Theoretical possibilities

As a rule, to determine carbon, nitrogen or oxygen in pure metals, a maximum energy (equal to the kinetic energy of the electrons used to generate bremsstrahlung photons) is chosen between 25 and 35 MeV. In these conditions, the and 0 yields from elements heavier than fluorine are 

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Other chlorinated naphthalenes. The other monochloronaphthalene (2-), the ten theoretically possible dichloronaphthalenes, and the fourteen trichloronaphthalenes have all been prepared, generally from the corresponding amino-derivatives by diazotization and treatment with CuCl. They are of little industrial importance. 

More sophisticated pulse sequences have been developed to detect nuclear modulation effects. With a five-pulse sequence it is theoretically possible to obtain modulation amplitudes up to eight times greater than in a tlnee-pulse experunent, while at the same time the umnodulated component of the echo is kept close to zero. A four-pulse ESEEM experiment has been devised to greatly improve the resolution of sum-peak spectra. 

Calculation of Yield. The yield of a compound obtained in an organic preparation, in addition to being stated in grams, should also be calculated as a percentage of the yield theoretically possible from the weight of the original... 

It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

Although two isomeric esters are theoretically possible, the main product is the 2-ester (formulated above) traces of the isomeric l-ester are eliminated during purification. These derivatives possess a free carboxyl group their equivalent weights may therefore be determined by titration with standard alkali and thus serve as an additional check upon the identity of the compound. 

It is interesting to note that altliough cis-lrans isomerism about the double bond is theoretically possible in cinnamic acid, the Perkin reaction gives rise only to the trans form, m.p. 133°, the cis form, m.p. 68° (termed aHo-cinnamic acid) being unstable and easily converted into the trails acid. 

Each of the following reactions has been reported m the chemical literature and proceeds m good yield What are the principal organic products of each reaction" In some of the exercises more than one diastereomer may be theoretically possible but m such instances one diastereomer is either the major product or the only product For those reactions m which one diastereomer is formed preferentially indicate its expected stereochemistry... 

The equilibrium is more favorable to acetone at higher temperatures. At 325°C 97% conversion is theoretically possible. The kinetics of the reaction has been studied (23). A large number of catalysts have been investigated, including copper, silver, platinum, and palladium metals, as well as sulfides of transition metals of groups 4, 5, and 6 of the periodic table. These catalysts are made with inert supports and are used at 400—600°C (24). Lower temperature reactions (315—482°C) have been successhiUy conducted using 2inc oxide-zirconium oxide combinations (25), and combinations of copper-chromium oxide and of copper and silicon dioxide (26). 

Additioaal components such as alumiaa [1344-28-1] are also added to obtaia more favorable thermodyaamics, and to obtain a slag having favorable properties. Many different feed and slag compositions exist, as do alternative reductants for ferrosiUcon. It is also theoretically possible to manufacture magnesium metal by the reduction of MgO with carbon. 

Ta.utomerism. Although tautomerism is theoretically possible ia amino and hydroxy anthraquiaone dyes, none has been observed. Studies by C nmr have shown convincingly that amino and hydroxy dyes of 9,10-anthraquiaone exist as such. 

Unlike the conservation guaranteed by the first law, the second law states that every operation involves some loss of work potential, or exergy. The second law is a very powerful tool for process analysis, because this law tells what is theoretically possible, and pinpoints the quantitative loss in work potential at different points in a process. 

Table 6 shows the effect of varying coil oudet pressure and steam-to-oil ratio for a typical naphtha feed on the product distribution. Although in these tables, the severity is defined as maximum, in a reaUstic sense they are not maximum. It is theoretically possible that one can further increase the severity and thus increase the ethylene yield. Based on experience, however, increasing the severity above these practical values produces significantly more fuel oil and methane with a severe reduction in propylene yield. The mn length of the heater is also significantly reduced. Therefore, this is an arbitrary maximum, and if economic conditions justify, one can operate the commercial coils above the so-called maximum severity. However, after a certain severity level, the ethylene yield drops further, and it is not advisable to operate near or beyond this point because of extremely severe coking. 

The concept of a 1,5-dipolar cyclization gives rise to a general method for the synthesis of an appreciable number of heterocyclic systems. 1,5-Dipoles are derived from 1,3-dipoles by conjugation with different double bond systems, and it is possible to derive 98 theoretically possible 1,5-dipolar systems. The general expression for a 1,5-dipole and some possible combinations of double bond systems are shown in Scheme 14. 

Two points must be stressed that a 3-R-pyrazole (199a) gives a 1,5-disubstituted derivative (200) and that often the less abundant tautomeric species (Section 4.04.1.5.1) is the more reactive. It is theoretically possible to use the tautomeric composition to direct the synthesis towards one or another derivative. For instance, if (199a) is the more abundant tautomer, the condition to obtain a large proportion of (200) is that The factors... 

Theoretical possible heat removal per pound of air circulated in a cooling tower depends on the temperature and moisture content of air. An indication of the moisture content of the air is its wet-bulb temperature. Ideally, then, the wet-bulb temperature is the lowest theoretical temperature to which the water can be cooled. Practically, the cold-water temperature approaches but does not equal the air wet-bulb temperature in a coohng tower this is so because it is impossible to contact all the water with fresh air as the water drops through the wetted fill surface to the basin. The magnitude of approach to the wet-bulb temperature is dependent on tower design. Important factors are air-to-water contact time, amount of fill surface, and breakup of water into droplets. In actual practice, cooling towers are seldom designed for approaches closer than 2.8°C (5°F). 

The variable that has the most significant impact on the economics of an extractive distillation is the solvent-to-feed (S/F) ratio. For closeboiling or pinched nonazeotropic mixtures, no minimum-solvent flow rate is required to effect the separation, as the separation is always theoretically possible (if not economical) in the absence of the solvent. However, the extent of enhancement of the relative volatihty is largely determined by the solvent concentration and hence the S/F ratio. The relative volatility tends to increase as the S/F ratio increases. Thus, a given separation can be accomplished in fewer equihbrium stages. As an illustration, the total number of theoretical stages required as a function of S/F ratio is plotted in Fig. 13-75 7 for the separation of the nonazeotropic mixture of vinyl acetate and ethyl acetate using phenol as the solvent. 

Coatings of more noble metals than the substrate metal (e.g., Cu on Fe) are only protective when there are no pores. In other cases severe local corrosion occurs due to cell formation (bimetallic corrosion). Cathodic protection is theoretically possible. This protection combination is not very efficient since the coating usually consumes more protection current than the uncoated steel. 

There are two types of impressed current anodes either they consist of anodically stable noble metals (e.g., platinum) or anodically passivatable materials that form conducting oxide films on their surfaces. In both cases, the anodic redox reaction occurs at much lower potentials than those of theoretically possible anodic corrosion. 

A back-pressure (noncondensing) turbine may also be used if there is a profitable use for intermediate-pressure steam. In the unlikely event that large quantities of steam are required, additional high-pressure steam from an external source might be necessary. However, while it is theoretically possible that the amount of heat generated in the nitric acid plant will be insufficient to cover the entire demand, this is not usually a valid concern. 

WASH-740,1957, Theoretical Possibilities and Consequences of Major Nuclear Accidents at Large Nu( ar Plants, March. 

Absolute ventilation efficiency A value that provides a means of determining the actual ability of a ventilating system to reduce the concentration of a pollutant, compared to that theoretically possible. 

Nelson and Scliut investigated the reaction of 5a-cholestanone (lb) with diazomethane in a search for a direct, one-step preparation of A-homo ketones. Using a large excess of diazomethane generated in situ from A-methyl-nitrosourea with potassium hydroxide in ether-methanol at 0°, 5a-cholestanone (lb) is converted into the 7-membered ring homolog (3b) as the predominant product. Both theoretically possible A-homo ketones can be expected with an unsymmetrically-substituted cyclohexanone such as 5a-cholestanone (lb). 

Although some tautomerism betw een 1,4- and 3,4-dihydroquinazoline is theoretically possible, the dihydro compound always behaves as the 3,4-derivative except, of course, when a substituent is on N-1. 

These findings accord with the semiempirical AMI calculations [92JCS(P1)2779] of the heats of formation of all theoretically possible tautomeric forms of 4-aminoimidazole 53. The most stable are the tautomers 53a AHf = 213 kJ mol ) and 53d AHf = 215 kJ mol ) (Scheme 29). All... 

A typical example of MDGC in environmental analysis is the determination of PCBs. These are ubiquitous contaminants of the environment in which they occur as complex mixtures of many of the 209 theoretically possible congeners. The compositions of environmental mixtures vary according to sample type. 

The N,N -dibenzyl-N,N -bis-[2-(3, 4 -dihydroxyphenyl)-2-oxoethyl] -hexamethylene-diamine-dichlorohydrate-monohydrate used as the starting material was prepared as follows 2 mols of chloroaceto pyrocatechin were dissolved in 2,000 cc of acetone and heated to boiling with 2 mols of N,N -dibenzylhexamethylene-diamine for 12 hours, almost the theoretical quantity of N,N -dibenzylhexamethylene-diamine-dichlorohydrate being precipitated and removed by suction after cooling. Excess HCI was added to the filtrate, approximately 66% of the theoretically possible quantity of crude dichlorohydrate of the N,N -dibenzyl-N,N -bis-[2-(3, 4 -dihydroxyphenyl)-2-oxoethyl] -hexamethylene-diamine being precipitated. The product was cleaned by recrystallization from water with the addition of animal charcoal. After drying the substance contained water of crystallization at ambient temperature, MP 206° to 209.5°C. 

The collected ethereal filtrates were acidified with 50 ml of 4 N hydrochloric acid and tills solution was stirred vigorously. The hydrochloride of 1-(4 -benzyloxyphenyl)-2-(1 -methyl-2-phenoxy-ethylamino)propanone-1 precipitated out, was filtered off, washed with water and then with diethyl ether. Then this substance was dried in vacuo. The yield was 37.7 g, i.e., 89% of the theoretically possible yield, calculated on 1-(4 -benzyloxyphenyl)-2-bromine propanone-1. This substance had a light yellow color and melted at 197° to 198°C, while decomposing. 

Then 21.89 g of the hydrochloride salt was dissolved in 600 ml of 80% aqueous ethanol. With the addition of a palladium carbon catalyst, this solution was hydrogenated at room temperature under a hydrogen pressure of about 1.1 atmospheres. After 2 mols hydrogen had been absorbed, the catalyst was filtered off and the filtrate was evaporated in vacuo until crystallization occurred. Then the crystals were dissolved by heating in the smallest possible quantity of water and after cooling, the crystallized substance was filtered off, washed with water and dried in vacuo. The yield was 6.80 g, i.e., 39% of the theoretically possible yield. The resultant product recrystallized from water melted at 203° to 204°C. 

Theoretically, the first type ot propulsion, where the interaction is with a relatively immovable object, is the most energy efficient. In the absence of friction, it is theoretically possible to convert 100 percent of the available energy into kinetic energy, the energy of motion. This is because the more massive immovable object takes away a very small amount of kinetic energy even though it shares equally (but oppositely) in the impulse or change of momentum. 

Stirling engines also have the maximum theoretical possible efficiency because their power cycle (their theoretical pressure volume diagram) matches the Carnot cycle. The Carnot cycle, first described by the French physicist Sadi Carnot, determines the maximum theoretical efficiency of any heat engine operating between a hot and a cold reservoir. The Carnot efficiency formula is... 

Because the rate of entropy production is negative, the device violates the second law and is therefore impossible. Note that the device would be theoretically possible if the final pressure were specified as 400 psia or less by the inventor. That is, at = 400 psia, T = 40°F, h = 290 Btu/lb, and S, = 1.25 Btu/lb °R, the entropy production rate would be... 

Ps = 2(1.25-1.318)-1-0.1875= -t0.0515Btu/s °R Because entropy is produced in this case, the device is theoretically possible. 

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