Unimolecular decompositions Lindemann mechanism

Using the known parameters K, a, b, and the measured values of y as a function of t, we can plot the left-hand side of Eq. (32.58) against t to obtain the value of the rate constant from the slope. The value of K is measured independently. Using Eq. (32.58), Bodenstein obtained satisfactory values of the rate constant at several temperatures. 

Equation (32.58) should be compared to the second-order rate law without the reverse reaction, Eq. (32.43), which with = Vg = — 1 can be written as 

For many years the hydrogen-iodine reaction had been the traditional example of opposing second-order reactions. Recent work by J. H. Sullivan indicates that the mechanism is not as simple as we have assumed here in fact, the mechanism now seems to be unresolved. For a discussion and references see R. M. Noyes, J.Chem. Phys. 48, 323 (1968). 

When it is necessary for a reaction to proceed through several successive elementary steps before the product is formed, the rate of the reaction is determined by the rates of all these steps. If one of these reactions is much slower than any of the others, then the rate will depend on the rate of this single slowest step. The slow step is the rate-determining step. The situation is analogous to water flowing through a series of pipes of different diameters. The rate of delivery of the water will depend on the rate at which it can pass through the narrowest pipe. An apt illustration of this feature of consecutive reactions is offered by the Lindemann mechanism of activation for unimolecular decompositions. 

Before 1922 the existence of unimolecular decompositions posed a severe problem in interpretation. The unimolecular elementary step consists of the breaking of a molecule into fragments  

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The following Lindemann mechanism for the unimolecular decomposition of a molecule A in the presence of a species Y (which may be any molecule such as inert gas like Helium or even A itself)y considered ... 

Use the following data for a unimolecular decomposition to determine k and k2 which appear in the simple Lindemann mechanism assume that k has a value of 5.0 x 1010 mol 1 dm3 s From this determine the mean lifetime of the activated molecule. Comment on the results. 

Conditions necessary for neglecting dc i/dt in the manner employed above may be investigated through formal approximations in reaction-rate theory. This will be considered further, with application to the Lindemann mechanism, in Section B.2.5. The mechanism itself generally contains fundamental inaccuracies and is best viewed as a simplified approximation to more-complex mechanisms. In particular, molecules capable of experiencing unimolecular decomposition or isomerization may exist in many different vibrationally excited states, and the rate constant for the reaction may differ in each state. Approximate means for summing over states to obtain average rate constants have been developed an introduction to these considerations maybe found in [3]. 

Radical decompositions are unimolecular reactions and show complex temperature and pressure dependence. Section 2.4.l(i) introduces the framework (the Lindemann mechanism) with which unimolecular reactions can be understood. Models of unimolecular reactions are vital to provide rate data under conditions where no experimental data exist and also to interpret and compare experimental results. We briefly examine one empirical method of modelling unimolecular reactions which is based on the Lindemann mechanism. We shall return to more detailed models which provide more physically realistic parameters (but may be unrealistically large for incorporation into combustion models) in Section 2.4.3. 

M is Br2 or any other gas that is present. By the principle of microscopic reversibility , the reverse processes are also pressure-dependent. A related pressure effect occurs in unimolecular decompositions which are in their pressure-dependent regions (including unimolecular initiation processes in free radical reactions). According to the simple Lindemann theory the mechanism for the unimolecular decomposition of a species A is given by the following scheme (for more detailed theories see ref. 47b, p.283)... 

Summary.—The mechanism of the activation process in gaseous systems has been investigated from the point of view of (1) activation by radiation (2) activation by collision. An increase in the radiation density of possible activating frequencies has resulted in no increased reaction velocity. The study of the bimolecular decomposition of nitrous oxide at low pressures has led to the conclusion that the reaction is entirely heterogeneous at these pressures. A study of the unimolecular decomposition of nitrogen pentoxide between pressures of 7io mm. Hg and 2 X 10 3 mm. Hg shows no alteration in the rate of reaction such as was found by Hirst and Rideal but follows exactly the rate determined by Daniels and Johnson at high pressures. No diminution of the reaction velocity as might be ex-expected from Lindemann s theory was observed. 

Collision theory does not deal directly with unimolecular reactions but touches on the subject through the Lindemann mechanism. Once the molecule has been provided with sufficient energy by collision, the problem is to calculate the rate constant for the unimolecular decomposition,... 

In one sense this mechanism is akin to Lindemann s picture of unimolecular decomposition reactions (see Section 4.3.1.3). An initial reaction produces a reactive intermediate that subsequently decomposes irreversibly to yield products or is reversibly decomposed into enzyme and substrate. 

Figure 14.21 Plot of the pressure dependence of the rate for a unimolecular decomposition that follows the Lindemann mechanism.

In this case, the rate law is first order in A and independent of the total pressure. A plot of the pressure dependence of a unimolecular decay that obeys the Lindemann mechanism is shown in Figure 14.21. This dependence is consistent with that which is experimentally observed in many unimolecular decompositions in the gas phase. 

The mechanism (5.24) is, in its deactivation step, the converse of the Lindemann mechanism (5.18). Whereas unimolecular decomposition poses... 

Since the mechanism (5.28) was postulated before Lindemann s rationalization of unimolecular decomposition, buffer gas was not included in steps (1) or (5) of the original proposal. Since there is preequilibration of Br2 and Br, the rate law does not reflect the participation of buffer gas. 

Historically, the theory of the termolecular reaction mentioned in the previous paragraph has been developed through the unimolecular reaction theory. This paragraph describes unimolecular decomposition reacticms in some detail. The chemical formula for the unimolecular decomposition reactions corresponding to the Lindemann mechanism can be shown as... 

We have calculated the addition channel rate constant using the RRKM approach to unimolecular reaction rate theory, as formulated by Troe ( ) to match RRKM results with a simpler computational approach. The pressure dependence of the addition reaction (1) can be simply decribed by a Lindemann-Hinshelwood mechanism, written most conveniently in the direction of decomposition of the stable adduct ... 

A two-step mechanism, first suggested by LINDEMANN /135/, is accepted in all contemporary theories of unimolecular reactions The first step is the formation of an "activated molecule by ineleastic bimolecular collisions, which supply it with an internal total energy amount over a critical value E, and the second step is the decomposition of the activated molecule. At high presure, there exist a thermal equilibriiam between the activated molecules (E>E ) and the normal molecules (E[Pg.230]

After Lindemann and Christiansen put forward their mechanism, experimental work was carried out to verify if the unimolecular reactions did become second order at sufficiently low pressures. Figure 8.1 illustrates the order of dimethyl ether decomposition in the vapour phase as a function of the addition of a foreign gas. In qualitative terms, the mechanism of Lindemann-Christiansen gives a good account of the experimental observations,... 

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