The compensation effect

The compensation effect occurs in a group of related reactions for which the influence of changes in A on reaction rate is offset to a greater or lesser extent by a sympathetic variation in E, often expressed as [36] 

Zsako [519] accepts certain points in Gam s reappraisal of compensation behaviour but stresses that the existence of a linear relation between log A and E is a more general characteristic. Thus, while a physical interpretation for obedience to eqn. (21) cannot at present be provided, the relationship provides parameters which are useful in describing the reactivities of groups of related rate processes. 

There have been several reviews of literature reports of compensation behaviour [36,521,522]. The observations made are relevant in the present context since kinetic characteristics of surface processes may be applicable also to changes proceeding at a solid—solid interface (i.e., two surfaces). Some of the explanations proposed for compensation behaviour (discussed in greater detail, with citations, in ref. 36) are that 

The possibility that compensation effects arise as a result of surface 

A and E refer to the desorption, dissociation, decomposition or other surface reactions by which the reactant or reactants represented by M are converted into products. If [M] is constant within the temperature interval studied, then the values of A and E measured refer to this process. Alternatively, if the effective magnitude of [M] varies with temperature, the apparent Arrhenius parameters do not specifically refer to the product evolution step. This is demonstrated quantitatively by the following example [36]. When E = 100 kJmole-1 andA [M] = 3.2 X 1030 molecules sec-1, then rate coefficients at 400 and 500 K are 2.4 X 1017 and 1.0 X 1020 molecules sec-1, respectively. If, however, E is again 100 kJ mole-1 and A [M] varies between 3.2 X 1030 molecules sec-1 at 500 K and z X 3.2 X 1030 molecules sec-1 at 400 K, the measured values of A and E vary significantly, as shown in Fig. 7, when z ranges from 10-3 to 103. Thus, the measured value of E is not necessarily identifiable with the rate-limiting step if a concentration of a participant is temperature-dependent. This 

Removal of the proton produces a negative charge in the position trans to where the Cl- leaves, which enhances the process by a trans effect (see Section 20.9). After the dissociation of Cl- from the transition state, the reaction with H20 is rapid. A proton from H20 replaces the one that was lost from the central nitrogen atom, and the remaining OH- completes the coordination sphere of the Pd2+. 

Although it is AG that determines the concentration of the transition state and hence the rate of a reaction, it is possible that reactions can proceed at considerably different rates even though the AG values are essentially the same. This situation can arise because AG is made up of contributions from both AH and AS, as illustrated by the equation 

The relationship between AH and AS shown in the graph is satisfactory considering that the nature of the ligands varies widely. Ligand substitution in this case follows a mechanism in which there is loss of OTP followed by X- entering the coordination sphere of the metal. The fact that the graph is linear is considered to be indicative of a common mechanism for all of the substitution reactions. 

For simplicity we assumed that the transition states are charged. However, it is not necessary to do so because the only requirement is that the difference in entropy of forming the transition states be offset by the difference in enthalpy of activation. The transition states could have different polarities and the same result be obtained. In fact, the transition states need not have high polarity. Forming a transition state in which there is a reduction in charge separation could result in more favorable solvation when the solvent is nonpolar. For there to be an isokinetic relationship for a series of reactions, it is required only that AH and AS be related in such a way that AG be approximately constant. 

When a series of reactions involving similar reactants (e.g., a series of substituted molecules having different substituents in a particular position) is studied, it is possible to find that AG may show Htde variation for the series. This may be indicative of there being a relationship of the Hammett or Taft type. However, another explanation that is appropriate in some cases is the so-called compensation effect. 

Therefore, if Ah is more negative than AHj and As is more n ative than ASj, it is possible that AG may be approximately constant for the two cases. For a series of reactions, we might find that 

Although we have interpreted the compensation effect in terms of transition states having different charges, there is no reason that transition states having different polarities could not behave similarly when the solvent is polar. Also, if a reduction in charge separation occurs as the transition state forms and the solvent is nonpolar, more favorable solvation 

FIGURE 5.5 An isokinetic plot for the formation of [Cr(H20)5X] by replacement of OH . (Constructed from the data given in D. Thusius, Inorg. Chem., 1971, 10, 1106.) 

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The relationship of thermodynamic functions of selective bonding of Hb to a series of carboxylic CP in the variation of the degree of ionization of carboxylic groups is expressed by the effect of enthalpy-entropy compensation (Fig. 18). The compensation effect of enthalpy and entropy components is the most wide-spread characteristic of many reactions in aqueous solutions for systems with a cooperative change in structure [78],... 

G. Parravano and M. Boudart The Compensation Effect in Heterogeneous Catalysis E. Cremer... 

Figure 8.75 shows the dependence of the apparent activation energy Ea and of the apparent preexponential factor r°, here expressed as TOF°, on Uwr. Interestingly, increasing Uwr increases not only the catalytic rate, but also the apparent activation energy Ea from 0.3 eV (UWr=-2 V) to 0.9 eV (UWr-+2V). The linear variation in Ea and log (TOF°) with UWr leads to the appearance of the compensation effect where, in the present case, the isokinetic point (T =300°C) lies outside the temperature range of the investigation. 

For catalytic reactions and systems that are related through Sabatier-type relations based on kinetic relationships as expressed by Eqs. (1.5) and (1.6), one can also deduce that a so-called compensation effect exists. According to the compensation effect there is a linear relation between the change in the apparent activation energy of a reaction and the logarithm of its corresponding pre-exponent in the Arrhenius reaction rate expression. 

The occurrence of a compensation effect can be readily deduced from Eqs. (1.6) and (1.7). The physical basis of the compensation effect is similar to that of the Sabatier volcano curve. When reaction conditions or catalytic reactivity of a surface changes, the surface coverage of the catalyst is modified. This change in surface coverage changes the rate through change in the reaction order of a reaction. 

A consequence of the compensation effect is the presence of an isokinetic temperature. For a particular reaction, the logarithm of the rate of a reaction measured at different conditions versus 1/T should cross at the same (isokinetic) temperature. For conditions with varying n, this isokinetic temperature easily follows from Eq. (1.19) and is given by... 

It is important to realize that the compensation effect in catalysis refers to the overall catalytic reactions. 

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. 

Figure 7.8. The compensation effect in the desorption ofAg from a ruthenium surface activation energy and pre-exponential factor depend in the same way on coverage. The...

Such behavior is known as the compensation effecf . The important point is that if we ignore the additional term in Eq. (18), we essentially force the kinetic parameters to satisfy Eq. (19) resulting in a correlation between the prefactor and the desorption energy according to the compensation effect ... 

The time delay is removed. With the delay compensator included, we can now use a larger proportional gain without going unstable. Going back to the fact that the feedback information is GCGR, we can also interpret the compensator effect... 

To see the compensation effect by the pair of PIPs, the interaction exerted on the 13C spins needs to be known. For a 13C peak with an offset <5, the Hamiltonian of the system can be expressed as... 

The compensating effect becomes quite poor when the order of the two PIPs is changed (Fig. 22d). The distorted excitation prohle can be corrected if an inherited phase

phase coherence in PIPs. 

The downward force from the overpressure on the roof is applied simultaneously with the horizontal force from the peak reflected pressure on the front wall, However, the compensating effects of blast forces acting on the rear wall may be conservatively neglected. 

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... 

L. S. Shvindlerman, G. Gottstein, The compensation effect in thermally activated interface processes, to be published. 

The correlation between activation energy and preexponential factor is known as the compensation effect. 

There are a number of possible explanations for the compensation effect ... 

The most interesting case is when the compensation effect is caused by differences in the transition state. In this case the compensation effect is a real physical effect. 

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