Reaction reactions, independent

Hess s law Sometimes called the law of constant heat summation, it states that the total heat change accompanying a chemical reaction is independent of the route taken in reactants becoming products. Hess s law is an application of the first law of thermodynamics to chemical reactions. 

The order of the rate law with respect to the three reactants can be determined by comparing the rates of two experiments in which the concentration of only one of the reactants is changed. For example, in experiment 2 the [H+] and the rate are approximately twice as large as in experiment 1, indicating that the reaction is first-order in [H+]. Working in the same manner, experiments 6 and 7 show that the reaction is also first-order with respect to [CaHeO], and experiments 6 and 8 show that the rate of the reaction is independent of the [I2]. Thus, the rate law is... 

Norrish type I chemistry is claimed to be responsible for about 15% of the chain scission of ethylene—carbon monoxide polymers at room temperature, whereas at 120°C it promotes 59% of the degradation. Norrish I reactions are independent of temperature and oxygen concentration at temperatures above the T of the polymer (50). 

Model Reactions. Independent measurements of interfacial areas are difficult to obtain in Hquid—gas, Hquid—Hquid, and Hquid—soHd—gas systems. Correlations developed from studies of nonreacting systems maybe satisfactory. Comparisons of reaction rates in reactors of known small interfacial areas, such as falling-film reactors, with the reaction rates in reactors of large but undefined areas can provide an effective measure of such surface areas. Another method is substitution of a model reaction whose kinetics are well estabUshed and where the physical and chemical properties of reactants are similar and limiting mechanisms are comparable. The main advantage of employing a model reaction is the use of easily processed reactants, less severe operating conditions, and simpler equipment. 

The oxidation of chlorate to perchlorate, CIO, is an electrochemical anode reaction independent of pH. 

As an example the use of ceramic membranes for ethane dehydrogenation has been discussed (91). The constmction of a commercial reactor, however, is difficult, and a sweep gas is requited to shift the product composition away from equiUbrium values. The achievable conversion also depends on the permeabihty of the membrane. Figure 7 shows the equiUbrium conversion and the conversion that can be obtained from a membrane reactor by selectively removing 80% of the hydrogen produced. Another way to use membranes is only for separation and not for reaction. In this method, a conventional, multiple, fixed-bed catalytic reactor is used for the dehydrogenation. After each bed, the hydrogen is partially separated using membranes to shift the equihbrium. Since separation is independent of reaction, reaction temperature can be optimized for superior performance. Both concepts have been proven in bench-scale units, but are yet to be demonstrated in commercial reactors. 

To simplify matters, it is assumed that the current densities for the partial reactions are independent of position on the electrode surface. Equation (2-10 ) can then be used to designate the current densities ... 

The result of the steady-state condition is that the overall rate of initiation must equal the total rate of termination. The application of the steady-state approximation and the resulting equality of the initiation and termination rates permits formulation of a rate law for the reaction mechanism above. The overall stoichiometry of a free-radical chain reaction is independent of the initiating and termination steps because the reactants are consumed and products formed almost entirely in the propagation steps. 

A new general synthesis of 3-substituted derivatives has been reported (99MC13) (Scheme 9). Thus, the nitro group of furoxan 27 underwent a facile hydride replacement on treatment with NaBH4 in EtOH to give 3-monosubstituted furoxans 23. The result of this reaction is independent of the nature of R. 

The ability of a nltro group in the substrate to bring about electron-transfer free radical chain nucleophilic subsdnidon fSpj li at a saniratedcarbon atom is well documented. Such electron transfer reacdons are one of the characterisdc feanires of nltro compounds. Komblum and Russell have established ihe Spj l reaction independently the details of the early history have been well reviewed by them. The reacdon of -nitrobenzyl chloride v/ith a salt of nitro ilkane is in sharp contrast to the general behavior of the ilkyladon of the carbanions derived from nitro ilkanes here, carbon ilkyladon is predominant. The carbon ilkyladon process proceeds via a chain reacdon involving anion radicals and free radicals, as shovmin Eq. 5.24 and Scheme 5.4 fSpj l reacdoni. 

Luchkevich et al. (1986, Table 6) demonstrated that for the three isomeric nitro-benzenediazonium ions and their (Z)-diazohxydroxides the acidity constants can be determined by ultraviolet spectrophotometry, by potentiometry, from the kinetics of reaction with hydroxide ions, from the (Z) (E) isomerization kinetics, and from the kinetics of azo coupling reactions. These independent methods gave surprisingly consistent results. ... 

The half-time (or half-life) of the reaction is independent of [A]o. The reciprocal of the rate constant, t = l/k, is referred to as the lifetime or the mean reaction time. In that time [A] falls to l/e of its initial value. The pharmaceutical industry refers to the shelf life or t90, the time at which [A]/[A]o reaches 0.90. Both t and t90 are also independent of [A]o. 

Negative evidence for a common intermediate is just as important, for it can thereby eliminate a contending mechanism. The solvolysis of 2-halo-2,3,3-trimethylbutanes in methanol provides such an example.17 If it occurs by the elimination of a carbocation, the intermediate should undergo elimination and substitution reactions independent of the identity of the halide. These are shown as follows ... 

The formation of isomeric aldehydes is caused by cobalt organic intermediates, which are formed by the reaction of the olefin with the cobalt carbonyl catalyst. These cobalt organic compounds isomerize rapidly into a mixture of isomer position cobalt organic compounds. The primary cobalt organic compound, carrying a terminal fixed metal atom, is thermodynamically more stable than the isomeric internal secondary cobalt organic compounds. Due to the less steric hindrance of the terminal isomers their further reaction in the catalytic cycle is favored. Therefore in the hydroformylation of an olefin the unbranched aldehyde is the main reaction product, independent of the position of the double bond in the olefinic educt ( contrathermodynamic olefin isomerization) [49]. 

The half-life of a first-order reaction is characteristic of the reaction and independent of the initial concentration. A reaction with a large rate constant has a short half-life. 

The equilibrium constant K is the same for R =t-C4HJ and t-CsHi. As also the rate constants of carbonylation and decarbonylation are about equal for these two ions, it is concluded that both the thermodynamics and the kinetics of the carbonylation reaction are independent of the structure of R+, if R+ is an acyclic tertiary alkyl cation. This agrees with former findings (Brouwer, 1968) on the relative stabilities of such ions. 

Note that the matrix of stoichiometric coefficients devotes a row to each of the N components and a column to each of the M reactions. We require the reactions to be independent. A set of reactions is independent if no member of the set can be obtained by adding or subtracting multiples of the other members. A set will be independent if every reaction contains one species not present in the other reactions. The student of linear algebra will understand that the rank of v must equal M. 

Consecutive Reactions. The prototypical reaction is A B C, although reactions like Equation (6.2) can be treated in the same fashion. It may be that the first reaction is independent of the second. This is the normal case when the first reaction is irreversible and homogeneous (so that component B does not occupy an active site). A kinetic study can then measure the starting and final concentrations of component A (or of A and A2 as per Equation (6.2)), and these data can be used to fit the rate expression. The kinetics of the second reaction can be measured independently by reacting pure B. Thus, it may be possible to perform completely separate kinetic studies of the reactions in a consecutive sequence. The data are fit using two separate versions of Equation (7.8), one for each reaction. The data will be the experimental values of for one sum-of-squares and b ut for another. 

AG, the overall change in free energy for a reaction, is independent of reaction mechanism and provides no information concerning rates of reactions. 

A change in any thermodynamic state function is independent of the path used to accomplish that change. This feature of state functions tells us that the energy change in a chemical reaction is independent of the manner in which the reaction takes place. In the real world, chemical reactions often follow very complicated paths. Even a relatively simple overall reaction such as the combustion of CH4 and O2 can be very complicated at the... 

Another piece of information available concerns the surface intermediates. By using the l C labelling and by monitoring the reaction of a molecule which is an "archtype" for two types of complexes the following has been established (31-33) i) dilution of Pt by Cu increases the relative contribution to isomerization of the 5-C-intermediates (something like an adsorbed methylcyclo-pentane) in comparison with that of 3C-intermediates. ii) The contribution of various types of the 3C-(ay) and 2C-(aB) intermediates to the overall reaction is independent of the Cu-content, but with Cu increasing, the proportion increases to which the 3C-(ay) intermediates are hydrogenolysed (as compared with their isomerization). 

In the absence of K the enzyme exhibits a basal Mg -ATPase activity that can be reduced, but not completely removed, upon further purification of the enzyme by free-flow or zonal electrophoresis [66,89]. Wallmark et al. [104] demonstrated that the rate of spontaneous breakdown of phosphoenzyme corresponded very well to the Mg -ATPase activity at low ATP concentrations, implying that this activity was not due to a contaminating Mg -ATPase with a reaction path independent of the phosphoenzyme. This conclusion was confirmed by Reenstra et al. [129] in a study on the nonhyperbolic ATP dependence of ATPase activity and phosphoenzyme... 

The operation of these hydrolytic reactions is independent of the oxygen concentration of the system so that—in contrast to biotic degradation and transformation—these reactions may occur effectively under both aerobic and anaerobic conditions. 

Figure 6.7 shows a typical special feature of the polarization curves. In the case of reversible reactions (curve 1), the anodic and cathodic branches of the curve form a single step or wave. In the case of irreversible reactions, independent, anodic and cathodic, waves develop, each having its own inflection or half-wave point. The differences between the half-wave potentials of the anodic and cathodic waves will be larger the lower the ratio fH. ... 

Returning to the example sequence in Scheme 4.7 and using the minimum values of AE determined and setting the reaction yields also as minimum values, it is possible to evaluate the probabilities that each reaction will have an RME of at least 0.618 and also the probability that both reactions will achieve it simultaneously. Figures 4.10 and 4.11 illustrate the relevant regions in the graphs. We can conclude that the probabilities for the Petasis condensation and the coupling reaction are 77% and 94%, respectively. Since the reactions are independent of each other, that is, the individual probabilities are mutually exclusive, the combined probability that both reactions will have RME values of at least... 

The value of the equilibrium constant, K, for any reaction is independent of (i) the actual quantities of the substances involved, (ii) the direction from which the equilibrium is attained, (iii) the presence of inert substances, and (iv) the presence of a catalyst. However, it depends upon certain factors as indicated in the following ... 

The above equation implies that the half-life of a first-order reaction is independent of concentration. This result in only true for a first-order reaction. 

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