Activation parameters

Activation Parameters.— Negative heats of activation have previously been reported for some outer-sphere reactions, - and it has been suggested that some special factor, not covered by the simple Marcus theory, might need to be invoked to explain them. (It will be recalled that negative heats of activation of some inner-sphere reactions have been rationalized in terms of the energetics of formation of precursor complexes.) Marcus and Sutin point out, however, that negative AH values are theoretically predicted, under certain conditions. On differentiating equation (1) with respect to temperature, they obtain 

The activation parameters for the CM-catalyzed and uncatalyzed Claisen rearrangement are listed in Table 1.2 [20, 21, 26, 42]. For the uncatalyzed reaction, the activation barrier (AG ) is 24.5 kcal/mol. Chorismate mutase is able to reduce the activation barrier by 7-10 kcal/mol. Table 1.2 shows that the rate acceleration is due to a reduction in the entropy of activation to near zero and a decrease in the enthalpy of activation by about 5 kcal/mol the only exception is the BsCM-catalyzed reaction for which there is a significant unfavorable AS. However, the reliability of these data has been called into question [44], and it was suggested [44] that both the substrate binding and product leaving are expected to show large solvent compensation effects involving AH and AS [45, 46). 

Within this section will be discussed the activation parameters (A/f, AS and AK ) that have been measured for the reactions between metal nucleophiles and carbon compounds. The values of the enthalpy and entropy of 

The solvent has a relatively large influence on the activation parameters as demonstrated in the reaction of cA-[Rhl2(CO)2] with Mel (Hickey and Maitlis, 1984). For the range of solvents, methanol, chloroform, THF and methyl acetate the values of AH progressively decrease from 16.5 to 11.2 kcalmol , and AS decreases from —22.0 to —42.1 calK mol .  

The values of the activation parameters, together with the influence of the solvent on these parameters, has been interpreted in terms of a highly linear, polar transition state (Fig. 2) (Halpern, 1970 and references therein), or a transition state containing unusually stringent stereochemical restrictions. These conclusions are further substantiated by the comparable reactivities of substituted benzyl bromides towards both /ra/i5-[IrCl(CO)(PPh3)2] and tertiary amines. 

The large negative values of AS in the reactions of the iridium(I) complexes have been rationalised in terms of increased solvation of the transition state, attributable to its increased dipole. Such a dipole results not only from the interaction of the alkyl halides with the metal centre, but also from deformation of the iridium complex from planar to pseudo-octahedral geometry as would occur in a three-centre cw-addition (Harrod and Smith, 1970). In some cases the values of AS and the influence of solvent on AH and AS have been explained in terms of a polar, asymmetric, three-centre transition state, in which the interaction of the metal is predominantly with the carbon centre (Ugo et al., 1972). 

The characteristic values of AH and AS have been taken to indicate that a nucleophilic displacement reaction is rate-limiting in a multistep reaction. For instance reaction (42) occurs in two stages, but the intermediate which is detected is too reactive to be isolated and characterised. The 

Rondestvedt and Wark studied the effect of temperature on the rate of the ene reaction of MA with 3. Activation energy was determined to be 20kcal/mole in the temperature range 127-153°C. Benn et have 

Entropy of activation is a more conclusive parameter in this case. Large negative entropy suggests a highly organized transition state. The values are similar to the concerted Diels-Alder reaction. Thus, based on kinetic and 

These conclusions are similar to those reached earlier on the ene reaction in general. It is generally recognized that the reaction is related to the Diels-Alder reaction and can be considered to be an intermolecular analogue of the symmetry-allowed 1,5-hydrogen shift. 

It may be recognized that the bonding in the transition state may be maximized differently for each reaction For the concerted ene reaction, allylic resonance and hence the stabilization is maximized by turning the axis of the C—H bond undergoing breakage parallel to the p orbital of the double bond.  

The diagram opposite which distinguishes between a transition state and an intermediate also shows the Gibbs energy of activation, AG for each step in the 2-step reaction path. Enthalpies and entropies of activation, and 

A5 obtained from temperature dependence of rate constants, can shed light on mechanisms. Equation 26.8 (the Eyring equation) gives the relationship between the rate constant, temperature and activation parameters. A linearized form of this relationship is given in equation 26.9.  

Values of AS are particularly useful in distinguishing between associative and dissociative mechanisms. A large negative value of AS is indicative of an associative mechanism, i.e. there is a decrease in entropy as the entering group associates with the starting complex. However, 

The pressure dependence of rate constants leads to a measure of the volume of activation, AV (equation 26.10). 

A reaction in which the transition state has a greater volume than the initial state shows a positive AV, whereas a negative AV corresponds to the transition state being compressed relative to the reactants. After allowing for any change in volume of the solvent (which is important if solvated ions 

The author has tried to collect in Table 9 a representative sample of Diels-Alder reactions with different types of reactants, for which the usual activation parameters could be determined with care (in most cases from kinetic runs at four or more different temperatures, in a range of at least 20°C). Other data (E and log A values) have been given in Tables 2 and 3 (pp. 93, 94) the relevant values of the activation entropy can be calculated from log A by the conversion formulae  

Gas-phase, pure liquid-phase and solution reactions, involving either electron-rich or electrophilic dienes, and dienophiles with C=C, C C or N=0 

The cyclic transition state and the one-step mechanism are also consistent with the di-stereospecificity of the reaction (Section 4.1.1), the small medium effects (Section 4.1.2) and the observations concerning substituent effects (Section 4.1.3). 

However a typical Diels-Alder reaction, the butadiene dimerisation (Table 3, p. 94), and its reversal (case (g) in Table 10) have been recently considered by Benson - as examples of two-step processes. The initial argument is that 1,5-cyclooctadiene, when pyrolysed in the gas phase, gives 4-vinylcyclohexene as the main product but also a small amount of butadiene, which cannot be produced from 4-vinylcyclohexene under the conditions of the experiments. A kinetic and thermochemical analysis shows that the ds-ds-l,7-octadiene-3,6-diyl biradical (singlet) could be the common precursor of 4-vinylcyclohexene 

ENERGY AND ENTROPY OF ACTIVATION OF REVERSE DIELS-ALDER REACTIONS 

An intermediate occurs at a local energy minimum it can be detected and, sometimes, isolated. A transition state occurs at an energy maximum, and cannot be isolated. 

In most metal complex substitution pathways, bond formation between the metal and entering group is thought to be concurrent with bond cleavage between the metal and leaving group (equation 25.5). This is the interchange (I) mechanism. 

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Because of these difficulties, special mechanisms were proposed for the 4-nitrations of 2,6-lutidine i-oxide and quinoline i-oxide, and for the nitration of the weakly basic anilines.However, recent remeasurements of the temperature coefficient of Hq, and use of the new values in the above calculations reconciles experimental and calculated activation parameters and so removes difficulties in the way of accepting the mechanisms of nitration as involving the very small equilibrium concentrations of the free bases. Despite this resolution of the difficulty some problems about these reactions do remain, especially when the very short life times of the molecules of unprotonated amines in nitration solutions are considered... 

For the nitration of the very weak base, acetophenone, there is reasonable agreement between observed and calculated activation parameters, and there is no doubt that nitration of the free base occurs at acidities below that of maximum rate. In this case the equilibrium concentration of free base is much greater than in the examples just discussed and there is no question of reaction upon encounter. ... 

For this series of compounds qualitative information is quite extensive. Application of the criteria discussed in 8.2, in particular comparison with the corresponding methyl quaternary salt, establishment of the rate profile for nitration in sulphuric acid, and consideration of the encounter rate and activation parameters, shows that 2,4,6-collidine is nitrated as its cation. The same is true for the 3-nitration of 2,4- ... 

Activation energy Activation of cellulose Activation parameters Activation volume Activators... 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

The activation parameters for an initiator can be deterrnined at normal atmospheric pressure by plotting In vs 1/T using initiator decomposition rates obtained in dilute solution (0.2 M or lower) at several temperatures. Rate data from dilute solutions are requited in order to avoid higher order reactions such as induced decompositions. The intercept for the resulting straight line is In and the slope of the line is —E jR therefore both and E can be calculated. 

The Activity Parameter. Another measure (a) of plasticizer activity that is an extension of and based on earlier work gives an iadication of the ease of processiag for a givea plasticizer with a givea resia, but does aot give estimates of plasticizing performance ia the fiaal product (12). M and y are as previously defiaed. 

Hydrolysis of dialkyl sulfites under acidic and alkaline conditions, which is followed by the use of OH2, proceeds by attack at sulfur to give S—O cleavage (72). The rate of hydrolysis is generally faster for cycHc and aryl sulfites than for dialkyl sulfites (73). Activation parameters of hydrolysis are known for some sulfites, and the increased rate for ethylene sulfite results from a reduced entropy of activation which results from a rigid ring stmcture (74). 

Table 4. Water Exchange Rates and Activation Parameters of Hexaaqua Complexes at 25°C, ...

The influence of temperature, acidity and substituents on hydrolysis rate was investigated with simple alkyldiaziridines (62CB1759). The reaction follows first order kinetics. Rate constants and activation parameters are included in Table 2. 

Table 2 Rate Constants and Activation Parameters of Diaziridine Hydrolysis...

The reaction is about 50% faster in ethoxyethanol than in decane. Calculate the activation parameters at 150°C. Although precisely comparable data are not available, for the gas-phase isomerization of norbomadiene is 50kcal/mol. Draw a sketch... 

Z7. The cotr arison of activation parameters for reactions in two different solvents requires consideration of differences in solvation of both the reactants and the transition states. This can be done using a potential energy diagram such as that illustrated below, where A and B refer to two different solvents. By thermodynamic methods, it is possible to establish values which correspond to the enthalpy... 

Table 5.P27B. Activation Parameters for Nucleophile-Hexyl Tosylate Reactions...

An interpretation of activation parameters has led to the conclusion that the bromination transition state resembles a three-membered ring, even in the case of alkenes that eventually react via open carbocation intermediates. It was foimd that for cis trans pairs of alkenes tiie difference in enthalpy at the transition state for bromination was greater than the enthalpy difference for the isomeric alkenes, as shown in Fig. 6.2. This... 

Whereas Freeman and Lewis reported the first comprehensive analysis of hydroxymethylation of phenol, they were not the last to study this system. A number of reports issued since their work have confirmed the general trends that they discovered while differing in some of the relative rates observed [80,84-99], Gardziella et al. have summarized a number of these reports ([18], pp. 29-35). In addition to providing new data under a variety of conditions, the other studies have improved on the accuracy of Freeman and Lewis, provided activation parameters, and added new methodologies for measuring product development [97-99],... 

Fig. 9. Activation parameters for resole methylolation in the presence of NaOH in concentrated solutions [80,90].

Eyring activation parameters for NaOH-catalyzed methylolation in relatively concentrated aqueous solutions... 

The evaluation of the activation parameters AG, A//, and AS proceeds as follows. From the Arrhenius equation, Eq. (5-1), we have... 

The values of A and E provide a full description of the kinetic data, but it may be desirable, for mechanistic interpretation, to express the results in terms of the activation parameters A// and A5. We developed equations in Section 5.2 for this purpose for convenience these are repeated here ... 

Kinetic studies at several temperatures followed by application of the Arrhenius equation as described constitutes the usual procedure for the measurement of activation parameters, but other methods have been described. Bunce et al. eliminate the rate constant between the Arrhenius equation and the integrated rate equation, obtaining an equation relating concentration to time and temperature. This is analyzed by nonlinear regression to extract the activation energy. Another approach is to program temperature as a function of time and to analyze the concentration-time data for the activation energy. This nonisothermal method is attractive because it is efficient, but its use is not widespread. ... 

Usually the Arrhenius plot of In k vs. IIT is linear, or at any rate there is usually no sound basis for coneluding that it is not linear. This behavior is consistent with the conclusion that the activation parameters are constants, independent of temperature, over the experimental temperature range. For some reactions, however, definite curvature is detectable in Arrhenius plots. There seem to be three possible reasons for this curvature. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

We can make two different uses of the activation parameters AH and A5 (or, equivalently, E and A). One of these uses is a very practical one, namely, the use of the Arrhenius equation as a guide for interpolation or extrapolation of rate constants. For this purpose, rate data are sometimes stored in the form of the Arrhenius equation. For example, the data of Table 6-1 may be represented (see Table 6-2) as... 

The second use of activation parameters is as criteria for mechanistic interpretation. In this application the activation parameters of a single reaction are, by themselves, of little use such quantities acquire meaning primarily by comparison with other values. Thus, the trend of activation parameters in a reaction series may be suggestive. For example, many linear correlations have been reported between AT/ and A5 within a reaction series such behavior is called an isokinetic relationship, and its significance is discussed in Chapter 7. In Section 5.3 we commented on the use of AS to determine the molecularity of a reaction. Carpenter has described examples of mechanistic deductions from activation parameters of organic reactions. 

The dependence of the rate constant on pressure provides another activation parameter of mechanistic utility. From thermodynamics we have (dGldP)T = V, where V is the molar volume (partial molar volume in solutions). We define the free energy of activation by AG = G — SGr. where SGr is the sum of the molar free energies of the reactants. Thus, we obtain... 

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