Second-order rate coefficient

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. 

As the medium is still further diluted, until nitronium ion is not detectable, the second-order rate coefficient decreases by a factor of about 10 for each decrease of 10% in the concentration of the sulphuric acid (figs. 2.1, 2.3, 2.4). The active electrophile under these conditions is not molecular nitric acid because the variation in the rate is not similar to the correspondii chaise in the concentration of this species, determined by ultraviolet spectroscopy or measurements of the vapour pressure. " ... 

Fig. 2.4, illustrates the variation with the concentration of sulphuric acid of the logarithm of the second-order rate coefficients for the nitration of a series of compounds for which the concentration of effective... 

Rates of nitration in perchloric acid of mesitylene, luphthalene and phenol (57 I-6i-i %), and benzene (57 i-64 4%) have been deter-mined. The activated compounds are considered below ( 2.5). A plot of the logarithms of the second-order rate coefficients for the nitration of benzene against — ( f + log over the range of acidity... 

Second-order rate coefficients for nitration in sulphuric acid at 25 °C fall by a factor of about 10 for every 10 % decrease in the concentration of the sulphuric acid ( 2.4.2). Since in sulphuric acid of about 90% concentration nitric acid is completely ionised to nitronium ions, in 68 % sulphuric acid [NO2+] io [HNO3]. The rate equation can be written in two ways, as follows ... 

The phenomenon was established firmly by determining the rates of reaction in 68-3 % sulphuric acid and 61-05 % perchloric acid of a series of compounds which, from their behaviour in other reactions, and from predictions made using the additivity principle ( 9.2), might be expected to be very reactive in nitration. The second-order rate coefficients for nitration of these compounds, their rates relative to that of benzene and, where possible, an estimate of their expected relative rates are listed in table 2.6. 

TABLE 2.6 Second-order rate coefficients and relative rates for nitration at 2 -0 °C in 68- % sulphuric acid and 6i-o % perchloric acid ° ... 

The above difference in reactivity of benzene and toluene is close to that observed in a less viscous system so that the results for compounds of the reactivity of benzene (and perhaps toluene) or less in these media are meaningful, but not for compounds which are normally more reactive. This conclusion was confirmed for nitration in nitric acid-perchloric acid of a range of compounds which normally are fairly reactive. The derived second-order rate coefficients (10k2) for nitration... 

The conclusion that the nitration of quinoline in sulphuric acid takes place via the conjugate acid has been confirmed by Moodie et al.50, who measured the rates of nitration of a wide range of heterocyclic compounds in nitric acid-sulphuric acid mixtures at a range of temperatures. A summary of the second-order rate coefficients and Arrhenius parameters is given in Table 4. From an analysis of the shapes of the plots of log k2 versus sulphuric acid acidity (or some function of this), it was concluded that all of the compounds starred in Table 4... 

A comparison of the second-order rate coefficients for nitration of 2,4,6-tri-methylpyridine and 1,2,4,6-tetramethylpyridinium ion (both at the 3-position) shows similarity of profile in the common acidity region and a rapidly increasing rate with acidity for the trimethyl compound at acidities below 90 wt. % (where the usual maximum is obtained). These two pieces of evidence show reaction to occur on the conjugate acid as also indicated by the large negative entropy of activation. Surprisingly, the tetramethyl compound is less reactive than the trimethyl compound so maybe this is an example of steric hindrance to solvation. Calculation of the encounter rate also showed that reaction on the free base was unlikely. 

Ridd et a/.48 have studied the nitration of aniline by nitricacid in 82.0-100.0 wt. % sulphuric acid, and the second-order rate coefficients were separated (from product analysis) into those appropriate for ortho, meta, and para substitution (Table 5). 

The large activating effect of a methyl group upon the reactivity of aromatic quaternary nitrogen compounds noted above has been confirmed by Utley and Vaughan55, who have measured the second-order rate coefficients and the... 

SECOND-ORDER RATE COEFFICIENTS FOR NITRATION OF ArH BY N2Oj IN CCI4 AT 15 °C 97... 

EFFECT OF ADDED HNO3 ON CALCULATED AND OBSERVED SECOND-ORDER RATE COEFFICIENTS FOR NITRATION OF 1,4-C6H4CI2 (0.6 Af) BY N2Os (0,04 M) IN CC14 AT... 

The constancy of the second-order rate coefficients (k2) in the presence of tetra-alkyl-ammonium nitrates (Table 26) indicates the validity of the assumptions. 

The kinetics of nitrosation of phenol in aqueous mineral acid have been studied in some detail. Suzawa et a/.118 showed that, with 0.01 M nitrous acid at 0° a second-order rate coefficient of 0.00148 was obtained and that this was increased to 0.00225 by the addition of hydrochloric acid to pH 1.3. Morrison and Turney119... 

In hydroxylation, quinones are usually obtained since the initial hydroxyl product is further oxidised. Kinetic studies on the hydroxylation of 1,3,5-tri-methoxybenzene with perbenzoic acid gave second-order rate coefficients (Table 29) which remained fairly constant for a wide variation in concentration of aromatic and acid thus indicating that the rate-determining step is bimolecular133. The variation was considered to be within the rather large experimental error for the reaction which was very fast and, therefore, studied at low temperature (—12.4 °C). Since more than one mole of acid per mole of aromatic was eventually consumed, the mechanism was formulated as... 

Second-order rate coefficients are given in Table 30. The predominance of ortho-... 

The benzenesulphonylation of benzene did not give a single kinetic form. Satisfactory second-order rate coefficients could be obtained provided that the initial benzene concentration was not small, when a small increase in the calculated rate coefficients as the reaction proceeds is observed. However, the values of the second-order rate coefficients are not independent of the initial concentration of reactants (Table 51). It was concluded that benzene reacts by both mechanisms ... 

With 77 % aqueous acetic acid, the rates were found to be more affected by added perchloric acid than by sodium perchlorate (but only at higher concentrations than those used by Stanley and Shorter207, which accounts for the failure of these workers to observe acid catalysis, but their observation of kinetic orders in hypochlorous acid of less than one remains unaccounted for). The difference in the effect of the added electrolyte increased with concentration, and the rates of the acid-catalysed reaction reached a maximum in ca. 50 % aqueous acetic acid, passed through a minimum at ca. 90 % aqueous acetic acid and rose very rapidly thereafter. The faster chlorination in 50% acid than in water was, therefore, considered consistent with chlorination by AcOHCl+, which is subject to an increasing solvent effect in the direction of less aqueous media (hence the minimum in 90 % acid), and a third factor operates, viz. that in pure acetic acid the bulk source of chlorine ischlorineacetate rather than HOC1 and causes the rapid rise in rate towards the anhydrous medium. The relative rates of the acid-catalysed (acidity > 0.49 M) chlorination of some aromatics in 76 % aqueous acetic acid at 25 °C were found to be toluene, 69 benzene, 1 chlorobenzene, 0.097 benzoic acid, 0.004. Some of these kinetic observations were confirmed in a study of the chlorination of diphenylmethane in the presence of 0.030 M perchloric acid, second-order rate coefficients were obtained at 25 °C as follows209 0.161 (98 vol. % aqueous acetic acid) ca. 0.078 (75 vol. % acid), and, in the latter solvent in the presence of 0.50 M perchloric acid, diphenylmethane was approximately 30 times more reactive than benzene. 

SECOND-ORDER RATE COEFFICIENTS (I04/c2) FOR REACTION OF ArH WITHClj IN VARIOUSSOLVENTS235... 

Dewar and Mole236 derived second-order rate coefficients for chlorination at 25 °C of benzene (6xl0-7), diphenyl (6.9 xlO-4), naphthalene (6.3 xlO-2), phenanthrene (2.9xl0 1) and triphenylene (2.2xlO-2) in Analar acetic acid and of diphenyl (9 x 10-7), naphthalene (1.9 x 10-4), phenanthrene (1.3 x 10-3),... 

SECOND-ORDER RATE COEFFICIENTS FOR REACTION OF ArH WITH Cl2 IN VARIOUS... 

The kinetics of the chlorination of some alkylbenzenes in a range of solvents has been studied by Stock and Himoe239, who again found second-order rate coefficients as given in Table 57. Although the range of rates varies by a factor of 104, there was no marked change in the toluene f-butylbenzene reactivity ratio, and it was, therefore, concluded that the Baker-Nathan order is produced by a polar rather. than a solvent effect. 

Finally, a 1 1 mixture of acetic and propionic acids containing 2 % of water has been used in order to study the rates of chlorination of polyalkylbenzenes at low temperatures. Second-order rate coefficients were obtained and the values are recorded in Table 58 together with the energies and entropies of activation (which are given with the errors for 95 % confidence limits) from which it was concluded... 

De la Mare and Hassan254 obtained second-order rate coefficients (in parenthesis) for the following 4-methylacetanilide (1.53), 2-methylacetanilide (0.193), 2,6-dimethylacetanilide (0.0118), acetanilide (0.93), 4-acetamidodiphenyl (0.248) and 1,4-diacetamidobenzene (0.231) the results for the acetanilides demonstrated the effect of steric hindrance to coplanarity thereby inhibiting resonance of the nitrogen lone pair with the aromatic ring. The rate coefficients for chlorination of 3-chloroacetanilide (0.215), 4-chloroacetanilide (0.010) 3-nitroacetanilide (6.7 x 10 5) and phenyl benzoate (3.2 x 10-6) have also been measured258,261. 

Mason256 has measured the second-order rate coefficients and Arrhenius parameters for the chlorination of benzene, biphenyl, naphthalene, and phe-nanthrene in acetic acid (containing 0.05 % water) and these are given in Table 62. 

SECOND-ORDER RATE COEFFICIENTS (10" A 2) AND ARRHENIUS PARAMETERS FOR REACTION of ArH with Cl2 in HOAc236... 

Stock and Baker2 5 9 measured the relative rates of chlorination of a number of halogenated aromatics in acetic acid containing 20.8 M H20 and 1.2 M HC1 at 25 °C and the values of the second-order rate coefficients (103Ar2) are as follows p-xylene (11,450), benzene (4.98), fluorobenzene (3.68), chlorobenzene (0.489), bromobenzene (0.362), 2-chlorotoluene (3.43), 3-chlorotoluene (191), 4-chloro-toluene (2.47), 4-fluorotoluene (9.70), 4-bromotoluene (2.47). Increasing the concentration of the aromatic, however, caused, in some cases, a decrease in the rate coefficients thus an increase in the concentration of chlorobenzene from 0.1 M to 0.2 M caused a 20 % decrease in rate coefficient, whereas with 4-chloro-and 4-bromo-toluene, no such change was observed. 

De la Mare et al.260 measured the rates of chlorination of biphenyl, a wide range of its methyl derivatives, and anisole in acetic acid at 25 °C. Second-order rate coefficients (104 2) were biphenyl (6.40), 2-methylbiphenyl (3.20), 3-methyl-biphenyl (820), 4-methylbiphenyl (30.0), 2.2 -dimethylbiphenyl (4.40), 3.3 -dimethylbiphenyl (2,630), 4,4 -dimethylbiphenyl (70.0), 2,6 -dimethylbiphenyl (1,130), 3,4,3, 4 -tetramethylbiphenyl (19,300), anisole (12.5 x 104), and these results showed very clearly the effect of steric inhibition of resonance between the phenyl rings through the presence of ortho methyl groups260. Similar (but rather more emphatic) results were obtained262 in chlorination of the /-butyl derivatives for which the corresponding rate coefficients were 2-/-butylbiphenyl (1.0) 4-/-butylbiphenyl (25.7), 2,2 -di-/-butylbiphenyl (1.8), 4,4 -di-/-butylbiphenyl (70.0). 

The rates of chlorination of bridged biphenyls have also been measured and show the effect of coplanarity on reactivity. Second-order rate coefficients (104A 2) at 25 °C were fluorene (1,700), 9,10-dihydrophenanthrene (170), 1,2 3,4-di-benzocyclohepta-1,3-diene (9.70), 5-methyl-l,2 3,4-dibenzocyclohepta-l,3-diene... 

Despite the relative simplicity of the kinetics of molecular chlorination, there has so far been only one measurement of the rate coefficient with a heterocyclic compound and the need for more work in this area is indicated. Marino265 found that chlorination of thiophene by chlorine in acetic acid at 25 °C gave the second-order rate coefficient of 10.0 1.5, so that thiophene is 1.7 x 109 times as reactive as benzene in this reaction and this large rate spread is clearly consistent with the neutral and hence relatively unreactive electrophile. 

Second-order rate coefficients have been obtained for chlorination of alkyl-benzenes in acetic acid solutions (containing up to 27.6 M of water) at temperatures between 0 and 35 °C, and enthalpies and entropies of activation (determined over 25 °C range) are given in Table 63 for the substitution at the position indicated266. 

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