Yield ratio equations

For elucidation of networks, yield-ratio equations are much more convenient than rate equations. The (instantaneous) yield ratio PpQ is defined as the ratio of the molar conversion rates of a reactant to products P and Q ... 

The principal application of yield ratio equations is in network elucidation, to be discussed in Section 7.3.2. An additional example will be given in that context. Further examples for establishment of yield ratio equations and their application in network elucidation can be found in Temkin s book on reaction networks [24], although not under that name. Also, in mathematical modeling, simple algebraic yield ratio equations can sometimes be substituted for rate equations, which may be differential (see Section 11.2). 

For elucidation of all but quite small networks, rate equations are too unwieldy even if the network is simple. Here, the much more compact yield ratio equations are a better tool. These can also profitably be used to replace rate equations in modeling. 

The procedure of arriving at a probable mechanism via an empirical rate equation, as described in the previous section, is mainly useful for elucidation of (linear) pathways. If the reaction has a branched network of any degree of complexity, it becomes difficult or impossible to attribute observed reaction orders unambiguously to their real causes. While the rate equations of a postulated network must eventually be checked against experimental observations, a handier tool in the early stages of network elucidation are the yield-ratio equations (see Section 6.4.3). This approach relies on the fact that the rules for simple pathways also hold for simple linear segments between network nodes and end products. 

Yield ratio equations assume simple forms if product formation is irreversible. If it is not, the equations for irreversible formation are reasonable approximations at very low conversions. Equations for products arising from the same or different network nodes were given in Section 6.4.3. The procedure of application will be illustrated here. 

The yield ratio equations, obtained as ratios of the segment coefficients according to eqn 6.38, are shown with the respective networks in Table 7.4 (preceding page). For network I, the yield ratio is proportional to the partial pressure of H2. In the other three cases, the yield ratio is seen to depend only on the H2-to-CO ratio, not on total pressure at same H2-to-CO ratio. However, the dependence on that ratio differs. For network II it is of the form... 

Stoichiometric constraints and yield ratio equation. The stoichiometric constraints are... 

Two variables of primary importance, which are interdependent, are reaction temperature and ch1orine propy1ene ratio. Propylene is typically used ia excess to act as a diluent and heat sink, thus minimising by-products (eqs.2 and 3). Since higher temperatures favor the desired reaction, standard practice generally involves preheat of the reactor feeds to at least 200°C prior to combination. The heat of reaction is then responsible for further increases in the reaction temperature toward 510°C. The chlorine propylene ratio is adjusted so that, for given preheat temperatures, the desired ultimate reaction temperature is maintained. For example, at a chlorine propylene molar ratio of 0.315, feed temperatures of 200°C (propylene) and 50°C (chlorine) produce an ultimate reaction temperature of approximately 500°C (10). Increases in preheat temperature toward the ultimate reactor temperature, eg, in attempts to decrease yield of equation 1, must be compensated for in reduced chlorine propylene ratio, which reduces the fraction of propylene converted and, thus aHyl chloride quantity produced. A suitable economic optimum combination of preheat temperature and chlorine propylene ratio can be readily deterrnined for individual cases. 

Durst and coworkers were the first to report the condensation of chiral a-sulphinyl carbanions with carbonyl compounds477. They found that metallation of ( + )-(S)-benzyl methyl sulphoxide 397 followed by quenching with acetone gives a mixture of dia-stereoisomeric /i-hydroxy sulphoxides 398 in a 15 1 ratio (equation 233). The synthesis of optically active oxiranes was based on this reaction (equation 234). In this context, it is interesting to point out that condensation of benzyl phenyl sulphoxide with benzaldehyde gave a mixture of four / -sulphinyl alcohols (40% overall yield), the ratio of which after immediate work-up was 41 19 8 32478. 

Sulfinyldiene 40 reacts, regio- and stereo selectively, with methylacrylate in the presence of a catalyst, affording carbomethoxycyclohexene derivatives [45]. Among the catalysts examined, the best was lithium perchlorate used as a suspension in DCM it gave only endo isomers in 70% yield in a 96 4 d.e. ratio (Equation 3.11). 

Sulphines may react as dienophiles with 1,3-dienes with the formation of cyclic sulphoxides. Unstable 2,2-dichloro-5,6-dihydro-2ff-thiin-l-oxide 191 was formed in an exothermic reaction between 173aandcyclopentadieneat — 40 (equation 101). The simplest, parent sulphine, CH2 = S = O, prepared in situ by treatment of a-trimethylsilylmethanesulphinyl chloride with cesium fluoride, reacts with cyclopentadiene to give bicyclic, unsaturated sulphoxide 192 as a mixture of two diastereoisomers in a 9 1 ratio (equation 102). On the other hand, a,j8-unsaturated sulphine 193 (generated by thermolysis of 2-benzylidene-l-thiotetralone dimer S-oxide) in boiling toluene behaves as a 1,3-diene and was trapped by norborene forming sulphoxide 194 in 78% yield ° (equation 103). 

Gosselin and colleagues169 prepared Karahana ether (264), starting with an asymmetric Diels-Alder reaction between chiral diene 261 and maleic anhydride. This reaction yielded diastereomers 262 and 263 in a 1 4 ratio (equation 72). 

In contrast with the metal-free cycloaddition again, the efficiency of metal mediated cycloaddition reactions is relatively insensitive to the electronic nature of the reactants. This has been nicely demonstrated by Rigby and colleagues305 who treated complex 494 with a 1 1 mixture of methyl sorbate (502) and 1-trimethylsilyloxy-l,3-butadiene (50). The reaction proceeded in 90% yield and afforded 503 and 504 in a 46 54 ratio (equation 146). 

The (V-Boc-l,3-oxazolidine 173 was deprotonated at the 2-position by i-BuLi/(—)-sparteine (11) and added to benzaldehyde to yield a synlanti mixture of hydroxybenzyl derivatives 174 with good enantiomeric ratios (equation 40) . The synlanti-ratio is improved by magnesium-lithium exchange. The major enantiomers arise from the substitution of the pro-S-H in 173. 

It has been demonstrated by Pancrazi, Ardisson and coworkers that an efficient kinetic resolution takes place when an excess (2 equivalents) of the racemic titanated alkenyl carbamate rac-334a (R = Me) is allowed to react with the enantiopure )-hydroxyaldehyde 341 or alternatively the corresponding y-lactol 340, since the mismatched pair contributes to a lower extent to the product ratio (equation 91) . Under best conditions, the ratio of the enantiomerically pure diastereomers 3,4-anti-4,5-syn (342) and 3,4-anti-4,5-anti (343) is close to 14 1. Surprisingly, approximately 9% of the iyw,iyw-diastereomer 344 resulted when the starting (ii)-crotyl carbamate was contaminated by the (Z)-isomer. The reasons which apply here are unknown. Extra base has to be used in order to neutrafize the free hydroxy group. The pure awft, awfi-product 345 was obtained with 85% yield from the reaction of the (W-oxy-substituted titanate rac-334b and lactol 340. 345 is an intermediate in the asymmetric synthesis of tylosine . ... 

Cycloadditions with monosubstituted oleflns proceed rapidly and regioselectively to yield the 5-substituted dihydroisoxazoles. Thus, addition of styrene to nitrile oxide 164, formed from oxime 163, results in the formation of the 5-phenyl- 165 and 4-phenyldihy-droisoxazoles 166 in a 99 1 ratio (equation 72) ° °. ... 

Fluoride ion catalyzed 1,3-dipolar cycloaddition of bromo nitrile oxide, obtained in situ from dibromoformaldehyde oxime 184, to nonactivated alkynes provides a new approach to the synthesis of neuroactive isoxazoles. However, the regioselectivity of cycloaddition in this case is not high—products 185 and 186 are obtained in a 1 1 to 1 1.4 ratio (equation 80). Cycloaddition reaction of hydroximoyl chlorides and acetylene was snc-cessfully carried out also in the presence of NaHCOs as a base. For instance, a-keto oximes 187 were reacted with acetylene and NaHCOs to give isoxazoles 188 in good yields (equation 81). 

Investigations similar to the ones just mentioned have focussed on (trimethylgermyl) (trimethylsilyl)carbene 3441. Photolysis of diazo compound 33 in MeOD yielded a mixture of methoxysilane 37 and methoxygermane 38 in a 79 21 ratio (equation 8). This result suggests that carbene 34 underwent a 1,2(Si C) and a l,2(Ge -C) methyl shift... 

An intriguing variant of this coupling process was reported in 1995. Treatment of acetone with SmD in the presence of 42 resulted in the formation of allene 43 in 81% yield and a 5.7 1 diastereomeric ratio (equation 25)74. Although no mechanism was suggested, it is likely that the reaction involves addition of (CH3)2C=0 to the terminal alkyne,... 

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