One-Step Reactions

The transport equations for the three chemical species have the form 

The reaction coefficient matrix T for this case is rank one. Thus, a linear transformation can be found that generates one reacting scalar and two conserved scalars. Moreover, if the flow system has only two inlet streams, and the initial conditions are a linear mixture of the 

As discussed in Section 5.1, the extension to non-isothermal conditions is straightforward under the assumption that the thermodynamic properties are constant. 

As shown above, a linear relationship between c and (Co, Y, f) can easily be derived starting from (5.162) by letting y = A0B0/(Bq + r Aq) 93 

Note that the reaction-progress variable is defined such that 0 Y 1. However, unlike the mixture fraction, its value will depend on the reaction rate k = kB0. The solution to the reacting-flow problem then reduces to solving two transport equations  

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The Diels-Alder cycloaddition is one example of a pencyclic reaction, which is a one step reaction that proceeds through a cyclic transition state Bond formation occurs at both ends of the diene system and the Diels-Alder transition state involves a cyclic array of six carbons and six tt electrons The diene must adopt the s cis conformation m the transition state... 

Hydrazine as Nucleophile. Reaction of hydrazine and carbon dioxide or carbon disulfide gives, respectively, hydrazinecarboxyhc acid [471-31-8], NH2NHCOOH, and hydrazinecarbodithioic acid [471-32-9], NH2NHCSSH, in the form of the hydrazinium salts. These compounds are useful starting materials for further synthesis. For example, if carbon disulfide reacts with hydrazine in basic medium with an alkyl haUde, an alkyl dithiocarbazate ester is obtained in a one-step reaction ... 

Reaction measurement studies also show that the chemistry is often not a simple one-step reaction process (37). There are usually several key intermediates, and the reaction is better thought of as a network of series and parallel steps. Kinetic parameters for each of the steps can be derived from the data. The appearance of these intermediates can add to the time required to achieve a desired level of total breakdown to the simple, thermodynamically stable products, eg, CO2, H2O, or N2. 

Saponification can proceed direcdy as a one-step reaction as shown above, or it can be achieved indirectly by a two-step reaction where the intermediate step generates fatty acids through simple hydrolysis of the fats and oils and the finishing step forms soap through the neutralization of the fatty acid with caustic soda. There are practical considerations which must be addressed when performing this reaction on a commercial scale. 

Another process involves a one-step reaction of isobutylene with formaldehyde and acetone under high temperature and pressure (eq. 2) (20). a-MethyUieptenone (2) (6-methyIhept-6-en-2-one [10408-15-8]) is the product, but it is easily catalyticaHy isomerized to P-methyUieptenone (21,22). Unconverted isobutylene and acetone can be recycled to the process, thus making it commercially viable (23,24). Variations of this process have also been described in the Hterature (25—28). 

The mechanism of the reaction is unknown. The stereospecificity observed with (E)- and (Z)-l-methyl-2-phenylethylene points to a one-step reaction. The very low Hammett constant, -0.43, determined with phenylethylenes substituted in the benzene ring, excludes polar intermediates. Yields of only a few percent are obtained in the reaction of aliphatic alkenes with (52). In the reaction of cyclohexene with (52), further amination of the aziridine to aminoaziridine (99) is observed. Instead of diphenylazirine, diphenylacetonitrile (100) is formed from diphenylacetylene by NH uptake from (52) and phenyl migration. 

Iodine azide, on the other hand, forms pure adducts with A -, A - and A -steroids by a mechanism analogous to that proposed for iodine isocyanate additions. Reduction of such adducts can lead to aziridines. However, most reducing agents effect elimination of the elements of iodine azide from the /mwj -diaxial adducts of the A - and A -olefins rather than reduction of the azide function to the iodo amine. Thus, this sequence appears to be of little value for the synthesis of A-, B- or C-ring aziridines. It is worthy to note that based on experience with nonsteroidal systems the application of electrophilic reducing agents such as diborane or lithium aluminum hydride-aluminum chloride may yet prove effective for the desired reduction. Lithium aluminum hydride accomplishes aziridine formation from the A -adducts, Le., 16 -azido-17a-iodoandrostanes (97) in a one-step reaction. The scope of this addition has been considerably enhanced by the recent... 

A one-step reaction has a single transition state such a process is called an elementary reaction. Many observed ( overall ) chemical reactions consist of two... 

Figure l-I. Schematic diagram for a hypothetical one-step reaction. (In this example the final state is of lower energy than the initial state, but this need not be so.)... 

Irradiation of Z-but-2-ene 8 initiates a cyclodimerization reaction, even without a photosensitizer." This cycloaddition proceeds from a singlet state and is likely to be a concerted, one-step reaction. Bond formation occurs suprafacial with respect to both reactants, whereupon only the tetramethylcyclobutanes 9 and 10 can be formed ... 

Consider the cathodic reduction of a hydrated metal ion M (aq.) to a lattice metal atom at the interface M/M (aq.) by a simple one-step reaction... 

Multistep reactions Previous considerations have been based on a simple one-step reaction involving one electron, but if the reaction occurs by a series of steps of which one is significantly slower than all the others, which may be regarded as at equilibrium, and is thus rate determining, equation 20.61 is not valid and becomes... 

These are the coefficients that determine the Tafel slope of the log / against q curve of a multistep reaction, and they are of fundamental importance in providing information on the mechanism of the reaction. Equations 20.86 and 20.87 are of the same form as equations 20.59 and 20.58 that were derived for a simple one-step reaction involving a symmetrical energy barrier, and under these circumstances equations 20.90 and 20.91 simplify to... 

This analysis explains why the rate expression for the two-step mechanism is different from that for the direct, one-step reaction. 

For this reaction, CALB catalyzes the amidation between a racemic P-hydroxyester and racemic amines, leading to the corresponding amide with very high enantiomeric and diastereomeric excesses. Besides, the remaining ester and amine are recovered from the reaction media, also showing good enantiomeric excesses. By this method, three enantioenriched interesting compounds are obtained from an easy one-step reaction. 

Rather than always occurring in one step, reactions in the natural world often result from a series of simple processes between atoms and molecules resulting in a set of intermediate steps from reactants to products. The way multistep reactions occur can have a strong effect on the kinetics of the overall reaction. For instance, in... 

The Marcus equation says that the overall AG for a one-step reaction is ... 

The rate law of a reaction is an experimentally determined fact. From this fact we attempt to learn the molecularity, which may be defined as the number of molecules that come together to form the activated complex. It is obvious that if we know how many (and which) molecules take part in the activated complex, we know a good deal about the mechanism. The experimentally determined rate order is not necessarily the same as the molecularity. Any reaction, no matter how many steps are involved, has only one rate law, but each step of the mechanism has its own molecularity. For reactions that take place in one step (reactions without an intermediate) the order is the same as the molecularity. A first-order, one-step reaction is always unimolecular a one-step reaction that is second order in A always involves two molecules of A if it is first order in A and in B, then a molecule of A reacts with one of B, and so on. For reactions that take place in more than one step, the order/or each step is the same as the molecularity for that step. This fact enables us to predict the rate law for any proposed mechanism, though the calculations may get lengthy at times." If any one step of a mechanism is considerably slower than all the others (this is usually the case), the rate of the overall reaction is essentially the same as that of the slow step, which is consequently called the rate-determining step. ... 

The per acid first adds to the ketone to give adduct (30) which rearranges via a transition state (31) which is electron-deficient around the former carbonyl group. Consequently,the group which can best supply electrons to combat the deficiency migrates best. It does so with retention as it is a one step reaction in which the chiral centre ( in 30) never becomes detached. 

The exchange CD determined by different methods will coincide only in the case of quasi-one-step reactions mentioned above. Thus, when the value of if is so much higher than if that the extreme anodic section cannot be measured and there is no break in the polarization curve, all three methods of determination lead to the same value of if. This implies that step 1 has no effect at all on the kinetics of the overall reaction and that its (high) exchange CD cannot be determined. The same conclusion holds in the opposite case of if [Pg.227]

Consider the case of a quasi-one-step reaction for which step 1 is rate determining at all potentials, while step 2 is in equilibrium. When using the Nemst equation (3.40) for this equilibrium, we hnd that... 

On the contrary, the Lewis acid sites present on the snrface of sepiolite make the Cn/sepiolite catalyst extremely active in promoting the ene reaction of citronellal. Thns, citronellal never accnmnlates in the reaction mixtnre bnt it is com erted into isopulegol as soon as it forms. Hydrogenation of isopnlegol is very slow nnder these reaction conditions, bnt this simple catalyst is able to produce menthol in a one-pot-one-step reaction under very mild experimental conditions. Notably dehydration products, which give account of 40% of the reaction mixture obtained over Ni-H-MCM-41 [4], are kept under 20% over both Cu catalysts. 

Mannich condensations permit one-step reactions to form the following substances from substantially less complex starting materials. Identify a potential starting material that would give rise to the product shown in a single step under Mannich reaction conditions. 

The one-step reaction of H2prCl6] with MeC02Li under 02 in a mixed solvent of acetic acid and acetic anhydride yields the Ir11 binuclear complex [Ir2(/u-02CMe)2Cl2(C0)2].483 Crystal-structure determinations of [Ir2(/x-02CMe)2Cl2(C0)2L2], (295), where L = MeCN, DMSO, and py, are reported. The one-electron oxidation product for (295), L = py, is EPR active at 77 K the odd electron occupies the 6Ir Ir orbital. 

Tc-99 is usually available in the form of an aqueous (NH4)[Tc04] (3) solution or as Tc-metal. Most of the syntheses originally started from one of these two materials. The arrangement of the following sections relates to Tc-compounds which can be synthesized in a one step reaction from one of these two available forms and can be considered, due to their chemical reactivity and the numbers of compounds prepared, as synthons. These precursors either already contain a Tc-carbon bond or allow the convenient formation of such a bond. 

The character of an FCS autocorrelation function for a chemical reaction system depends on the relative rates of reaction and diffusion. It is useful to illustrate this dependence by calculating the autocorrelation functions to be expected for a simple one-step reaction system (Elson and Magde, 1974). We take as an example the simplest possible isomerization within the unfolded state, a single-step isomerization ... 

These one-step reactions display the following characteristics (1) the nitrogen-containing linking reagent is reactive at a relatively low temperature, (2) the reagents should be mixed carefully with the R-chloroborazine in such a way as to prevent the... 

Symmetrical, aniline-based, and aromatic oxo-squaraines are synthesized via a one-step reaction by heating two equivalents of the appropriate /V,/V-dialkylaniline or other reactive aromatic or heteroaromatic derivatives with squaric acid (Fig. 6) [38, 41]. Unsymmetrical aniline-type squaraines can be synthesized in two steps first one component is reacted with squaric acid dichloride to yield a mono-squaraine intermediate, which in a subsequent step is then reacted with the second component to yield the unsymmetrical squaraine dye [53]. 

Chang et al. reported a mild tandem intramolecular hydroamination of yne amines to form an endo-adduct intermediate, which reacts with electron-deficient azides to produce cyclic amidines <06JA12366>. Selected examples of an interesting synthetic route to tropene derivatives 165 via a dual hydroamination strategy is shown below. This one-step reaction makes use of a palladium catalyst and takes place by sequential intermolecular hydroamination of cycloheptatriene with aryl, heteroaryl, and primary alkyl amines to generate intermediate 166, followed by transannular intramolecular hydroamination <06JA8134>. 

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