First-order rate coefficient

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

It can be shown2 that the first-order rate coefficient for the A-l mechanism kx... 

Kinetic studies with benzene in acetic anhydride containing 0.4-2 M nitric acid at 25 °C show the reaction to be first-order in benzene and approximately second-order in nitric acid this falls to first-order in nitric acid on addition of sulphuric acid, which also increases the first-order rate coefficient (first-order in benzene) from 4.5 x 10-4 to 6.1 x 10 4. By contrast the addition of as little as 0.001 M sodium nitrate reduced the rate to 0.9 x 10-4 without affecting the kinetic order70. These results were, therefore, interpreted as nitration by nitronium ion via equilibria (21a) and (22). 

Ingold et al." showed that rates of nitration by benzoyl nitrate in carbon tetrachloride were depressed by the addition of benzoic anhydride. Thus addition of 0.035 M of the anhydride to a solution 2.36 M in benzene and 0.030 M in nitrate decreased the first-order rate coefficient from 44x 10-4 to 20xl0-4. This is consistent with nitration by dinitrogen pentoxide formed via equilibrium (37), viz. 

For a given concentration of nitrous acid, the first-order rate coefficients increase as the sixth to seventh power of the nitric acid concentration and this catalysed nitration is presumed to be nitrosation followed by oxidation, reactions (41) and (42), viz. 

For 4-nitrophenol (studied in the range 1.4-10 M nitric acid) the first-order rate coefficients (at constant nitrous acid concentration) decrease approximately 50 % as the nitric acid concentration is increased from 2 M to 5 M but increase considerably as it is further increased to 10 M the increase is greater the lower the fixed concentration of nitrous acid and is attributed to the catalysed reaction. The rate decrease was attributed to superimposition upon the normal catalysis noted above for 4-chloroanisole of the effect of lowering of the concentration of the highly reactive phenoxide ion as the acidity was increased. In 10 M nitric acid the anti-catalysed reaction was again observed. 

Eaborn and Taylor147 measured first-order rate coefficients for sulphonation of some aromatics in mixtures of trifluoroacctic acid-aqueous sulphuric acid, as sulphonation proved to be a troublesome side reaction accompanying hydrogen exchange in these media. They introduced a technique which has been found useful by later workers and makes use of the high solubility of sulphonic acids in... 

The first kinetic study appears to have been that of Martinsen148, who found that the sulphonation of 4-nitrotoluene in 99.4-100.54 wt. % sulphuric acid was first-order in aromatic and apparently zeroth-order in sulphur trioxide, the rate being very susceptible to the water concentration. By contrast, Ioffe149 considered the reaction to be first-order in both aromatic and sulphur trioxide, but the experimental data of both workers was inconclusive. The first-order dependence upon aromatic concentration was confirmed by Pinnow150, who determined the equilibrium concentrations of quinol and quinolsulphonic acid after reacting mixtures of these with 40-70 wt. % sulphuric acid at temperatures between 50 and 100 °C the first-order rate coefficients for sulphonation and desulphonation are given in Tables 34 and 35. The logarithms of the rate coefficients for sulphonation... 

Lauer and Irie154 also reported two sets of unitless rate coefficients for the sulphonation of 1,8-benzanthrone in 80.6-99.0 wt. % acid. First-order rate coefficients (believed to be in min-1 and extrapolated to ca. 95 °C from rates obtained at temperatures up to 170 °C) and activation energies relating to acid strengths (in parentheses) were 12, 30.1 (91 %) 110, 26.6 (95.6%), 2500, 24.8 (99%). With... 

Brand et al.15B made extensive measurements of the rates of sulphonation of a range of unreactive aromatics by oleum containing up to 41 % of sulphur trioxide at temperatures between 0 and 45 °C, and found the reaction to be first-order in aromatic. First-order rate coefficients at 25 °C are given in Table 37, some of the... 

FIRST-ORDER RATE COEFFICIENTS FOR REACTION OF 2,4,6-Me3C6H2S03H WITH... 

The kinetics of the sulphonation of alkylbenzenes have been examined and the first-order rate coefficients are gathered together in Table 42147 1164- 167 168 ... 

FIRST-ORDER RATE COEFFICIENTS (106fci) FOR REACTION OF AfH WITH H2S04141,7Z... 

The kinetics of the sulphonation of chlorobenzene have been examined by Kort and Cerfontain176 in order to obtain further information regarding the sulphonation mechanism in very concentrated aqueous sulphuric acid media. First-order rate coefficients (obtained at assorted temperatures) are given in Table 45 and plots of the logarithms of the para partial rate coefficient (used in... 

FIRST-ORDER RATE COEFFICIENTS SULPHONATE WITH Br (104fci) FOR i IN AQUEOUS REACTION OF 2-NAPHTHOL-6,8-DIBUFFERS AT 20 °C303 ... 

Olivier and Berger335, who measured the first-order rate coefficients for the aluminium chloride-catalysed reaction of 4-nitroben2yl chloride with excess aromatic (solvent) at 30 °C and obtained the rate coefficients (lO5/ ) PhCI, 1.40 PhH, 7.50 PhMe, 17.5. These results demonstrated the electrophilic nature of the reaction and also the unselective nature of the electrophile which has been confirmed many times since. That the electrophile in these reactions is not the simple and intuitively expected free carbonium ion was indicated by the observation by Calloway that the reactivity of alkyl halides was in the order RF > RC1 > RBr > RI, which is the reverse of that for acylation by acyl halides336. The low selectivity (and high steric hindrance) of the reaction was further demonstrated by Condon337 who measured the relative rates at 40 °C, by the competition method, of isopropylation of toluene and isopropylbenzene with propene catalyzed by boron trifluoride etherate (or aluminium chloride) these were as follows PhMe, 2.09 (1.10) PhEt, 1.73 (1.81) Ph-iPr, (1.69) Ph-tBu, 1.23 (1.40). The isomer distribution in the reactions337,338 yielded partial rate factors of 2.37 /mMe, 1.80 /pMe, 4.72 /, 0.35 / , 2.2 / Pr, 2.55337 339. 

The most valuable and comprehensive kinetic studies of alkylation have been carried out by Brown et al. The first of these studies concerned benzylation of aromatics with 3,4-dichloro- and 4-nitro-benzyl chlorides (these being chosen to give convenient reaction rates) with catalysis by aluminium chloride in nitrobenzene solvent340. Reactions were complicated by dialkylation which was especially troublesome at low aromatic concentrations, but it proved possible to obtain approximately third-order kinetics, the process being first-order in halide and catalyst and roughly first-order in aromatic this is shown by the data relating to alkylation of benzene given in Table 77, where the first-order rate coefficients k1 are calculated with respect to the concentration of alkyl chloride and the second-order coefficients k2 are calculated with respect to the products of the... 

Analysis of the first-order rate coefficient in terms of the two consecutive reactions which were occurring, yielded values of 5.3 xlO-4 and 2.64 xlO-4 the latter value was confirmed as arising from reaction on the first reaction product, 3,4-dichlorodiphenylmethane, because separate 3,4-dichlorobenzylation of this gave a rate coefficient of 2.98 x 10-4. The first-order (overall) rate coefficients obtained at 15 °C (0.665 x 10-4) and 35 °C (6.1 x 10-4) yielded Ea = 19.6, and log A = 14.3, the rate ratio for the consecutive reactions being the same (0.5) at both temperatures later studies have tended to confirm this order of activation energy. 

FIRST-ORDER RATE COEFFICIENTS AND ORDER IN AlClj FOR RBACTION OF C6HhC1... 

FIRST-ORDER RATE COEFFICIENTS AND ACTIVATION ENERGIES FOR REACTION OF RX WITH BENZENE IN PhN02 CATALYSED BY A1C13352... 

FIRST-ORDER RATE COEFFICIENTS FOR CYCLIALKYLATION OF 2-R"COC6H4.CHMe.Ph by aqueous HBr-HOAc at 133-4 °C369... 

Values of k2 (the first-order rate coefficient, viz. rate = kt [aromatic]), k2 and k3 are given in Table 104, and the third-order coefficients show slightly greater consistency than the second-order coefficients. 

FIRST-ORDER RATE COEFFICIENTS (107ki) AND ARRHENIUS PARAMETERS FOR REACTION... 

VARIATION OF FIRST-ORDER RATE COEFFICIENTS WITH ATOM FRACTION OF... 

Other examples of linear correlations of log rate coefficients with — H0 have been reported though most of them are deficient in some respect. Satchell474 observed such a correlation in the dedeuteration of anisole and benzene in various aqueous or acetic acid solutions of sulphuric acid, and aqueous perchloric acid, media at 25 °C. First-order rate coefficients are given in Table 127 along with those for dedeuteration of [4,5-2H2]-l,3,5-trimethoxybenzene and -2-hy-droxy-l,3-dimethoxybenzene475. For the ortho- andpara-monodeuterated anisoles the slopes of the log rate versus — H0 plots were the same for aqueous sulphuric acid and for acetic acid-sulphuric acid so that it was concluded that the A-l mechanism therefore applied to non-aqueous media as well as to aqueous media. The fact that the slope of the log rate coefficient versus —H0 plot was less (1.12) for benzene in aqueous perchloric acid than that (1.36) previously found in aqueous... 

Satchell476 also measured the first-order rate coefficients for dedeuteration of [4-3H]-anisole by acetic acid or acetic acid-hydrochloric acid media containing zinc and stannic chlorides (Table 128). The rates here paralleled the indicator ratio of 4-nitrodiphenylamine and 4-chloro-2-nitroaniline, so that the implication is that a linear relationship exists between log k and the unknown H0 values. The results also show the rate-enhancing effect of these Friedel-Crafts catalysts, presumably through additional polarisation of the catalysing acid, for in the absence of them, exchange between acetic acid and anisole would be very slow. Other studies relating to the effect of these catalysts are reported below (p. 238). 

Kresge and Chiang480 measured the rate coefficients for detritiation of [1-3H]-2,4,6-trimethoxybenzene in acetate buffers and found the first-order rate coefficient (lO7 ) to increase from 2.5 at 0.01 M acetic acid to 8.3 at 0.1 M acetic acid, whereas if the reaction was specific acid-catalysed no change in rate should have been observed. A similar technique to that described above for separation of the rate coefficients due to hydronium ions and other acids was used, the values for the former being obtained using dilute hydrochloric acid at which acidities no undissociated acid was present (Table 131). Rate coefficients were then measured... 

The detritiation of [l-3H]-azultne in aqueous hydrochloric acid has been examined more extensively by Schulze and Long489, using media of constant ionic strength (0.1) at 25 °C. Average first-order rate coefficients for detritiation by 0.001, 0.005, and 0.01 M hydrogen ion were 1.75 xlO"4, 9.35 xlO-4, and... 

Another method of ascertaining the nature of the reacting species is to compare the reactivity of a heterocyclic compound with its derivative methylated at the heteroatom. Thus Katritzky and Ridgewell507 measured first-order rate coefficients (lO7 ) for reaction of 2,6-dimethoxypyridine, 2,4,6-trimethylpyridine and 1,2,4,6-tetramethylpyridinium sulphate with tritiated sulphuric acid over a range of temperatures (Table 145). 

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