Deceleratory rate

Pre-irradiation of the salt with X-rays [1075] increased the extent of the initial deceleratory rate process, an effect attributed to the promotion of the electron transfer step. Neutron irradiation [1074] accelerated the decomposition rate and reduced the magnitude of E for the induction period from 216 to 159 kJ mole-1. 

As shown by Eq. (8.15), the reaction is a "two-thirds" order, but that does not involve the concept of molecularity. Since the surface area is a maximum at the beginning of the reaction, the rate is maximum at that time and decreases thereafter. A rate law of this type is known as a deceleratory rate law. As will be shown later, there are several rate laws that show this characteristic. 

Curves D and E are difficult to distinguish. There may be a short acceleratory stage before onset of the dominant or exclusively deceleratory rate process. Examples of behaviour of fliis type include the dehydrations of Li2S04.H20 [70,92], lignite [93] and Ca(OH)2 [94]. 

Giovanoli and Brutsch [37] emphasize the necessity for supplementing thermoanalytical kinetic data for the dehydration of y-FeOOH yFcjOj) with diffraction and electron microscopy studies. The deceleratory rate process can be described by either the first- order, or various diffusion-controlled expressions and thus a specific reaction model does not result from this kinetic analysis. Values of... 

The thermal decompositions of copper(II) fiimarate and of copper(II) maleate [125] showed some important chemical similarities with the reaction of the malonate. The most notable common feature was that the Cu " content in both salts diminished to 5% of the original value when a= 0.5, so that all three decompositions proceed with stepwise cation reduction Cu " Cu" Cu . The first reaction in the copper(II) maleate decomposition was accompanied by melting and or-time values fitted the Prout-Tompkins equation with ii, = 225 6 kJ moT between 473 and 508 K. During these reactions the maleate anion isomerized to the fiimarate and the extent of the second, deceleratory, rate process (f, = 139 15 kJ mol ) decreased as the reaction temperature was increased in the range 509 to 528 K. 

The rate law for the contracting area shows that a plot of 1 — (1 — versus time wiU lead to a straight Hne if the reaction follows a 1 /2-order rate law. This is another of the deceleratory rate laws. 

X X Two- and three-dimension growing of nuclei (Avrami-Erofeev equation), acceleratory or deceleratory rate of nuclei growth... 

Figure A3.14.1. Rate-extent plots for (a) deceleratory and (b) acceleratory systems.

Fig. 1. Generalized a—time plot summarizing characteristic kinetic behaviour observed for isothermal decompositions of solids. There are wide variations in the relative significance of the various stages (distinguished by letter in the diagram). Some stages may be negligible or absent, many reactions of solids are deceleratory throughout. A, initial reaction (often deceleratory) B, induction period C, acceleratory period D, point of inflection at maximum rate (in some reactions there is an appreciable period of constant rate) E, deceleratory (or decay) period and F, completion of reaction.

X= 2) or (P = 0, X = 3) and the distinction between these possibilities is most satisfactorily based upon independent evidence, such as microscopic observations. The growth of compact nuclei inevitably results in the consumption of surfaces and when these outer faces, the sites of nucleation, have been eliminated, j3 necessarily is zero this may result in a diminution of n. The continued inward advance of the reaction interface at high a results in a situation comparable with the contracting volume reaction (discussed below) reference to this similarity was also made in consideration of the Mampel approach discussed above. Shapes of the deceleratory region of a time curves for nucleation and growth reactions and the contracting volume rate process are closely similar [409]. 

Since the interposition of a barrier layer diminishes the effective contact between reactants, the nucleation step in solid + solid reactions is Usually completed very rapidly at temperatures conveniently used in studies of the bulk reaction and, accordingly, the rate processes are often deceleratory throughout. In addition to the progressive diminution in rate... 

Kinetic expressions for appropriate models of nucleation and diffusion-controlled growth processes can be developed by the methods described in Sect. 3.1, with the necessary modification that, here, interface advance obeys the parabolic law [i.e. is proportional to (Dt),/2]. (This contrasts with the linear rate of interface advance characteristic of decomposition reactions.) Such an analysis has been provided by Hulbert [77], who considers the possibilities that nucleation is (i) instantaneous (0 = 0), (ii) constant (0 = 1) and (iii) deceleratory (0 < 0 < 1), for nuclei which grow in one, two or three dimensions (X = 1, 2 or 3, respectively). All expressions found are of the general form... 

Fig. 3. Reduced time plots, tr = (t/t0.9), for the contracting area and contracting volume equations [eqn. (7), n = 2 and 3], diffusion-controlled reactions proceedings in one [eqn. (10)], two [eqn. (13)] and three [eqn. (14)] dimensions, the Ginstling— Brounshtein equation [eqn. (11)] and first-, second- and third-order reactions [eqns. (15)—(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers.

While it is generally true to state that reaction rates increase with temperature, such a qualitative statement is not specific enough to be useful and in some circumstances can be incorrect, e.g. at high a values when the deceleratory character of the reaction may be sufficiently great to offset the acceleratory effect of a slow temperature rise. 

The initial stage of vacuum dehydroxylation of 3-Be(OH)2 (408— 493 K) [620] was deceleratory (E 59 kj mole-1), ascribed to diffusion control. During the subsequent main stage of reaction, interface penetration (E = 115 kJ mole-1) was rate-determining. 

This deceleratory reaction obeyed the parabolic law [eqn. (10)] attributed to diffusion control in one dimension, normal to the main crystal face. E and A values (92—145 kJ mole-1 and 109—10,s s-1, respectively) for reaction at 490—520 K varied significantly with prevailing water vapour pressure and a plot of rate coefficient against PH2o (most unusually) showed a double minimum. These workers [1269] also studied the decomposition of Pb2Cl2C03 at 565—615 K, which also obeyed the parabolic law at 565 K in nitrogen but at higher temperatures obeyed the Jander equation [eqn. (14)]. Values of E and A systematically increased... 

While there is agreement that the rates of clay dehydroxylations are predominantly deceleratory and sensitive to PH2G, there is uncertainty as to whether these reactions are better represented by the first-order or by the diffusion-control kinetic expressions. In the absence of direct observational evidence of interface advance phenomena, it must be concluded that the presently available kinetic analyses do not provide an unambiguous identification of the reaction mechanisms. The factors which control the rates of dehydroxylation of these structurally related minerals have not been identified. 

An initial deceleratory process ( 1%) in KN3 decomposition is ascribed to reaction at superficial imperfections [712]. The subsequent constant rate of product evolution corresponds to an interface process but this is not a nucleation and growth mechanism since the product metal is volatile (as in NaN3). The catalytic properties of potassium vapour are attributed... 

At low pressures, NH3 is desorbed and HC104 is also volatilized. Both may rapidly diffuse from the heated zone and recombine elsewhere on the cool walls of the vacuum envelope as sublimate. The kinetics of sublimation, which may accompany the low temperature reaction [926], have been studied and discussed in detail [931,932]. The rate of this process is deceleratory throughout, empirically obeying eqn. (7) [931]... 

Most processes were deceleratory throughout, fitting a rate equation based on the reaction order eqns. (15)—(17). ( indicates a nucleation and growth reaction.)... 

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