Compensation effect illustration

As a further illustration of the compensation effect, we use solid-acid-catalyzed hydrocarbon activation by microporous zeolites. A classical issue in zeolite catalysis is the relationship between overall rate of a catalytic reaction and the match of shape and size between adsorbate and zeolite micropore. 

Thusius, O. (1971). Inorgo Chem. 10, 1106. A kinetic study illustrating the add compensation effect. 

It has been shown that for many of the hard-hard complexation systems, there is a linear correlation between the experimental AH° and Ab° values. Figure 3.11 shows such a correlation for actinide complexes. These AH and AS data involve metal ions in the -i-3, +A, and +6 oxidation states and a variety of both inorganic and organic ligands. Such a correlation of AH° and Ab° has been termed the compensation effect. To illustrate this effect, reconsider the... 

Fig. 2. Adjustment of fluorescence compensation. Lymphocytes stained with FITC-anti-CD8 (A-C), PE-anti-CD8 (D—F) and PECy5-anti-CD8 (G—1) were analyzed, to compensate FL1, FL2 and FL3, respectively. The effects of under- (A) and over- (B) compensation are illustrated. The compensation network is adjusted systematically to adjust for FL1 fluorescence in FL2, FL2 spilling into FL1 and FL3, and FL3 spilling into FL2.

Several compensation effects have been reported for the decomposition of formic acid on metals (231) particular interest has been shown in the silver-catalyzed reaction (19, 35, 232, 233). The available data for this rate process do not, however, define a single compensation relation, and, even for groups of closely related reactions, it is difficult to decide which of the various possible calculated lines provides the most meaningful representation of the kinetic measurements. Values of B and e, obtained from various sets of reported results, extend over a significant range and, moreover, there is an apparent tendency for an increase in the value of one of these parameters to be offset by a diminution in the other. Such behavior can, in the widest sense of the word, be described as compensatory. To illustrate the difficulties inherent in this analysis of the published data, some calculated values of B and e derived from possible alternative groups of observations are discussed here. Values of (log A, E) reported by Sosnovsky (35), for the decomposition of formic acid on silver, may be considered either as the three different lines, Table III, K, L, and M for reactions on the (111), (110), and (100) planes, respectively, or as the single line,Table III, N. These combined data (Table III, N and x on Fig. 6) intersect with the line obtained from a different set of results... 

The condition of interest is illustrated in Figure 16.6. Here the open arrows represent effects discussed in Chapter 13 these by themselves would lead to change of phase or migration of the interface through the material. But the solid arrows show a compensating effect, so that the set of processes all operating together keep the interface stationary. We consider the open arrows and then the solid arrows in turn. 

Figure 6.11 illustrates several results of this simulation. The frequency response in Fig. 6.11a shows the band rejection filter characteristic required for the compensation of the force Pi lying between about 70 Hz and 329 Hz. In Fig. 6.11b the effect of the closed-loop force compensation is illustrated within the time domain, over the time interval of Os... 0.4s. During the interval... 

A second point of interest that emerges from Table 4 is that in compounds with several cations but only one kind of anion, there is a compensating effect that makes Tq close to unity. This is illustrated in more detail for the garnets A3Al2Si30i2 ... 

Likewise when there is only one kind of cation, but very different anions, the compensation effect still appears as may be illustrated by the example of La203 already adduced ... 

Let s examine an Sn2 reaction between an amine and an alkyl halide to illustrate enthalpy-entropy compensation effects due to differential solvation (Eq. 8.67). The transition state is polar relative to the reactants, so the enthalpy of activation should be lower in increasingly polar solvents. In addition, the developing charges in the transition state will cause the solvent to be more constrained than when solvating the neutral amine or alkyl halide, and this effect will be greater with the more polar solvent. Hence, a higher polarity solvent leads to a lower AH, but also makes AS more unfavorable as a result, these are compensating effects. 

Figure 5.13. The variation of logiofc k = reaction rate constant) with activation energy for the reaction of molecular oxygen (Pq = 1.25 kPa) with non-graphitizable and graphitizable carbons, to illustrate the compensation effect which occurs in heterogeneous reactions (Marsh et al, 1981).

One of the most important parameters is the temperature, the starting temperature, and the initial reaction rate. One can determine experimentally the initial reaction rate after elimination of diffusion and mass transport effects and then determine the Arrhenius constants, which depend on the temperature. The collision factor (ko) and activation energy (E) parameters influence significantly the activity pattern and selectivity. Figure 3.1 illustrates the influence of the temperature on these parameters for different reactions and metallic catalysts. This effect is known as compensation effect, although empirically there are attempts on theoretical interpretations for different heterogeneous systems [1, 2]. 

However, this is not the case. The changes in AW and in AS show a considerable scatter when compared with AG, and there is a compensating effect between AW and AS. A substituent group that induces a strong interaction of the solute with solvent molecules and decreases AW, also decreases AS. Figure 7.7 illustrates this effect of compensation in the alkaline hydrolysis of ethyl benzoate in water/alcohol and water/dioxane mixtures [8], which can be translated by the linear relationship... 

A cocurrent evaporator train with its controls is illustrated in Fig. 8-54. The control system applies equally well to countercurrent or mixed-feed evaporators, the princip difference being the tuning of the dynamic compensator/(t), which must be done in the field to minimize the short-term effects of changes in feed flow on product quality. Solid concentration in the product is usually measured as density feedback trim is applied by the AC adjusting slope m of the density function, which is the only term related to x. This recahbrates the system whenever x must move to a new set point. 

A consequence of single-ion diffusion is that the mass movement must be compensated for by an opposing drift (relative to a fixed point deep in the metal) of the existing oxide layer if oxidation is not to be stifled by lack of one of the reactants. The effect may be illustrated by reference to a metal surface of infinite extent (Fig. 1.81). 

Although reactions in which molecules are cleaved into two or more pieces have favorable entropy effects, many potential cleavages do not take place because of large increases in enthalpy. An example is cleavage of ethane into two methyl radicals. In this case, a bond of 79 kcal mol (330 kJ mol ) is broken, and no new bond is formed to compensate for this enthalpy increase. However, ethane can be cleaved at very high temperatures, which illustrates the principle that entropy becomes more important as the temperature increases, as is obvious from the equation AG = AH — TAS. The enthalpy term is independent of temperature, while the entropy term is directly proportional to the absolute temperature. 

Figure 23.2 A schematic diagram illustrating the ways in which the CNS counters the depressant effects of a drug such as alcohol or an opioid and how this leads to the manifestation of physical dependence when there is abstinence from the drug. These excitatory compensations produce symptoms opposite to the acute effects of the drug...

In order to systematically remedy the previous drawbacks, we recently proposed to perform a perturbation treatment, not on a wavefunction built iteratively, but on a wavefunction that already contains every components needed to properly account for the the chemistry of the problem under investigation [34], In that point of view, we mean that this zeroth-order wavefunction has to be at least qualitatively correct the quantitative aspects of the problem are expected to be recovered at the perturbation level that will include the remaining correlation effects that were not taken into account in the variational process any unbalanced error compensations or non-compensations between the correlation recovered for different states is thus avoided contrary to what might happen when using any truncated CIs. In this contribution, we will report the strategy developed along these lines for the determination of accurate electronic spectra and illustrate this process on the formaldehyde molecule H2CO taken as a benchmark. 

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