Equimolarity

The use of an excess of ammonia is home out in practice. A mole ratio of ammonia to ethylene oxide of 10 1 3delds 75 percent monoethanolamine, 21 percent diethanolamine, and 4 percent triethanolamine. Using equimolar proportions under the same reaction conditions, the respective proportions become 12, 23, and 65 percent. 

Heuristic 4 Favor near-equimolar splits between top and bottom products in individual columns. 

It is interesting to note that this is the sequence that would have been obtained had only heuristic 4 been used (favor near-equimolar splits between top and bottom products) throughout. 

Diffusivity measures the tendency for a concentration gradient to dissipate to form a molar flux. The proportionality constant between the flux and the potential is called the diffusivity and is expressed in m /s. If a binary mixture of components A and B is considered, the molar flux of component A with respect to a reference plane through which the exchange is equimolar, is expressed as a function of the diffusivity and of the concentration gradient with respect to aji axis Ox perpendicular to the reference plane by the fpllqvving relatipn 6 /... 

Fig. IV-20. Film pressure-area plots for cerebronic acid (a long-chain a-hydroxy carboxylic acid) and cholesterol (see insert) and for an equimolar mixture. At low pressures the r-a plot is close to that of the average (dashed line), an unanticipated kink then appears, and finally, the horizontal portion probably represents ejection of the cholesterol. (From Ref. 239.)...

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

The previous seetion showed how the van der Waals equation was extended to binary mixtures. However, imieh of the early theoretieal treatment of binary mixtures ignored equation-of-state eflfeets (i.e. the eontributions of the expansion beyond the volume of a elose-paeked liquid) and implieitly avoided the distinetion between eonstant pressure and eonstant volume by putting the moleeules, assumed to be equal in size, into a kind of pseudo-lattiee. Figure A2.5.14 shows sohematieally an equimolar mixture of A and B, at a high temperature where the distribution is essentially random, and at a low temperature where the mixture has separated mto two virtually one-eomponent phases. 

Figure A2.5.14. Quasi-lattice representation of an equimolar binary mixture of A and B (a) randomly mixed at high temperature, and (b) phase separated at low temperature.

The advantage of the method, readily seen from the equation, is that the other products of the reaction are gaseous and escape. Hence equimolar quantities of reactants are used. 

The creatmenc of the boundary conditions given here ts a generali2a-tion to multicomponent mixtures of a result originally obtained for a binary mixture by Kramers and Kistecnaker (25].These authors also obtained results equivalent to the binary special case of our equations (4.21) and (4.25), and integrated their equations to calculate the p.ressure drop which accompanies equimolar counterdiffusion in a capillary. Their results, and the important accompanying experimental measurements, will be discussed in Chapter 6 ... 

Condition (iv). For equimolar counter diffusion in a binary mixture, the... 

In equimolar mixtures of nitric acid and water a monohydrate is formed whose Raman spectrum has been observed. There is no evidence for the existence of appreciable concentrations of the nitric acidium ion in aqueous nitric acid. 

Vandoni and Viala examined the vapour pressures of mixtures of nitric acid in acetic anhydride, and concluded that from o to mole-fraction of nitric acid the solution consisted of acetyl nitrate, acetic acid and excess anhydride in equimolar proportions the solution consisted of acetyl nitrate and acetic acid, and on increasing the fraction of nitric acid, dinitrogen pentoxide is formed, with a concentration which increases with the concomitant decrease in the concentration of acetyl nitrate. 

In addition to the initial reaction between nitric acid and acetic anhydride, subsequent changes lead to the quantitative formation of tetranitromethane in an equimolar mixture of nitric acid and acetic anhydride this reaction was half completed in 1-2 days. An investigation of the kinetics of this reaction showed it to have an induction period of 2-3 h for the solutions examined ([acetyl nitrate] = 0-7 mol 1 ), after which the rate adopted a form approximately of the first order with a half-life of about a day, close to that observed in the preparative experiment mentioned. In confirmation of this, recent workers have found the half-life of a solution at 25 °C of 0-05 mol 1 of nitric acid to be about 2 days. ... 

Although Strike found most of these articles on Strike s own, our good friend and learned scholar Osmium emailed Strike some of the above group s articles and quite a few more that we will get at in just a bit. The following methods can be read about in the original articles in which they were published [49-51]. But there is a nice review by the same authors in which a representative example of each of their methods is included [52]. The following were taken from that review. X and speed chemists just substitute an equimolar amount of their respective p-Nitropropene for the one in the methods below. Also, it should be obvious that these reduction methods will work just fine on 2CB and other phenethylamine intermediates. 

METHOD 5 Contributed by Osmium [53], The paper reads (at least to Strike) that this reduction method can work to reduce the formyl intermediate made in the Leuckart reaction directly into MDMA instead of needing to hydrolyze to MDA with HCi (don t ask). For this reaction one substitutes an equimolar amount of p-Nitropropene for the 3,4-dimethoxybenzylcyanide in the representative experimental below ... 

So if one were to replace sec-butyl alcohol in the recipe above with an equimolar amount of safrole in the above reaction, Strike will wager that a positive bromination experience will occur. And all this using the very common 48% aq. HBr The oniy difference being that once the reaction mix had cooled, one should do either of two things (1) distill as described except the bromosafrole will be the last thing to come over (not the first), or (2) flood the reaction mix with water to bring the product out of solution after which it can be physically separated by decanting or sep funnel or some such shit. 

Esters are alkylated in the presence of strong bases in aprotic solvents. A common combination is LDA in tetrabydrofuran at low temperatures. Equimolar amounts of base are sufficient and only the mono-carbanion Js formed. After addition of one mole of alkyl halide the products form rapidly, and no dialkylation, which is a problem in the presence of excess base, is possible. Addition of one more mole of LDA and of another alkyl halide leads to asymmetric dialkylation of one or-carbon atom in high yield (R.J. Cregge, 1973). 

The preparative method for the Pd(0) catalyst active in these regioselective eliminations under mild conditions is crucial. The very active catalyst is prepared by mixing equimolar amounts of Pd(OAc) or Pd(acac)2 and pure n-... 

Syntheses of a,)3-dihalogenoethers can be achieved in various ways the classical method (37), wherein a current of dry gaseous hydrochloric acid, is made to react in an equimolar mixture of ethanol and aldehyde at 20°C first to form the monochloroether (50% yield) and then by the action of bromine, the dibromoether (80 to 90% yield) can be used. The second and simpler method is the direct bromination of ethylvinylether in a chloroformic or dioxane solution if the product is used directly without purification,... 

These products are used as starting material for the preparation of 2-substituted thiazol-4-ylacetic acids. a-Benzoyloxythiopropionamide and a-benzoyloxy-a-benzoylthioacetamide condensed with an equimolar amount of an a-haloketone in alcoholic solution yield the following compounds (409, 419, 569) 24, Rj = CH3, PhCO, R2 = Me... 

The reaction can be carried out in two steps (641). First, equimolar amounts of amide and phosphorus pentasulfide are mixed under stirring in dioxane, the temperature being kept below 45°C. After 20 minutes, the a-halocarbonyl compounds (in dioxane solution) are added in small portions. At the end of the addition the temperature reaches 80 to 100°C, and the reaction mixture is kept at this temperature for another hour. 

Of all the methods described for the synthesis of thiazole compounds, the most efficient involves the condensation of equimolar parts of thiourea (103) and a-haloketones or aldehydes to yield the corresponding 2-aminothiazoles (104a) or their 2-imino-A-4-thiazoline tautomers (104b) with no by-products (Method A, Scheme 46). 

The normal acid chloride is obtained by reaction between equimolar quantities of acid and thionyl chloride in the presence of pyridine at 0 C. 

A dihaloalkene is an intermediate and is the isolated product when the alkyne and the halogen are present m equimolar amounts The stereochemistry of addition is anti... 

Give the structure of an ester that will yield a mixture contain mg equimolar amounts of 1 propanol and 2 propanol on reduction with lithium aluminum hydride... 

Digestion of the tetrapeptide of Problem 27 13 with chy motrypsin gave a dipeptide that on ammo acid analysis gave phenylalanine and valine in equimolar amounts What ammo acid sequences are possible for the tetrapeptide ... 

Barnett and colleagues developed a new method for determining the concentration of codeine during its extraction from poppy plants. As part of their study they determined the method s response to codeine relative to that for several potential interferents. For example, the authors found that the method s signal for 6-methoxycodeine was 6 (arbitrary units) when that for an equimolar solution of codeine was 40. 

Since equimolar concentrations of analyte and interferent were used (Ca = Cl), we have... 

Perhaps the most obvious limitation imposed by Ks is the change in pH during a titration. To see why this is so, let s consider the titration of a 50 mb solution of 10 M strong acid with equimolar strong base. Before the equivalence point, the pH is determined by the untitrated strong acid, whereas after the equivalence point the concentration of excess strong base determines the pH. In an aqueous solution the concentration of H3O+ when the titration is 90% complete is... 

The titration of a mixture ofp-nitrophenol (pfQ = 7.0) and m-nitrophenol pK = 8.3) can be followed spectrophotometrically. Neither acid absorbs at a wavelength of 545 nm, but their respective conjugate bases do absorb at this wavelength. The m-nitrophenolate ion has a greater absorbance than an equimolar solution of the p-nitrophenolate ion. Sketch the spectrophotometric titration curve for a 50.00-mL mixture consisting of 0.0500 M p-nitrophenol and 0.0500 M m-nitrophenol with 0.100 M NaOH, and compare the curve with the expected potentiometric titration curves. 

Of course, in reactions (5.A) and (5.B) the hydrocarbon sequences R and R can be the same or different, contain any number of carbon atoms, be linear or cyclic, and so on. Likewise, the general reactions (5.C) and (5.E) certainly involve hydrocarbon sequences between the reactive groups A and B. The notation involved in these latter reactions is particularly convenient, however, and we shall use it extensively in this chapter. It will become clear as we proceed that the stoichiometric proportions of reactive groups-A and B in the above notation—play an important role in determining the characteristics of the polymeric product. Accordingly, we shall confine our discussions for the present to reactions of the type given by (5.E), since equimolar proportions of A and B are assured by the structure of this monomer. 

For a fixed extent of reaction, the presence of multifunctional monomers in an equimolar mixture of reactive groups increases the degree of polymerization. Conversely, for the same mixture a lesser extent of reaction is needed to reach a specified with multifunctional reactants than without them. Remember that this entire approach is developed for the case of stoichiometric balance. If the numbers of functional groups are unequal, this effect works in opposition to the multifunctional groups. 

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