Hinshelwood theory

Show that the excitation rate constant from the Hinshelwood theory (Eq. 10.132) decreases with increasing e. ... 

Derive an expression for the activation energy for the collision theory rate constant (i.e., Acoil of Eq. 10.76). Derive a similar expression for the activation energy for the unimolec-ular excitation reaction predicted by Hinshelwood theory (i.e., ke(e ) of Eq. 10.132). The activation energy is predicted to be larger for which theory ... 

Derive an expression for the decomposition rate constant kd (e ) for the Hinshelwood theory of unimolecular reactions. 

Compute the fall-off curve using Hinshelwood theory. For this calculation, take the effective number of vibrational modes s to be one-half of the actual number of vibrational modes for the the species. vacluai ... 

In the Hinshelwood theory the time lag corresponds to the time taken for the activated molecule to rearrange configuration into the critical configuration of the activated complex. The Kassel theory deals explicitly with this process, and imposes a much more severe restriction than does Hinshelwood. Before an activated molecule can react there must be a flow of energy at least 0 into a... 

In the Lindemann-Hinshelwood theory the Lindemann expression for the uni-molecular rate constant, Eq. (9), is still assumed to be correct, but an improved activation rate coefficient is obtained from the Hinshelwood formulation. The shape of the fall-off curve should therefore still be the simple form predicted by Lindemann. Reference to Fig. 2 shows that, for the cyclobutane decomposition reaction, the change in the activation rate coefficient brings the theory much closer to the experimental results, particularly at low pressure. However, the shape of the fall-off curve is still not correct the Lindemann-Hinshelwood model predicts a faU-off region that is too narrow, the true fall-off is broader. 

The second problem of the Lindemann-Hinshelwood theory is that the Lindemann plot is often far from a straight line, as can be seen by the example... 

Figure 2. Fall-off data for the dissociation of cyclobutane at 722 K [6,7], and comparison with Lindemann-Hinshelwood theory with 11 or 12 oscillators. The true number of vibrations is 30.

There is no reason for this expression to be consistent with the Lindemann straight line plot, but it is instructive to examine the physical reasons for the curvature. The low pressure limit is the same as in the Lindemann-Hinshelwood theory because the rate determining step is activation, which is dealt with in the same way in the two theories. This can be seen by taking the low pressure limit of Eq. (21). 

In contrast, the Lindemann-Hinshelwood model assumes that all energized molecules react with the same rate constant k2- This model overestimates the contributions to uni from high energy states, and underestimates those from low-energy states. The true rate coefficient at some intermediate pressure will fall off faster than predicted by the Lindemann-Hinshelwood theory because of... 

The low pressure limit is identical to that of the Hinshelwood theory because the same expression for the density of states has been used. However, the fall-off is calculated from Eq. (24), which can be written in the form... 

For the reactions of medium-sized molecules we have the following Lindemann-Hinshelwood theory, RRK theory. Slater s harmonic theory, RRKM theory, phase-space theory, absolute reaction rate theory, quasi-equilibrium theory, and several others. All of those are grouped under the umbrella of "transition state theory" (Robinson Holbrook, 1972 Forst, 1973). Among these theories, some are regarded as "inaccurate" or "outdated." But several rivals remain as viable alternatives on which to base a theoretical study of a reaction system, at least as far as Joiunal referees are concerned. 

The concepts of adsorption and kinetics rest on the Langmuir-Hinshelwood theories referred to earlier. 

Lindemann-Hinshelwood theory makes the assumption that a single collision with a bath gas molecule M is sufficient to deactivate AB to AB. In reality, each collision removes only a fraction of the energy. To account for the fact that not all collisions are fully deactivating, Troe (1983) developed a modification to the Lindemann-Hinshelwood rate expression. In the Troe theory, the right-hand side of... 

The Hinshelwood theory predicts a straight-line plot for l//exp versus 1/P with an intercept l/i( and slope... 

The derivation of a theoretical relation for is similar to that in the Hinshelwood theory except that the starting relations are differential equations because /( ) is no longer a constant but a function of energy. The balance at any pressure between activation rate and deactivation rate plus reaction rate is... 

The LINDEMANN-HINSHELWOOD theory for unimolecular reactions is based on the following mechanism ... 

This treatment is called the Lindemann-Hinshelwood theory. Although the treatment of Hinshelwood was successful in reproducing the experimental values of high-pressure limit rate constants k o, the theory stUl has one defect, that the values of s necessary to explain the experimental values differ largely from the acmal number of vibrational freedom and there is a large discrepancy of with experimental values in the fall-off region. 

The reaction mechanism and kinetics have been studied and described. Although it was not possible to develop theoretical kinetic equations based on the Langmuir-Hinshelwood theory, the empirical kinetic expressions deduced from experiments using aluminum silicate catalyst are in the form of ... 

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