Rate constant thermodynamic analogy

Various /-alkoxy radicals may be formed by processes analogous to those described for /-butoxy radicals. The data available suggest that their propensities for addition vs abstraction are similar.72 However, rate constants for [3-scission of /-alkoxy radicals show marked dependence on the nature of substituents a to oxygen (Figure 3.6).210 420,421 Polar, steric and thermodynamic factors are all thought to play a part in favoring this trend.393... 

The reverse rate constant, of course, can also depend on temperature, and can be specified in a three-parameter modified Arrhenius form analogous to Eq. 9.83. However, the reverse rate constant may also be specified from the reaction thermodynamics. If reaction i were at equilibrium, the forward and reverse rates of progress would be equal, so qt would be 0, and from Eq. 9.73,... 

The reason that the minor reactive intermediate leads to the major product is due to the large rate constant for hydrogenation (k ) associated with the S cycle compared to the R cycle. Clearly, the conventional lock and key analogy for the origin of enantioselectivity does not apply for this case since the selectivity is determined by kinetics of hydrogenation instead of thermodynamics of olefin binding. 

Figure 2.12 illustrates schematically the essential features of the thermodynamic formulation of ACT. If it were possible to evaluate A5 ° and A// ° from a knowledge of the properties of aqueous and surface species, the elementary bimolecular rate constant could be calculated. At present, this possibility has been realized for only a limited group of reactions, for example, certain (outer-sphere) electron transfers between ions in solution. The ACT framework finds wide use in interpreting experimental bimolecular rate constants for elementary solution reactions and for correlating, and sometimes interpolating, rate constants within families of related reactions. It is noted that a parallel development for unimolecular elementary reactions yields an expression for k analogous to equation 128, with appropriate AS °. 

By analogy with the thermodynamic treatment of the solute equilibrium, transition-state theory describes rates of chemical change by postulating that a transition state lies somewhere on the pathway between the reactants and the products and that this transition state can be characterized by its own thermodynamic parameters, including its partial molar volume. The difference between the partial molar volume of the transition state and that of the reactants is the activation volume, AU. The activation volume cannot be measured by a direct density measurement, because the transition state is not a chemical species, not even a short-lived one. It can be measured only by the effect of the pressure on some rate constant k that characterizes the chemical process ... 

The major product of the hydrolysis of cis-[(en)2lr(OH)(BNPP)] (10) the corresponding monoester, is also hydrolyzed by attack of the cis coordinated hydroxide ion with a rate constant of 8 x 10 s at 40 C, or 2 X 10 S at 25 °C in the pH independent region. The product of this reaction is the ring opened monodentate phosphato complex cis-[(en)2lr(0H)(0P03)j. Thus, unlike the corresponding Co(III) complex, the chelate is not thermodynamically stable even at pH 9. The rate of attack of the cis coordinated hydroxide ion on the P center is also —500-fold slower than that reported for the analogous Co(III) reaction. 

However, application of kinetic techniques to the study of the pH/rate profile (4 < pH < 14) permits determination of the equilibrium and rate constants for the formation of [6]. From comparison of these parameters with those for analogous tetrahedral intermediates, McClelland was able to conclude that (i) the pentavalent intermediates of phosphoryl transfer are thermodynamically unstable, but are thermodynamically more favoured with respect to their breakdown products than the tetrahedral intermediates of acyl transfer however, (ii) the intermediates of phosphoryl transfer are kinetically less stable. Thus the activation barriers for breakdown of a TBP phosphorus intermediate are lower than those for breakdown of a tetra-... 

The thermodynamic hydricity of an M-H bond is related to the ionicity of that bond, which can be calculated from the quadrupole coupling constant (available from the NMR spectrum of the M-D analog). Such data can be compared to rate constants for H transfer, or kinetic hydricities. The rate constants for transfer of the hydride in a series of complexes to trityl cation in CH Cl (Equation 3.130 and Table 3.6), - and from a series of CpRu(P-P)H complexes to the iminium cation in Equation 3.131 (Table 3.7) have been measured. 

The thermodynamic analogy is not to be used as a method for establishing absolute values for the various activation parameters these are of limited significance since they derive from an equilibrium thermodynamic interpretation of intrinsically nonequilibrium properties. Furthermore, to accept such numbers uncritically ascribes a measure of definiteness to the activated complex which is unwarranted. On the other hand, trends and similarities may be useful in helping to characterize reaction mechanism. In Table 9.4 the values of and AHq calculated from (9.43) and (9.44) are given for a number of gas-phase reactions. For the bimolecular reactions the value of ASq depends upon the choice of standard state for rate constants in units of cm mol sec the natural standard state is a concentration of 1 mol cm. ... 

Alternatively, the thermodynamic analogy can be used to provide estimates of rate constants. In equilibrium thermodynamics one uses... 

Perhaps the most straightforward relationship between temperature and rate constants was suggested by Svante Arrhenius (Figure 20.15) in 1889. He used a thermodynamic approach in the form of an analogy. According to an expression known as the van t Hoff equation not the van t Hoff equation from osmotic pressure considerations), the temperature variation in the equilibrium constant of a process is... 

---