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Thermal rate laws

If only the overall rate equation of a reaction is known, no information on the change of concentrations with time can be obtained. Therefore it is necessary to determine the mechanism of a reaction - that means the sequence of all the elementary partial steps. Then the rate law can be derived unambiguously in the following way  [Pg.37]

Therefore the rate of the A th partial reaction is determined by the product of the concentrations of the different disappearing reactants, the amount of the stoichiometric coefficients being the exponents. The concentrations of products, formed in the different k partial reactions, are not included in this equation. [Pg.38]

In consequence the problem is to find a method which allows the derivation of the differential equations by a systematic procedure. In the following, such a convenient and systematic method is discussed [10-12], which was used in part in Section 2.1.1.1  [Pg.38]

This procedure allows any differential equation to be set up schematically. The systematic approach helps to avoid errors with stoichiometric coefficients, signs in front of the rate constants, and will be useful to find linear dependencies between the different partial reactions later on. The application of this scheme is demonstrated in the following two examples. [Pg.38]

According to (a)-(c) the first row and first column are filled with the information from the two reactions  [Pg.38]


The system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... [Pg.786]

Two examples are (1) the thermal, gas-phase decomposition of acetaldehyde at high temperatures and (2) the reaction of the hydrated 2-propylchromium ion with molecular oxygen in aqueous solution. The reactions and their rate laws are as follows ... [Pg.182]

A full development of the rate law for the bimolecular reaction of MDI to yield carbodiimide and CO indicates that the reaction should truly be 2nd-order in MDI. This would be observed experimentally under conditions in which MDI is at limiting concentrations. This is not the case for these experimements MDI is present in considerable excess (usually 5.5-6 g of MDI (4.7-5.1 ml) are used in an 8.8 ml vessel). So at least at the early stages of reaction, the carbon dioxide evolution would be expected to display pseudo-zero order kinetics. As the amount of MDI is depleted, then 2nd-order kinetics should be observed. In fact, the asymptotic portion of the 225 C Isotherm can be fitted to a 2nd-order rate law. This kinetic analysis is consistent with a more detailed mechanism for the decomposition, in which 2 molecules of MDI form a cyclic intermediate through a thermally allowed [2+2] cycloaddition, which is formed at steady state concentrations and may then decompose to carbodiimide and carbon dioxide. Isocyanates and other related compounds have been reported to participate in [2 + 2] and [4 + 2] cycloaddition reactions (8.91. [Pg.435]

Garratt and Thompson [J. Chem. Soc., 1934, 524, 1817, 1822] have studied the photochemical and thermal decomposition of nickel tetra-carbonyl. Later work by Day, Pearson and Basolo [J. Am. Chem. Soc., 90 (6933), 1968] confirmed that the rate law postulated by Garratt and Thompson was obeyed for the homogeneous process. The mechanism postulated by both groups is ... [Pg.124]

The thermal decomposition of N02 has been studied222-224 in the temperature range 1400-2300 °K by the shock-tube technique. Changes in the concentration of N02 in shock-heated argon-diluted N02 were monitored by visible absorption222 or visible emission224 spectrophotometry. The data fitted a complex rate law of the form... [Pg.86]

Problem 3.7 (Chain Reaction) The thermal decomposition of acetone is found to follow the rate law as... [Pg.76]

Kinetics in polycrystals differ from those in solution phase, because in the former, the thermal reactions usually follow a nonexponential rate law, something that is attributed to a multiple-site problem. In contrast to a first-order reaction in solution, the rate constant of a nonexponential process in the solid state is time dependent molecules located in the reactive site will have decayed during the warmup procedure and/or the initial stage of the reaction at the given temperature. These considerations need to be taken into account when the decay of the intensity of the IR signals in a matrix at low temperature are used for kinetic measurements [70]. [Pg.142]

Another simple reaction with a complicated reaction rate law is Reaction 1-5, 203(gas) 302(gas), which may be accomplished thermally or by photochemical means. The reaction rate law for the thermal decomposition of ozone is d /df= c5[03] /[02] when [O2] is very high, and is d /dt=ks [O3] when [O2] is low. [Pg.15]

The thermal oxidation of NO by molecular oxygen, reaction (6), is another example where the stoichiometry and the molecularity of the reaction are directly related, and the rate law is... [Pg.132]

This expression is different from that first proposed by Bodenstein.28) Alyea and Lind2 found the same rate law for the reaction induced by a-particle bombardment, except that the specific ionization (number of ion pairs produced) replaced 70 in eq. (3-j). Bodenstein, Lenher, and Wagner28 further examined the photochemical reaction between 200 and 300°C and the thermal reaction at temperatures over 400°C. They proposed the mechanism... [Pg.95]

The rate law from the thermal decomposition of Cl2 between 350 and 450°C was29... [Pg.96]

Perikinetic Coagulation. If colloidal particles are of such dimensions that they are subject to thermal motion, the transport of these particles is accomplished by this Brownian motion. Collisions occur when one particle enters the sphere of influence of another particle. The coagulation rate measuring the decrease in the concentration of particles with time, N (in numbers/ml.), of a nearly monodisperse suspension corresponds under these conditions to the rate law for a second order reaction (15) ... [Pg.110]

From a structural point of view, mechanism in a single crystal can be much closer to a set of identical atomic trajectories than to the kind of fuzzy statistical average with which one must be content in solution. It is not surprising that with this kind of structural uniformity the site problems that plague kinetic studies in rigid glasses disappear. Adherence to first-order rate laws can be as close in single crystals as it is in fluids, and equally valid activation parameters can be obtained for thermal unimolecular reactions of reaction intermediates [12]. [Pg.287]

The photochlorination rate expressions may be expected to be somewhat modified as a result of the inclusion of the hot radical reactions. At temperatures below 150°C. the unimolecular decomposition of the (thermalized) AC1 radical, i.e., reaction ( — 2), may be expected to be negligible and the rate laws are... [Pg.169]

Many chemical processes are initiated simply by mixing the appropriate reagents, and (usually) the higher the temperature, the faster the reaction rate such reactions are classified as thermally activated or thermal reactions. Sometimes, thermal activation is not enough to initiate the reaction or, in orbital-symmetry-controlled concerted processes, initiates the wrong reaction, and photochemical activation is necessary. Although the procedure to obtain a mechanistic rate law also applies for photochemical reactions, we shall not consider them specifically in this chapter. [Pg.79]

Thermal decompositions may be exothermic or endothermic. Solids that decompose on heating without melting often form gaseous products. When the product is a gas, the reaction rate can be affected by diffusion so particle size can be important. Aging of solids can result in crystallization of the surface. Annealing reduces strains and slows the decomposition rate. The decomposition of some fine powders follows a first-order rate law. Otherwise, empirical rate equations are available (e.g., in Galwey, Chemistry of Solids, Chapman and Hall, 1967). [Pg.48]

On heating the neat sample or a solution in a variety of solvents, 2-allyloxythiazole (125) undergoes a thermal rearrangement to N-allyl-A-4-thiazoline-2-one (126) in excellent yield (Scheme 64) (283). Deuterium labeling reveals the complete inversion or the allylic moiety in the rearrangement. First-order rate law is found, and activation parameters show a negative entropy in accord with that measured in most of Claisen rearrangements. [Pg.212]


See other pages where Thermal rate laws is mentioned: [Pg.37]    [Pg.37]    [Pg.410]    [Pg.129]    [Pg.246]    [Pg.234]    [Pg.237]    [Pg.219]    [Pg.98]    [Pg.539]    [Pg.619]    [Pg.112]    [Pg.493]    [Pg.385]    [Pg.171]    [Pg.146]    [Pg.385]    [Pg.91]    [Pg.172]    [Pg.77]    [Pg.282]    [Pg.171]    [Pg.222]    [Pg.365]    [Pg.684]    [Pg.494]    [Pg.42]    [Pg.66]    [Pg.276]    [Pg.3]    [Pg.176]    [Pg.289]    [Pg.184]   


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Thermal rate

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