Fitting to a mechanism

The rank of the matrix, as we have seen, is the number of linearly independent vectors that we need to reconstruct the original matrix, and is a function of both the number of chemical components and the mechanism of the reaction. 

This also means that the knowledge of the rank of the matrix will enable us to restrict the possible mechanistic models to a handful. 

The aim of the fitting process is to obtain a concentration matrix C by vajying the values of the rate constants, so that the matrix V obtained from the relationship is as close as possible to V obtained from the data, i.e. V - V 0. For each set of estimated rate constants, a matrix V is produced V = 

C (C C ) C V, where C is the concentration matrix obtained from the solution of the differential equations derived from the mass action law. When the right set of rate constants are obtained, the relation is satisfied and the matrix H can be computed from the relationship  

A helpful him that can help during the selection of the best mechani.sm is that the plot of the V columns is characteristic of a particular mechanism. To this end, one can constrtict synthetic spectra and simulate the whole data set A for every particular mechanism. Kach synthetic matrix A can then be decomposed into the matrices U, V and S. Tlie plot of these synthetic V columns can 

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Most other studies have indicated considerably more complex behavior. The rate data for reaction of 3-methyl-l-phenylbutanone with 5-butyllithium or n-butyllithium in cyclohexane can be fit to a mechanism involving product formation both through a complex of the ketone with alkyllithium aggregate and by reaction with dissociated alkyllithium. Evidence for the initial formation of a complex can be observed in the form of a shift in the carbonyl absorption band in the IR spectrum. Complex formation presumably involves a Lewis acid-Lewis base interaction between the carbonyl oxygen and lithium ions in the alkyllithium cluster. 

The diffusional association constant K s was assumed to be equivalent to the value obtained for benzylic carbocation precursors. The parameters /Caz and ATas were fixed and the other parameters were adjusted to optimize the fit. The data could be fitted to a mechanism in which preassociation was... 

Cuprous cyanide solution. The most satisfactory method is to dissolve the cuprous cyanide (1 mol) in a solution of technical sodium cyanide (2 5-2-6 mols in 600 ml. of water). If it is desired to avoid the preparation of solid cuprous cyanide, the following procedure may be adopted. Cuprous chloride, prepared from 125 g. of copper sulphate crystals as described under 1 above, is suspended in 200 ml. of water contained in a 1-litre round-bottomed flask, which is fitted with a mechanical stirrer. A solution of 65 g. of technical sodium cyanide (96-98 per cent.) in 100 ml. of water is added and the mixture is stirred. The cuprous chloride passes into solution with considerable evolution of heat. As the cuprous cyanide is usually emplo3 ed in some modification of the diazo reaction, it is usual to cool the resulting solution in ice. 

Alternatively, place the mixture of alcohol and red phosphorus in a 500 ml. three-necked flask fitted with a mechanical stirrer, dropping funnel and double surface condenser. Heat the phosphorus - alcohol mixture to about 250°, and add the bromine whilst stirring vigorously. Work up the reaction product as above. 

In a 1-litre three-necked flask, fitted with a mechanical stirrer, reflux condenser and a thermometer, place 200 g. of iodoform and half of a sodium arsenite solution, prepared from 54-5 g. of A.R. arsenious oxide, 107 g. of A.R. sodium hydroxide and 520 ml. of water. Start the stirrer and heat the flask until the thermometer reads 60-65° maintain the mixture at this temperature during the whole reaction (1). Run in the remainder of the sodium arsenite solution during the course of 15 minutes, and keep the reaction mixture at 60-65° for 1 hour in order to complete the reaction. AUow to cool to about 40-45° (2) and filter with suction from the small amount of solid impurities. Separate the lower layer from the filtrate, dry it with anhydrous calcium chloride, and distil the crude methylene iodide (131 g. this crude product is satisfactory for most purposes) under diminished pressure. Practically all passes over as a light straw-coloured (sometimes brown) liquid at 80°/25 mm. it melts at 6°. Some of the colour may be removed by shaking with silver powder. The small dark residue in the flask solidifies on cooling. 

Methyl m-nitrobenzoate. In a 1 htre round-bottomed or bolt-head flask, fitted with a mechanical stirrer, place 102 g. (94 ml.) of pure methyl benzoate (Section IV,176) support a separatory funnel containing a mixture of 62 -5 ml, of concentrated sulphuric acid and 62 -5 ml. of concentrated nitric acid over the mouth of the flask. Cool the flask in an ice bath to 0-10°, and then run in the nitrating mixture, with stirring. 

Tricarballylic acid. Place 228 g. (204 ml.) of ethyl propane-1 1 2 3-tetracarboxylate and 240 ml. of 1 1 hydrochloric acid in a 1-litre threenecked flask, fitted with a mechanical stirrer and a fractionating column with condenser set for downward distillation attach a receiver with side tube to the condenser and connect the side tube to a wash bottle containing water. Boil the mixture, with continual stirring, at such a rate that the... 

Dissolve 100 g. of p-naphthol (Section IV,102) in a warm solution of 28 g. of sodium hydroxide in 1200 ml. of water contained in a 2-5 htre round-bottomed or bolt-head flask fitted with a mechanical stirrer. Cool the solution to 0° in a bath of ice and salt, and add 50 g. of powdered sodium nitrite. Start the stirrer and add, by means of a separatory funnel supported above the flask, 220 g. (166-5 ml.) of sulphuric acid (sp. gr. 1 32) at such a rate that the whole is added during 90 minutes... 

A 3-I. three-necked, round-bottom flask is fitted with a mechanical stirrer through a mercury seal, a reflux condenser and a i-l. separatory funnel. A mixture of 200 g. (r mole) of 2,3-dibromopropene (Org. Syn. 5, 49) and 200 cc. of dry ether is added. The flask is now cooled in an ice bath, the stirrer is started, and one molecular equivalent of cyclohexylmagnesium bromide, prepared from 31 g. of magnesium, 204 g. of cyclohexyl bromide and 400 cc. of dry ether (Note i) is added at such a rate that the mixture refluxes gently (Note 2). The addition takes about one-half to three-quarters of an hour. Two layers are formed and magnesium bromide may or may not separate. 

In a i-l. three-necked, round-bottom flask fitted with a mechanical stirrer through a mercury seal, a separatory funnel and an efficient reflux condenser to which a calcium chloride tube is attached, are placed 25 g. (1.03 moles) of magnesium turnings 140 cc. of dry ether, and a small crystal of iodine. The stirrei is started and a small portion (about 10 cc.) of a solution of 118.5 g. (i mole) of cyclohexyl bromide (Note i) in 120 cc. of dry ether is added through the separatory funnel. After the reaction starts, the remainder of the solution is run in at such a rate that the whole is added at the end of forty-five minutes. The mixture is stirred and refluxed for an additional thirty to forty-five minutes. 

In a 12-1. flask fitted with a mechanical stirrer and a short reflux condenser are placed 1800 g. (32.2 moles) of iron filings (Note i), 3 1. (52.5 moles) of glacial acetic acid, 3 1. of water, and 450 g. (3.95 moles) of heptaldehyde (Note 2). The mixture is heated on the steam bath, with stirring, for six to seven hours (Note 3). The flask is then fitted to an apparatus for steam distillation (Org. Syn. 2, 80) and the mixture distilled in a current of steam (Note 4) until no more oil passes over (7-8 1. of distillate). The oil is then separated, and the aqueous part distilled to recover a small quantity of dissolved or suspended heptyl alcohol. 

In a 4-I. wide-mouthed glass jar, fitted with a mechanical stirrer, is placed a solution of 150 g. (3 moles) of sodium cyanide (Note i) in 500 cc. of water and 318 g. (3 moles) of u.s.P. benz-aldehyde. The stirrer is started and 850 cc. of a saturated solution of sodium bisulfite (Note 2) is added to the mixture, slowly at first and then in a thm stream. The time of addition is ten to fifteen minutes. During the addition of the first half of this solution, 900 g. of cracked ice is added to the reaction mixture, a handful at a time. The layer of mandelonitrile which appears during the addition of the sulfite solution is separated from the water in a separatory funnel. The water is extracted once with about 150 cc. of benzene, the benzene is evaporated, and the residual mandelonitrile is added to the main portion. 

In a 500-cc. round-bottom flask (Note i) fitted with a mechanical stirrer and surrounded by an ice-salt cooling bath, are placed 54 g. (0.71 mole) of carbon disulfide and 90 cc. (1.3 moles) of concentrated ammonium hydroxide (sp. g. 0.9). The stirrer is started and 56 g. (0.6 mole) of aniline (Note 2) is run into the mixture from a separatory funnel at such a rate that the addition is complete in about twenty minutes. The stirring is continued for thirty minutes after all of the aniline has been added, and then the reaction mixture is allowed to stand for another, thirty minutes. During this time a heavy precipitate of ammonium phenyl dithiocarbamate separates and may even stop the stirrer. 

In a 2-1. three-necked flask fitted with a mechanical stirrer and thermometer, 72 g. (0.35 mole) of anthraquinone is dissolved in 1060 cc. of concentrated sulfuric acid by stirring at room temperature, and 42 cc. of water is then added to the red solution (Note i). The flask is immersed up to the neck in an oil bath, and 48 g. (0.76 mole) of precipitated copper (Note 2) is added over a period of one and one-half hours, keeping the reaction mixture at a temperature of 38-42°, if necessary by external heating, until all of the copper has dissolved, which requires about three hours (Note 3). 

In a 3-I. three-necked, round-bottomed flask fitted with a mechanical stirrer, reflux condenser, and separatory funnel is placed 400 cc. of absolute alcohol (Note i). Through the condenser tube is added slowly, 23 g. (i gram atom) of dean sodium cut into thin slices. The completion of the reaction is hastened by heating the flask on a steam bath. When the sodium has dissolved completely, 143 g. (i.i moles) of ethyl acetoacetate is introduced slowly. Alter starting the mechanical stirrer, 123 g. (i mole) of ethyl chloroacetate (Note 2) is added slowly over a period of an hour, and the reaction mixture is refluxed for five to six hours. At this point the reaction mixture should no longer give an alkaline reaction with moist litmus. 

In a 12-1. flask fitted with a mechanical stirrer, 62.3 g. (0.25 mole) of the azlactone is suspended in 6 1. of water, and II g. (0.275 mole) of sodium hydroxide is added as a lo per cent solution. The mixture is heated on the steam bath with stirring until solution is complete. This requires three to four hours. The hot solution is filtered and acidified with hydrochloric acid. The Of-benzoylaminocinnamic acid separates as white prisms in the hot solution, and when cold it is filtered. The yield is 55.5-64.5 g. (83-96.5 per cent) of almost pure product melting... 

In a 5-1, 3-necked flask fitted with a mechanical stirrer (Note 1), a dropping funnel, and a thermometer for reading low temperatures is placed 790 ml. (7 moles) of 48% h drobromic acid. The fl.ask and contents are cooled to 10-20 in an ice-salt bath, and 150 g, (1.59 moles) of 2-aminopyridine (Note 2) is added over a period of about 10 minutes. While the temperature is kept at 0° or lower, 240 ml. (4.7 moles) of bromine is added dropwise (Note 3). A solution of 275 g. (4 moles) of sodium nitrite in 400 ml. of water is added dropwise over a period of 2 hours, the temperature being carefully maintained at 0° or lower (Note 4). After an additional 30 minutes of stirring, a solution of 600 g. (15 moles) of sodium hydroxide in 600 ml. of water is added at such a rate that the temperature does not rise above 20-25° (Note 5). The nearly colorless reaction mixture is extracted with... 

To a solution of 33 g. (O.S mole) of potassium hydroxide (Note 1) in 1.5 1. of distilled water in a 5-1. flask or other appropriate container fitted with a mechanical stirrer is added 80 g. (0.5 mole) of methyl hydrogen adipate (Note 2). With continuous stirring a solution of 85 g. (0.5 mole) of silver nitrate in 1 1. of distilled water is added rapidly (about IS minutes). The precipitated methyl silver adipate is collected on a Buchner funnel, washed with methanol, and dried in an oven at 50-60°. For the next step the dried silver salt is finely powdered and sieved through a 40-mesh screen. The combined yield from two such runs is, 213 g. (80%). 

B. cis-1,2-Gyclohexanedimethanol Dimethanesulfonate. In a 5-1., three-necked, round-bottomed flask, immersed in an ice-salt bath and fitted with a mechanical stirrer and an addition funnel, is plaeed a solution of 111 g. (0.97 mole) of methanesulfonyl chloride in 1.21. of pyridine. While cooling and stirring, a solution of 46.4 g. (0.322 mole) of m-l,2-cyclohexanedimethanol in 250 ml. of pyridine is added dropwise at a rate such that the temperature does not exceed 0° (Note 5). Upon completion of the addition, the mixture is stirred at — 5° to 0° for an additional 2 hours. Two liters of cold 10% hydrochloric acid is introduced at a rate which maintains the reaction mixture below 20° (Note 5). The solid which separates is isolated by suction filtration, washed sequentially with 11. of dilute hydrochloric acid and 21. of water, and air-dried. There is isolated 93-95 g. (96-98%) of the dimethanesulfonate having m.p. 66-67.5°. Reorystallization from methanol gives needles melting at 75-76° (Note 6). 

In a r-1. three-necked flask fitted with a mechanical stirrer, a reflux condenser, a thermometer, and a dropping funnel is placed LOO g. (0.58 mole) of -bromotoluene (Org. Syn. Coll. Vol. i, 131). The stem of the dropping funnel and the thermometer should reach nearly to the bottom of the flask. The upper end of the condenser is connected to a gas absorption trap (Org. Syn. 14, 2). The flask is heated with stirring in an oil bath until the temperature of the liquid reaches 105. The liquid is illuminated with an unfrosted 150-watt tungsten lamp, and 197 g. (61.8 cc., 1.23 moles) of bromine is added slowly from the separatory funnel (Note i). About one-half of the bromine is added during the first hour, during which time the temperature is kept at 105-110°. The rest is added during about two hours, while the temperature is raised to 135°. When all the bromine has been added the temperature is raised slowly to 150°. 

The 3-I. flask containing the dark-colored sulfuric acid solution of the lactam is fitted with a mechanical stirrer and a separatory funnel and packed in an ice-salt mixture. The solution is cooled to 0° and carefully made faintly alkaline to litmus by the addition of 24 per cent potassium hydroxide solution, added very slowly (five to six hours) with good cooling (Note 4). Usually about 1550 cc. of the alkaline solution is needed. The tempera-... 

In a 3-I. three-necked flask, fitted with a mechanical stirrer, a reflux condenser, and a separatory funnel, are placed 24.3 g. (i gram atom) of magnesium turnings, 500 cc. of absolute ether, a crystal of iodine, and a 5- to lo-cc. portion of 126.5 g- cc., I mole) of freshly distilled benzyl chloride (b.p. 177-179°). In a few minutes the reaction starts (Note 1) and is controlled if necessary by cooling with a wet towel. The stirrer is started and the balance of the benzyl chloride is run in as fast as the refluxing will permit. The addition requires from one to two hours, and when completed the mixture is refluxed ofi the steam bath with stirring for three hours. With the stirrer stUl running, 182 g. (r mole) of benzophenone (Org. Syn. Coll. Vol. i, 89) dissolved in 500 cc. of absolute ether is added at such a rate that the mixture refluxes rapidly. This requires about twenty minutes and then the reaction mixture is allowed to stand for two hours (Note 2). 

A. ot-Chloroelhyl ethyl ether. A mixture of 200 g. (201 ml.) of redistilled paraldehyde, b.p. 121-122.5° (equivalent to 4.54 moles of acetaldehyde), and 200 g. (254 ml., 4.34 moles) of absolute ethanol is placed in a 1-1. three-necked flask fitted with a mechanical stirrer and a gas inlet tube reaching to the bottom of the flask. The mixture is cooled to —5° in a mixture of Dry Ice and acetone, and dry hydrogen chloride (Note 1) is passed into the stirred reaction mixture maintained at about —5° until 200 g. (5.48 moles) has been absorbed. During this operation, which requires about 2 hours, the reaction mixture separates into two layers. The upper layer of crude a-chloroethyl ethyl ether is re-... 

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