Meaning of the Rate Constant

The rate constants of unimolecular reactions have the dimension per second (s ). This means the process can happen that often per second, e.g., k = 6.3 x lO s being equivalent to 1.6 x 10 s per fragmentation on the average. It is important 

Although the general shape of any function resembles the ionization efficiency curve to the left of the maximum, these must not be confused. At an excess energy close to zero, the rate constant is also close to zero but it rises sharply upon slight increase of the excess energy. However, there is an upper limit for the rate of a dissociation that is defined by the vibrational frequency of the bond to be cleaved. The fragments are not able to fly apart at a higher velocity than determined by their vibrational motion (Fig. 2.6). 

Nevertheless, due to the strong dependence of the rate constant on the reaction over TS3 will be by far the least important. 

---

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

The simplest model describing the meaning of the rate constant is the Arrhenius equation, as shown in Eq. 4.5. 

What is the physical meaning of the rate constant of a chemical reaction What is the dimension of the rate constant of a first-(second-) order chemical reaction How does the rate constant depend on the temperature Write the Arrhenius equation. What is called the activation energy What substances are called catalysts and inhibitors ... 

Leahy [30], van de Waterbeemd [14] and Albery [16] discussed the meaning of the rate constants, koa, kao it is sufficient to state here that the primary process involved is the resolvation of the compound as it moves from the octanol to water environments, that is, the loss of any strongly associated octanol molecules and gain of water. Because of the mutual solubility of these solvents it seems reasonable to say that some solvent molecules may transfer along with the compound (which may not be true for other solvent systems where the mutual solubilities are lower). There may also be molecular conformation changes during this process of transfer, which would also be likely to affect solvation. 

At 1 IS °C e the text for the meaning of the rate constants. Extrapolated to zero concentration of model compound. 

Thus, according to mechanism, the ratios of mole fractions of different kinds of diads, triads, etc., lead to very different rate constant combinations (Table 15-7). For example, the mole fraction ratio of iso- and syndiotactic diads gives the ratio of rate constants for iso- and syndiotactic linking in the case of Bernoulli mechanisms, but gives the ratios of the rate constants for the cross-steps and not a mean of the rate constants in the case of first-order Markov mechanisms. 

In defining it is assumed that the rate constant of cross-termination is equal to the geometric mean of the rate constants of termination in homopolymerization. This relation is applicable in the case of gas reactions. In copolymerizations, however, the value of can increase up to about 400 (methyl methacrylate/vinyl acetate). In addition, depends on the composition of the mixture. The cause of this composition effect is unknown, although it is significant that is particularly large when the monomers tend toward alternating copolymerization. 

The terms B and BIA can be referred to as the parabolic and linear rate constants for describing the oxide growth kinetics. The physical meanings of the rate constants B and BjA are the oxidant diffusion and interface reaction rate, respectively. The corresponding values for B and BIA for dry and wet oxidation of (111) silicon are plotted in Fig. 3. For (100) silicon, these values should be divided by 1.68. These expressions are better fit for the cases of a very thin oxide layer and in dry O2 conditions. Solving Eq. 13 leads to the relationship between the oxide thickness and the growth time ... 

Both the exciton/radical pair equilibrium model and the bipartite model predict formally the same kinetics and thus both give rise also to a biexponential fluorescence decay. However, the two models are fundamentally different. This difference consists in the entirely different meaning of the rate constants involved and thus in the entirely different origin of the two observed lifetimes. In the bipartite model the biexponentiality is due to the equilibration of the excitons between antenna and reaction center. Thus one of the lifetime components reflects an eneigy transfer process. In contrast to the exciton/radical pair equilibrium model the bipartite model basically describes a diffusion-limited kinetics. Despite the fact that it formaUy can describe correctly the observed kinetics, the application of the bipartite model on experimental data leads to physically unreasonable results. First it results in a charge separation time in the reaction centers which is by one to two orders of magnitude too high. 

A simple example of the need to defme the rate in order to give the meaning of the rate constant is shown for the reaction... 

Let us first recall the meaning of the rate constant of the reaction described by eqn 16.2. In a protein solution at room temperature, incessant and random... 

The polymerizability of a monomer can be evaluated by means of the rate constant of polymerization which varies with the method of polymerization chosen. 

Table 18.27 displays the values of this rate constant at various conditions of pressure. Examine the results obtained it is observed that this constant varies in an erratic way when the pressure increases between 100 and 2,000 Pa However, this constant should not depend on the pressure since it has the meaning of the rate constant of an elementary step for this reason, we have to reject this pure mode. 

---