Plausible rate equations

To use the differential method it is necessary to propose a plausible rate equation and to do this the simplest proposal is made. 

It is important to recognize that the plausible rate equation is only a suggestion. Nonetheless it has the attraction of relative simplicity and, according to the discussion in Section 4.2, it has a strong likelihood of being correct since it is in a form that is found experimentally for many chemical reactions. 

If we continue with our example of the thermal decomposition of NO2 at 300 °C (and put to one side our knowledge that it is second-order) then, as already discussed, a plausible rate equation is... 

What would be a plausible rate equation for this reaction ... 

Propose a plausible rate equation and then, possibly in conjunction with an isolation method, use the differential method to determine whether the proposal is correct and, if so, establish the partial order with respect to each individual reactant. (Question 5.1 and Exercise 5.1)... 

The first step is to suggest a plausible rate equation which will be / = R[Am] [An] ... 

A plausible rate equation for the initial rate of reaction will be 7o = A R[Am]o [An]o ... 

The rate equation agrees with the experimental form, Eq. (6-14). However, it appears much less plausible than that in Eq. (6-14) in that it requires the intervention of two oxidation states of iron that are highly unusual and unstable under these reaction conditions. 

Such processes assume that molecules from a fluid phase in contact with a solid catalytic surface combine chemically with catalyst surface molecules and reaction subsequently proceeds between chemisorbed molecules followed by desorption of the products. A large number of different rate equations with varying numbers of constants can be derived by making various auxiliary assumptions and tested against experimental rate data. Since a more or less plausible mechanism is postulated, the feeling is that a chosen rate equation is somewhat extrapolatable outside an experimental range with greater... 

An analysis is terms of the normalized partial derivative (saturation parameter) is invariant with respect to the specific rate equation. Note that not all choices are necessarily equally plausible. 

Ruthenium has been investigated by many laboratories as a possible catalyst for ammonia synthesis. Recently, Becue et al. [T. Becue, R. J. Davis, and J. M. Garces, J. Catal., 179 (1998) 129] reported that the forward rate (far from equilibrium) of ammonia synthesis at 20 bar total pressure and 623 K over base-promoted ruthenium metal is first order in dinitrogen and inverse first order in dihydrogen. The rate is very weakly inhibited by ammonia. Propose a plausible sequence of steps for the catalytic reaction and derive a rate equation consistent with experimental observation. 

The rate constants presented are fairly consistent when based on this assumption, which seems plausible. However, the observed reaction rate may deviate somewhat from a calculated rate during the first minute or two of the reaction time. Consequently, on the assumption that the ozone concentration in the solution is constant, the rate equation can be simplified by combining the constants,... 

The derivation of rate equations for simultaneous hydrogenation of TMP-aldol and formaldehyde was based on a plausible surface reaction mechanism. According to the mechanism, the aldol, formaldehyde and hydrogen undergo competitive adsorption on the nickel-alumina surface. Adsorbed hydrogen atoms add to the carbonyl bonds of the aldol and formaldehyde. These irreversible reaction steps are presumed to be rate-determining, whereas the product desorption is regarded as rapid. Consequently, the reaction mechanism is written as follows ... 

In this paper, we have studied the kinetics of NO decomposition over Cu-ZSM5 in a range of experimental conditions quite close to those interesting for practical applications. The NO conversion data were modelled with several reaction rate equations, all based on different plausible reaction mechanisms. The ultimate goal of the work is to develop a kinetic model able to represent the reactor behaviour in all experimental conditions investigated. 

It is not always possible to solve kinetic problems using simple approaches. Even if the mechanism only involves a few steps the data may not readily suggest the coupled rate laws. Chemical intuition is required to propose a plausible mechanism which then must be tested. The natural procedure is to integrate the mechanistic rate equations and to compare the predicted concentrations with the observed ones. If a set of kinetic parameters can be found that satisfactorily accounts for the data, the mechanism is a possible one. Such calculations always involve extensive numerical work. Thus reasonable starting points are needed, even if modern high-speed computers are used. 

The rate constants for the nucleophilic addition of KCN to o ,Al-diphenyl nitrone and its derivatives (p-OCHs, p-CHs, p-Cl, and P-NO2) were detected by UV spectroscopy at 25 °C and rate equations, applied over a wide pH range, were obtained. On the basis of pH-rate profile, adduct analysis, general base catalysis, and substituent effect, a plausible mechanism for this addition reaction was proposed At high pH, the CN ion addition to the C=N bond was rate controlling, but in acidic media, the reaction proceeded by the addition of HCN to the C=N bond after protonation at oxygen of Q ,V-diphenyl nitrone. In the range of neutral pH, these two reactions occurred competitively. " ... 

MMA), when copol3rmerised with ethylene glycol dimethacrylate (EDMA) or polyethylene fumarate (PEF), but not with styrene, enters stage II sharply at the gel point. A plausible model proposed by Gordon and Roe leads to a parameter-free rate equation fig. M-), which fits extensive measurements on MMA/EDMA and MMA/PEF very well over the range 0 < < 6 Fig. M- contains... 

The aforementioned exception and the rather limited experimental material available do not allow any conclusions about the general applicability of the Hammett equation, using the same a- and p-values as for benzenes, to be drawn with certainty. The present author has pointed out that large deviations should be expected with strong - -M-substituents, as is also indicated from the rates of alkaline hydrolysis of methyl 5-amino- and 5-acylamino-2-thenoates. From the chemical shifts in the NMR spectra of thiophenes and benzenes it appears that another set of cr-values should be used in the thiophenes series which seems plausible since the transmission of the sub-... 

To evaluate the plausibility of this mechanism, we need to construct the overall rate law it implies. First, we identify any elementary reaction that results in product and write the equation for the net rate of product formation. In this case, N02 is formed only in step 2, and so... 

The rate law of an elementary reaction is written from the equation for the reaction. A rate law is often derived from a proposed mechanism by imposing the steady-state approximation or assuming that there is a pre-equilibrium. To be plausible, a mechanism must be consistent with the experimental rate law. 

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