Quantitative equation

Esters of acetylenedicarboxylic acid 1023 are commercially readily available, are very reactive as dipolarophiles, and the carboxylic groups in products of their reactions can be easily converted to many other functionalities. Therefore, they are often the first choice as substrates for 1,3-dipolar cycloaddition to azides 1024 (Huisgen reaction). The reactions are carried out at room or elevated temperature, and the yields of 1,2,3-triazoles 1025 are usually high to quantitative (Equation 22). Several products obtained in this way are presented as structures 1026-1034. Some details about the reactions leading to these products are given in Table 10. 

Ferric sulphate is a mild oxidant and is non-reactive with the steroid substrate. It liberates iodine quantitatively (equation 76), and the iodine is extracted into CH2CI2 and consumed as in equation 75. 

Dinuclear palladium complexes catalyze m-hydroarylation of alkynes with arenes.56 The reaction of 3-hexyne with benzene in the presence of a dinulear palladium complex Pd2R2(M-OH)(//-dpfam) [dpfam = j/V,Ar -bis[2-(diphenyl-phosphino)phenyl]formamidinate, R=/>-Tol] and tri(/z-butyl)borane at 100 °C for 4h affords ( )-3-phenyl-3-hexene quantitatively (Equation (53)). The hydroarylation of 3-hexyne with monosubstituted benzenes ( )-3-aryl-3-hexenes with a 2 1 ratio of the meta- and ra -isomers. This regioselectivity is different from that of the hydroarylation of diphenylacetylene catalyzed by Rh4(GO)12.57... 

The presence of electron-donating substituents in the diene enables it to react with simple aldehydes thus both acetaldehyde and benzaldehyde add to 1-methoxy-1,3-butadiene at 50-65 °C under high pressure (20 Kbar) to give dihydropyrans as 70 30 mixtures of cis- and frans-isomers (equation 5)4. The combination of electron-rich diene/electron-poor dienophile makes it possible to perform the reaction under milder conditions. 2-Alkyl-l-ethoxy-1,3-butadienes and diethyl mesoxalate afford dihydropyrans almost quantitatively (equation 6)5. 

The question now remains, can a transformation matrix be found that converts these E and C numbers into a set that is appropriate The algebra involved is tedious, and we can use a comparable approach which shows that the HSAB concept is incomplete. That this is so and the extent to which the HSAB concept fails as a quantitative model can be shown by converting the HSAB concept as qualitatively applied to a quantitative equation and attempting to fit enthalpy data to it. If a transformation matrix exists, our least squares program will find it and fit the data as well as our E and C equation does. 

It has proved possible actually to isolate the valence bond isomers from photolysis of some perfluoropyridines. Irradiation of (289) gives pentakis(pentafluoroethyl)-l-azabicyclo[2.2.0]hexa-2,5-diene (290), a colourless liquid (b.p. 176 °C), almost quantitatively (equation 186). Further irradiation gives pentakis(pentafluoroethyl)-l-azaprismane (291) which is also a stable colourless liquid (73JCS(Pl)l542). The remarkable stability of these products has been attributed in part to relief of steric strain when the planar adjacent bulky pentafluoroethyl groups take up a nonplanar position in the valence isomers. 

The lactonization of o-iodobenzyl alcohol 311 was performed in the presence of PdCl2[(P(OEt)3]2 (0.02 mol%) and triethylamine (2.2 equiv.) at 130°C and 5 atm of CO in SCCO2 (200atm) to give phthalide 312 quantitatively (Equation (28)). " In this reaction, the turnover number (TON) in SCCO2 reached 5000 after 18h, which was considerably better than that in toluene (3800). Moreovet, the reaction in SCCO2 reached 4700 TON after 6h as compared to only 1100 TON for that in toluene. 

While both hydrogenation and epoxidation reactions of (7) (and substituted forms) occur on the oxepin valence tautomer, cycloaddition reactions proceed more readily on the arene oxide form (where the diene is closer to planarity). Thus the dienophiles DM AD and maleic anhydride (MA) readily yielded [4 + 2] cycloadducts with (7) as shown in Scheme 22 (67AG(E)385). A similar type of singlet oxygen cycloaddition reaction gave an unstable endoperoxide (106) which upon heating yielded trans-benzene trioxide quantitatively (equation 14). (75JOC3743). 

However, when one gets down to detailed quantitative equations to represent real, actual reactions with several steps in consecutive sequence, the mathematics become very complex. Thus, the change in the limiting current with time introduces complications that one tries to avoid in other transient methods by working at low times (constant current or constant potential approaches) or at times sufficiently high that the current becomes entirely diffusion controlled. However, taking into account the... 

The treatment of ionic diffusion properties is a more difficult task. The obstruction effect of the polymer matrix can be represented by a number of semi quantitative equations, the most popular of which is 111 ... 

Intramolecular substitution for chloride or fluoride is particularly effective. Oxygen heterocycles with fused benzo rings are obtained from Cr(CO>3 complexes of fluorobenzene with an o-(hydroxyalkyl) side chain.39,60 For example, complexation of 3-(2-fluorophenyl)-l -propanol with [Cr(CO>3(pyridine)3] at 25 C in ether (promoted by BF3 Et20) followed by reaction in DMSO with excess potassium f-butoxide for 3 h at 25 C gave the chroman complex (14).60 The yield in the cyclization step was 75% and iodine decomplexation was quantitative (equation 12). Efforts to produce the dihydrobenzofuran under the same... 

Cathodic reduction of 1,1,1 -trimethyl-2,2,2-triphenyldisilane under constant current in MeCN provides triphenylsilane quantitatively (equation 55). The reaction involves an electrochemically initiated chain reaction73. The source of oxygen in (Me3Si)20 may be the residual water in acetonitrile. 

Find a quantitative equation that can be used to predict the yield at various operating conditions. 

Multiple regression can be used to develop a quantitative equation relating a dependent variable with several independent variables. In multiple linear regression, any number of independent variables may be considered ... 

Treatment of the l-benzyl-2-benzotelluropyrylium salts 55 with base, or even upon alumina column chromatography, leads to deprotonation affording the corresponding exocyclic (Z)-olefin 56 quantitatively (Equation 19)... 

Equation (25.7) now gives an expression for the rate of change of pressure with temperature (= dP/dT ) which corresponds to the gradient of the line representing the solid-liquid equilibrium in the phase diagram (gradient of AD Figure 25.1). This quantitative equation (25.7) now enables us to rationalise that since ... 

A reaction of acetyldimethylphenylsilane 166 with TBAF 3II20 in THF or with KF in DMS0/H20 gave [Me2SiO]v (167) and 1-phenylethanol 168 quantitatively (equation 100). The reaction was considered to involve a 1,2-phenyl shift followed by a Brook rearrangement (equation 101 )229. 

C4F9C2H4), are highly fluorophilic and exhibit large partition coefficients in favor of fluorocarbon solvents over common organic solvents due to a double-layered structure where the stannoxane core is covered by fluoroalkyl groups. Fluorous technology allows transesterification and esterification in which 100% yield of the desired esters is achievable with reactants in a strict 1 1 ratio. The tin catalysts are recovered from the fluorous phase quantitatively (Equation (95)).260... 

The sites where Ps can become trapped and decay in solids correspond to pre-existing voids, whether of intrinsic or extrinsic origin. A quantitative equation has been established, which has proven to be reliable in many cases, correlating X3 with the radius (R) of the supposedly spherical trap ... 

Imino-l,3-selenazolidin-4-one derivatives 37 were synthesized by the reaction of A, A -disubstituted selenoureas with a-haloacyl halides in the presence of pyridine in excellent yields (88% - quantitative) (Equation 20). Reaction of an A, A -unsubstituted selenourea gives 2-amino-4,5-dihydro-l,3-selenazolidin-4-one 32 in low yield (29%) (Equation 21) <2002S195>. 

Treating 19 with 2 mol equiv of benzylthiol generated the selenide 109 quantitatively (Equation 20) <2004AGE1268>. 

Most of the reactions where a side bond of bicyclobutane is formed involve the insertion of a carbenoid generated from a geminate dibromocyclopropane into a P-C-H bond. In some cases the yield of these reactions is almost quantitative (equation 8) . ... 

Mild dehydrating agents are available in yneamines and 1-alkoxyalkynes. They have been applied occasionally to the preparation of acid anhydrides.The great advantage of these reagents is that the reaction takes place under neutral conditions and, therefore, acid anhydrides of acid sensitive compounds can be obtained. An extension of this approach was described recently. Trimethylsilyl-ethoxyacetylene, which can be prepared from ethoxyacetylene, serves as a very mild dehydrating agent.By means of this compound various types of acid sensitive carboxylic acid anhydrides can be made quantitatively or almost quantitatively (equation 40). Some examples are collected in Table 11. 

In cyclic systems like (171), (173), (175) and (177) strain arguments are even more important. All four acids form the lactones only on heating to >130 °C, but the yields reflect the highly different ring strain encountered the most favorable diequatorial lactone (172) is formed quantitatively (equation 61), whereas the strained diastereomers (174), U76) and (178) form reluctantly (equations 62-64). The ring clo-... 

Thiiranimine (123) is unusually cleaved at the long S—C bond. Thus, when a chloroform solution of (123) is allowed to stand at room temperature for 3 days, the benzo[6]thiophene (124) is obtained in quantitative yield (Scheme 48) <78AG(E)195>. A similar reaction occurs in imine-conjugated thiiranimine (125) <77AG(E)722>. Thiiranimine (125) isomerizes to 2-alkylidene-l,3,4-thiadiazoline (126) in chloroform quantitatively (Equation (21)) (90TL3571,93T1189). 

The reader should note that cp and p are modified inertial impaction numbers based on the cake and fabric, respectively. Unfortunately, this key equation has been totally ignored by responsible EPA individuals in this field. Taxpayers dollars continue (for over a dozen years) to be provided to contractors whose research efforts have produced little, if any, usable results in developing quantitative equations to describe collection efficiency. 

Simple imines undergo Diels-Alder reactions in the presence of suitable catalysts. Lanthanide triflates, which are stable in water, are especially effective. Thus in the presence of 10 mol% of ytterbium or scandium triflate, Danishefsky s diene 4 reacts with benzylideneaniline in acetonitrile at 0 °C to give the dihydropyridone 76 quantitatively (equation 50) analogous products are obtained from 4 and furylideneaniline, benzyli-denebenzylamine and pentyIidenebenzylamine. In a one-pot version of the reaction, a mixture of an aldehyde, an amine and the diene 4 in acetonitrile containing magnesium sulfate is treated with 10 mol% ytterbium triflate to afford the dihydropyridone in ca 80% yield. Even phenylglyoxal monohydrate can be employed. ... 

Correlation of Xa2 with Pore Blocking for Benzene-Water Data. The blocking of the pores on the membrane surface by the preferentially sorbed solute, which was discussed qualitatively in the preceding section, is now treated more quantitatively. Equation 4 was used to estimate the appropriate k value for each cell. The diffuslvlty of the solute in water was estimated by the method of Wilke and Chang (27), and the diffusivity of sodium... 

---