that two-dimensional images of these sheet silicates allow determination of the basal spacing (spacing perpendicular to the sheets) and stacking order (relative rotations and shifts between sheets). Furthermore, these calculations show that at the Scherzer (optimum) focus, many, but not all, aspects of the structures may be interpreted directly. 

Bead biochips are characterized by a non-ordered relative position of each bead. The microspheres are in this case used to increase the specific surface of the support and to facilitate either the immobilization chemistry or the handling of the DNA probes. 

We will not concern ourselves here with the attempt to discern a true definition of aromaticity, nor with the largely unproductive " desire to rank-order relative aromaticity. Rather, we will focus on how computational chemistry has been used to help define two of the criteria of aromaticity. We will discuss how to compute the stabilization energy of an aromatic species and then how we can compute magnetic properties that can be related to aromaticity. We will then conclude with a discussion of how these measures have been employed to investigate the nature of annulenes and the MiUs-Nixon effect. 

---