Third-order rate constants

What are the units of first-order, second-order, and third-order rate constants ... 

Table 2 Third-order Rate Constants for the Bromination of Cyclohexene in 1,2-Dichloroethane a... 

If return occurs during the bromination of cw-stilbenes and rotation around the C-C bond is faster than collapse of the intermediates to dibromides, this process will lead to fra j-stilbene (Scheme 9). We used this test to check the possibility of return in the bromination of unsubstimted, 4-methyl, 4-trifluoromethyl-, and 4,4 -bis(trifluoromethyl)-stilbenes in DCE (ref. 24). All these olefins gave clean third-order rate constants spanning 7 powers of 10. For each cis-trans couple the cis olefin was brominated 3.5 to 5.5 times faster than the trans isomer. Reactions for products analysis were performed at initial molar ratios of Br2 to olefin of 1 to 2, so that products arose only from the cis olefin, the trans isomer being accumulated in the reaction medium. 

The oxidation of NO to NO2, which is an important step in the manufacture of nitric acid by the ammonia-oxidation process, is an unusual reaction in having an observed third-order rate constant (k o in ( rm) = kso Oc02) which decreases with increase in temperature. Show how the order and sign of temperature dependence could be accounted for by a simple mechanism which involves the formation of (NO)2 in a rapidly established equihbrium, followed by a relatively slow bimolecular reaction of (NO)2 with O2 to form NO2. 

Taking into account the reaction mechanism proposed for the same reaction in water, eq (4) and (5), BrN3 should be the reactive intermediate formed in a preequilibrium step, the rate of consumption of the total bromine is therefore expressed by eq (6). At sufficiently high N3 concentration, the BrN3 concentration is simply given by eq (7) and that of total bromine by eq (8). The introduction of eq (7) and (8) in eq (6) gives eq (9) from which the observed third-order rate constant, measurable by monitoring the free Br2 and the observed... 

Fig. 3 Correlation of the third-order rate constants for a-CD catalysis of bromine attack with the second-order rate constants for the uncatalysed reaction. Data from Tables A4.2 and A4.4 (Tee and Javed, 1993).

Intramolecular general base catalysed reactions (Section II, Tables E-G) present less difficulty. A classification similar to that of Table I is used, but since the electrophilic centre of interest is always a proton substantial differences between different general bases are not expected. This section (unlike Section I, which contains exclusively unimolecular reactions) contains mostly bimolecular reactions (e.g. the hydrolysis of aspirin [4]). Where these are hydrolysis reactions, calculation of the EM still involves comparison of a first order with a second order rate constant, because the order with respect to solvent is not measurable. The intermolecular processes involved are in fact termolecular reactions (e.g. [5]), and in those cases where solvent is not involved directly in the reaction, as in the general base catalysed aminolysis of esters, the calculation of the EM requires the comparison of second and third order rate constants. 

EM s calculated by comparing the second order rate constant for aminolysis by the diamine with the third order rate constant for aminolysis by a monoamine of the same pX,... 

Data of Alves el al. (1978), in 20% ethanol. The intermolecular reference reaction is the general acid catalysed addition of phenylhydrazine to the methyl ether, calculated from feH,o using a = 0.35 and determined for the reaction with o-methoxybenzaldehyde (Bastos and do Amaral, 1979). The EM, which is in some doubt because of possible mechanistic complications, is determined by comparison of the rate constant given (dm3 mol-1 s 1) with the third order rate constant for the reference reaction... 

TABLE 1. Values of the third-order rate constant for the acid catalysed nitrosation of thiols with nitrous acid in water at 25 °C... 

Figure T. Arrhenius plot of the TGMDA/DDS third-order rate constant k. ...

The recommended value of the third-order rate constant at room temperature is kt = 2.0 X 10-3X cm6 molecule-2 s- 1 (Atkinson et al., 1997a). At 1 Torr NO, for example, the initial rate of oxidation in 1 atm air is about 40% per minute, whereas at 1 mTorr (1.3 ppm at 1 atm, 298 K), it is only 0.04% per minute (see also Problem 1). Thus, at a concentration of NO of even 0.1 ppm, found as a peak concentration in some polluted areas, the rate is too slow to be consistent with observed conversion to N02 on a time scale of hours. 

The homogeneous gas-phase reaction is slow, depending on the square of the N02 concentration and with a third-order rate constant at room temperature of ku, = (5.7 0.6) X 10 17 cm6 molecule-2 s-1 (Niki et al., 1982 Koda et al., 1985). 

Table I . Third-Order Rate Constants Assigned to 1 1 Cu(ll) Chelates as Catalysts in the Hydrolysis of Sarin and DFP at 25°...

We can recognize that because kl and k2 have respectively the units of first-and third-order rate constants, the ratio (k2/k1)112 has the units of concentration. (For the data in Table 2.1 it has the value 2 x 10-5 moldm-3.) This quotient also turns out to be a sensible reference concentration, offering a natural scale on which to measure concentrations in this model. Some concentrations may be judged as being small compared with (k2/kl)u2,... 

We must note that kl is effectively a third-order rate constant, with units of (concentration)-2 (time)-1. Thus multiplying by al and then taking the inverse gives a chemical timescale... 

From their data, Bodenstein calculated a third-order rate constant that was in remarkable agreement with the value he obtained. 

Very recently Fontijn and Rosner145a have offered another explanation for the upper-atmosphere and wind-tunnel experiments. They propose that when the NO is adiabatically expanded, clustering (polymerization and perhaps condensation) occurs. Thus the third-order reaction (81) behaves as a second-order reaction, and has a correspondingly larger third-order rate constant. 

The investigations of early workers107 -252-269-423-426-426 -428,437 on the nitric oxide-chlorine system, while not immediately understandable, were concordant in their results. These results were critically reviewed and extended by Welinsky and Taylor,446 who recalculated the apparently inconsistent results of Trautz and co-workers and showed that the anomalous results they obtained in the presence of excess nitric oxide were due to incorrect analysis. Trautz had concluded that, in accordance with his general kinetic theory, the reaction proceeded by two consecutive steps, reactions (2) and (3). However, Welinsky and Taylor felt there was no basis for assuming any mechanism other than a single termolecular step. In Figure 5-1 values are shown for the third-order rate constant 1 for the reaction... 

Holmes and Sundaram210 photolyzed HI at 25 and 45°C with radiation at 3130 and 3660 A in the presence of NO. An analysis of their results indicated that the addition of H atoms to NO was not completely in the third-order region. Using a value for k6 of 1.22 x 1010 M 1 sec-1 from Sullivan s409 work, they deduced a second-order rate constant at 25°C of 6.1 x 1010 M 1 sec-1 at high pressures and a third-order rate constant of 3.2 x 1012 M2 sec-1 at low pressures, with HI and NO as the third bodies. Reaction (6) was... 

To produce CH3 radicals, Birss, Danby, and Hinshclwood44 pyrolyzed 50 torr of (ter/-C4H90)2 at 160°C. With NO present the C2H6 rate fell off, because of the competition between reactions (7) and (10). From the C2H6 rates and the value of 10,377 k7 was found to be 0.9 x 107 Af-1 sec-1, which corresponds to a third-order rate constant of 5.6 x 109 M 2 sec-1. Either constant seems to be too low to be correct. 

Table A-5A. Conversion Factors for Third Order Rate Constants (9)...

Energy Levels and Transition Probabilities of Some Atom of Photochemical Interest, 363 Conversion Factors for Absorption Cofficients, 373 Conversion Factors for Second Order Rate Constants, 37 1 Conversion Factors for Third Order Rate Constants, 374 Conversion from Pressure to Concentration Units, 375 Enthalpies of Formation of Atoms at 1 atm and 0°K in 11 . Idea Gas State, 375... 

Although the products do not allow one to distinguish between intra- and intermolecular processes, they found that the plots of kdecay versus quencher (alcohol) concentration are nonlinear. They have analyzed the data according to the quadratic expression shown in equation 16, where kq is the third-order rate constant corresponding to transient quenching by two molecules of alcohol. 

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