Third order rate equation

This third-order rate equation is interpreted as meaning that the process is first-order in each reactant, viz. N-chloroacetanilide, chloride ion and hydrogen ion. This has been confirmed10 for the reaction of N-chloroacetanilide with hydrogen bromide in a variety of aqueous media, under conditions where the dechlorination is rate-determining. The rate equation is... 

The hydrolysis of ethyl acetate (B) with an alkaline hydroxide (A] non-aqueous solutions is believed to have the third order rate equation... 

The reaction, 2 FeCl3 + SnCl2 Products, was studied with stoichiometric proportions of reactants. The data are time in minutes and tin chloride (B) mol/liter. Check the third order rate equation corresponding to the stoichiometry. 

There are two other implications (1) the relative magnitude of the rates validates Hui and Hameilec s simplifying assumption that lead to a third-order rate equation for thermal initiation (2) the uncertainty in the prediction of k precludes any argument for or against the possibility that acid catalyzes the Diels-Alder reaction as well as the aromatization of DH. 

Trautz and Wachenheim have studied the formation of NOCl from NO and CI2 by following the change in total pressure as a function of time. They suggest that reactions (I) and (2) are not adequate to account for their observations since CI2 enhances the rate coefficient of the reaction. Welinsky and Taylor criticize this interpretation because of the manner in which Trautz and Wachenheim handled their data. Upon recalculating the rates in a more reliable manner it is shown that within experimental error no effect of chlorine on the rate coefficient is observed. This appears to be consistent with the data of Welinsky and Taylor, Waddington and Tolman, Kiss ", and Krauss and Saracini . In every case the production of NOCl (1) follows the third-order rate equation. All of these workers followed the reaction via the change in total pressure with time. 

Reactions in melts, vitreous materials, polymers, etc. can justifiably be analyzed by equations based on a concentration dependence of rate. Some reactions proceeding in vitreous reactant phases have been shown to conform to second or even third-order rate equations. Progressive melting of a solid reactant during decomposition results in acceleratory behaviour [52,71-73] and comprehensive melting before dehydration was observed to result in an approximately constant rate of water evolution [74,75]. 

The isothermal a - time plots corresponding to the rate equations in Table 3.3. (calculated on the arbitrary basis that a 0.98 at t = 100 min) are illustrated in Figure 3.5. and some of the relative rate [= diCcldt)l d.cdAt) - time plots are shown in Figure 3. 6. (The relative rate - time plots for the third-order rate equation and the diffusion models are too deceleratory for comparison and have been omitted.)... 

You met this idea in Chapter 12 in the context of third-order rate equations. 

The mechanism of the uncatalyzed, gas-phase reaction has been of great interest for more than seven decades because it follows a third-order rate equation (—r o = k[NO] [H2]), leading to speculation that a termolecular collision might be involved. However, from the beginning of research on this reaction, it has been hypothesized that the overall reaction proceeds in stages, considered was... 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

The third-order rate expression (Equation 9) is applicable over the temperature range 121° to 187°C. The Arrhenius relationship describing the temperature dependence of the rate constant k3 (Figure 7) is... 

Ion-molecule association reactions and the collisional deactivation of excited ions have been the subjects of recent reviews.244-246 Several systematic studies have been performed in which the relative deactivating efficiencies of various Mf species have been determined. By applying the usual kinetic formulations for the generalized reaction scheme of equation (11.31), and assuming steady-state conditions for (AB+), an expression for the low-pressure third-order rate coefficient can be derived ... 

Although the products do not allow one to distinguish between intra- and intermolecular processes, they found that the plots of kdecay versus quencher (alcohol) concentration are nonlinear. They have analyzed the data according to the quadratic expression shown in equation 16, where kq is the third-order rate constant corresponding to transient quenching by two molecules of alcohol. 

This is precisely the behaviour predicted by the Kira mechanism, provided that the formation of the silene-ROH complex is reversible and the proton transfer steps are rate-limiting. The complete mechanism is shown in Scheme 4, while equation 27 gives the predicted expression for the pseudo-first-order rate constant for decay of the silene, derived assuming the steady-state approximation for the silene-alcohol complex. Equation 27 reduces to the quadratic expression in [ROH] of equation 28 when k c (A h + A h [ROII ), i.e. under the conditions of the equilibrium assumption for the complex. In practice, it is difficult to distinguish between the two situations given by equations 27 and 28. The experimentally determined second- and third-order rate constants roh and k2ROH are defined in equations 29 and 30, respectively, in terms of the mechanism of Scheme 4 and using the... 

But it isn t Experimental measurements show that the (overall) reaction is actually third-order (rate constant = kf) because the reaction is catalyzed by acids (so one of the reacting components also acts as a catalyst— Equation 4-12). 

In the absence of added nucleophiles, nitrosation occurs virtually irreversibly by an acid-catalysed pathway, presumably by attack by HjNO or NO". The third order rate constant from the rate equation equivalent to (46) has a value of 840 dm moF s- at 31°C (c/. 456 and 6960 dm mol- s for cysteine and thiourea respectively at 25°C) which suggests that for this neutral substrate the reaction rate is somewhat less than that expected for an encounter-controlled process. There is a major difference between the nitrosation of alcohols and that of thiols in that, whilst the former reactions are reversible (with equilibrium constants around 1), the reactions of thiols are virtually irreversible. It is possible to effect denitrosation of thionitrites but only at high acidity and in the presence of a nitrous acid trap to ensure reversibility (Al-Kaabi et al., 1982). Direct comparisons are not possible, but it is likely that nitrosation at sulphur is much more favoured than reaction at oxygen (by comparison of the reactions of N-acetylpenicillamine and t-butyl alcohol). This is in line with the greater nucleophilicity expected of the sulphur atom in the thiol. For the reverse reaction of denitrosation [(52) and (53)], the acid catalysis observed suggests the intermediacy of the protonated forms... 

Third-order reactions are uncommon. Fractional orders exist when the reaction represents a sequence of several elementary steps. Procedures for establishing the order and rate constants for these cases are similar to those given above. Experimental data that suggest fractional-order rate equations should be examined carefully for effects of physical resistances. Sometimes these effects, rather than a sequence of elementary processes, can be responsible for the fractional order. An example is the study of the hydrochlorination of lauryl alcohol with zinc chloride as a homogeneous catalyst ... 

The results at other conversions are shown in the third column of Table 4-4. Although there is some variation from point to point, there is no significant trend. Hence the differential method also confirms the validity of a second-order rate equation. The variation is due to errors associated with the measurement of slopes of the curve in Fig. 4-1. 

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