Statistical mixture products

Final state analysis is where dynamical methods of evolving states meet the concepts of stationary states. By their definition, final states are relatively long lived. Therefore experiment often selects a single stationary state or a statistical mixture of stationary states. Since END evolution includes the possibility of electronic excitations, we analyze reaction products in terms of rovibronic states. 

The synthetic utility of the alkene metathesis reaction may in some cases be limited because of the formation of a mixture of products. The steps of the catalytic cycle are equilibrium processes, with the yields being determined by the thermodynamic equilibrium. The metathesis process generally tends to give complex mixtures of products. For example, pent-2-ene 8 disproportionates to give, at equilibrium, a statistical mixture of but-2-enes, pent-2-enes and hex-3-enes ... 

In order to understand the relationship between the mixture component, physical properties and consumer acceptance of the lipstick, various lipstick formulations have to be produced. The physical properties of each formulation should be studied. The consumer acceptance towards the product also should be investigated. However, only a part of this work will be discussed in this paper. Here, natural waxes, oils and solvent have been used to produce natural ingredient based lipstick formulations based on the formulation suggested by the statistical mixture design. Contour plot and response surface graph were formed in order to understand the relationship between the mixture component and physical characteristic of the lipstick. 

It was synthesized from p-iodoanisole (65) by copper-catalyzed coupling with p-trifluoromethyliodobenzene (66) to give the expected statistical mixture from which unsymmetrical product 67 could be separated. Ether cleavage with HBr and HOAc gave 68 this was then alkylated with the aziridinium ion derived from N-(2-chloroethyl)pyrrolidine, using NaH as base, to complete the synthesis of boxidine (69). 

The two alkenes were so similar electronically and sterically, with the ester group too far away to have any affect on the double bond, that there was very little cross-/self-metathesis selectivity. An approximately statistical mixture of ester 13 and diester 14 was isolated. The high yield of the cross-metathesis product 13 obtained is due to the excess of the volatile hex-l-ene used, rather than a good cross-/self-metathesis selectivity. Although not as predominant as in the reactions involving styrene, trans alkenes were still the major products. 

Porphyrazines are typically synthesized by a templated cyclization of substituted dinitriles, Fig. 2 (2). The most common divalent metal used as the template for this reaction is Mg2+, usually as the butoxide or propoxide, although other group 1(1 A) and 2(IIA) metals have been reported (41). Mixed cyclizations, which utilize two different dinitriles, Fig. 3, in principal, would give a statistical mixture of six different products or isomers. The truly enabling synthetic foundation for modem pz chemistry is the development of strategies directed toward the synthesis... 

Other unsymmetrical aminoporphyrazines have been prepared accordingly. The base-catalyzed cross-condensation of bis(dimethylamino)maleonitrile (99) with 1,2-dicyanobenzene (132) produced a statistical mixture of six possible products that represent hybrids between a heterosubstituted aminoporphyrazine and pc (9). The individual yields of all six products depend on the molar ratio of both starting dinitriles. For instance, a 25 1 ratio of dinitriles 99 and 132 produced mainly pz 133 (35%) along with 100 (Scheme 23). 

If cyclopentene would react pair-wise with 2-pentene, only one product would form, namely 2,7-decadiene, and a similar result for cyclodimers etc. of cyclopentene. If somehow, the alkylidene species would be transferred one by one, we would obtain a mixture of 2,7-nonadiene, 2,7-decadiene, and 2,7-undecadiene in a 1 2 1 ratio. The latter turned out to be the case, which led the authors to propose the participation of metal-carbene (metal alkylidene) intermediates [6], Via these intermediates the alkylidene parts of the alkenes are transferred one by one to an alkene. The mechanism is depicted in Figure 16.4. In the first step the reaction of two alkylidene precursors (ethylidene -bottom- and propylidene -top) with cyclopentene is shown. In the second step the orientation of the next 2-pentene determines whether nonadiene, decadiene or undecadiene is formed. It is clear that this leads to a statistical mixture, all rates being exactly equal, which need not be the case. Sometimes the results are indeed not the statistical mixture as some combinations of metal carbene complex and reacting alkene may be preferred, but it is still believed that a metal-carbene mechanism is involved. Deuterium labelling of alkenes by Gmbbs instead of differently substituted alkenes led to the same result as the experiments with the use of 2-pentene [7],... 

Astatohalobenzenes can be synthesized directly in At recoil (Table III) experiments either via hydrogen replacement by recoil astatine in monohalobenzenes or by halogen replacement in dihalo-benzenes. In the former, total yields range from 5 to 15%, with an almost statistical mixture of ortho-, meta, and para-astatohalobenzene products 145, 150). The production of AtC5H4F from the corresponding CIC6H4F isomers has been achieved with yields of 14% without noticeable isomerization of the products (19). 

Two further stereospecific syntheses of selectively protected a-aminosuberic acid have been reported. One is based on the Kolbe electrolysis of an equimolar mixture of Boc-d-G1u-OtBu and monomethyl glutarate [4-(methoxycarbonyl)butanoate] to produce Boc-d-Asu(OMe)-OtBu 17 which, however, must be isolated from the statistical mixture containing besides the desired product also the two symmetrical dimers 18 and 19 as byproducts (Scheme 7).[2T ... 

As olefin CM is a thermodynamically controlled intermolecular reaction, there are several inherent challenges toward achieving product selectivity. First and foremost, if a catalyst cannot distinguish between the two olefin crosspartners, a statistical mixture of products will result (Scheme 2). In this situation, one of the olefin cross-partners would need to be added to the reaction in excess to achieve a synthetically useful yield (e.g., 10 equiv. required to attain a 91% yield). 

The Claisen Condensation between esters containing a-hydrogens, promoted by a base such as sodium ethoxide, affords 0-ketoesters. The driving force is the formation of the stabilized anion of the P-keto ester. If two different esters are used, an essentially statistical mixture of all four products is generally obtained, and the preparation does not have high synthetic utility. 

Using two different alkyl halides will lead to an approximately statistical mixture of products. A more selective unsymmetric modification is possible if starting materials have different rates of reactivity. 

A third driving force for the observed selectivity, complementing and amplifying copper s choice of the methylated aldehyde, is the preference of iron(II) to incorporate the nonmethylated aldehyde into complexes of type 14. As shown in Scheme 1.16, the addition of iron(II) to a mixture of triamine and both aldehydes gave a product mixture in which nonmethylated and methylated aldehydes are present in a 3 97 ratio following equilibration. Only the two products shown in Scheme 1.16 were observed in the product mixture. The reaction of Scheme 1.16 thus deviates substantially from a statistical mixture of products indeed, only two of the expected four products are observed to form. No evidence was found of complexes incorporating two or three equivalents of methylated aldehyde. 

Intermolecular dimerization has also been effected by a comparable protocol.24-26 Treatment of triethylborane with silver nitrate and sodium hydroxide in water at 25°C led to the rapid evolution of M-butane (72%), ethylene (9%), and ethane (9%). Reaction of two different alkylboranes led to statistical mixtures of dimerized and cross-coupled products. Furthermore, this strategy has been used successfully in the synthesis of olefins from dihydroborated internal acetylenes,27 and in polymerizations of bifunctional organoboron compounds.28... 

In earlier work by Wall and Moore on the decomposition of mixtures of C2ll6 + C2D6 the products were followed by mass-spectrographic analysis. The investigators found some evidence of surface catalysis in packed vessels and found too that NO enhances CII4 production and—contrary to the findings of other workers—is rapidly consumed. Their results were similar for reactions in quartz, pyrex, and KCl-coated vessels. They also found that the H2 produced was an almost statistical mixture of H2, HI), and D2 at all stages of the NO-inhibited reaction except possibly the very... 

The reaction of two acyclic olefins to produce a mix of new products is finding use in organic synthesis. The reaction under many circumstances produces the statistical mixture of products. High yields of the cross product can sometimes be obtained by either stoichiometric control or by the use of functional groups. When unfunctionalized olefins are used in the reaction, all the products are of similar stability and reactivity. Under these conditions, a 1 2 1 mixture of olefins will lead to only a 50% yield of the cross product. However, as shown below, if an excess of one of the olefins is used, the percentage yield based on the minor olefin may be much higher (Eq. 6.14) [1]. 

Hydroboration of acyclic, symmetrical, nonconjugated dienes with one equiv. of 9-BBN-H produces almost statistical mixtures of mono- and di-hydroborated species, but cyclic analogs may show substantial deviations from the statistical mixture. For example, monohydroboration of 1,5-cyclooctadiene occurs to the extent of 85% using 1 1 stoichiometry (equation 31), ° whereas disiamylborane gives predominantly dihydroboration product under such conditions. 

Under equilibrium conditions (thermodynamic control), the allylic source adds to the polarized multiple bond (path AdN). However, the allylic source can also serve as a base and may deprotonate the sink, creating a mixture of sources and sinks and thus a messy statistical mixture of products. Clean products result if the source is just the deprotonated sink or if the sink has no acidic protons. With ketones, the equilibrium of the attack step favors the starting materials, and therefore the reaction goes to completion only if driven by a following elimination. In the next Adisj2 example, the source is the deprotonated sink. The product is an aldehyde-alcohol, or aldol, a name now used for the general process of an enol (acidic media) or enolate (basic) reacting with an aldehyde or ketone. 

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