1st Order

Thermal Decomposition. The therm decompn was studied betw 380 and 430° and found to be homogeneous and apparently 1st order. The products were complex and included nitric oxide, methane, carbon monoxide, and w plus small amts of ethane, ethylene, and nitrous oxide (Ref 23)... 

Conversely the r vs pA behaviour (Fig. 6.20d) shifts from 1st order in A for positive AO to Langmuir-type or even negative order in A for very low O. 

Also in Figure 9.14 it is clear that decreasing Uwr (and O) causes a pronounced increase in 0NO (Eq. 9.9) as manifest by the shift in reaction order from 1st order at +1 V to near-zero order for -0.2 V. 

The Freeman and Carroll method has been shown by Fong and Chen to be the only one which gives satisfactory answers to known reactions, whether zero order, 1st order, 2nd order, or even higher. E)ven firactional orders of reaction may be determined. This method can be used with either DTA or TGA data. 

Time-scale of homogeneous reaction (1st order) Time-scale of heterogeneous reaction (1st order) Time-scale for reactor heat-up... 

The rearrangement of 24 to 19 is an intramolecular process with 1st order kinetics. The rearrangement does not occur by reductive elimination of TMS from 24 and by readdition of free TMS to the [(dtbpm)Pt(O)] fragment in a subsequent C-Si activation step. This possibility can be excluded rigorously by performing the 24 to 19 transformation in fully deuterated Si(CD3)4 or in hexamethydisi-loxane as solvents 24 only yields undeuterated 19 in d -TMS and does not lead to 21 in hexamethyl-disiloxane (which would have to be seen as a dissociative mechanism, as [(dtbpm)Pt(O)] had been previously shown to activate hexamethydisiloxane under the same reaction conditions). 

Kinetic studies (31P- and H-NMR) both of the direct reaction of 14 with TMS and of the rearrangement of 24 resulted in rate constants which were inconsistent with our original picture of C-Si activation exclusively via C-H insertion. The separate 1st order rearrangement of 24 occurs so slowly that 24, were it the only intermediate in the reaction of TMS with the [(dtbpm)Pt(O)] fragment, would accumulate and lead to an experimentally observable concentration, which was never observed in the kinetic runs. 

Berg, B.A. Neuhaus, T., Multicanonical algorithms for 1st order phase-transitions, Phys. Lett. B 1991, 267, 249-253... 

Partial order with respect to iodide ion = First order according to Graph for Part 4 Y = 1st order = 0.9789 slope = order = y... 

The carriers were impregnated and calcinated in the laboratory, and the activity was subsequently measured in the set-up shown in Fig. 9. The vanadium content was varied in the range 2-5 wt% and the molar ratios between alkali promoter and vanadium were varied in the ranges 0-4 for K/V, 0-2 for Na/V, and 0-3 for Cs/V. The sulphur content was about the same in all impregnations. The measured activities for 3 catalyst compositions A, B, and C impregnated on the same carrier and with the same vanadium content and molar ratios of K/V and Na/V are given in Table 1. The extrudates are made in the 9 mm Daisy form, which is the special 5-finned ring offered by Haldor Topsoe (Fig. 3). The observed pellet activity is reported as a pseudo-1st order rate constant calculated from... 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

The activity in terms of 1st order rate constant khcalc was calculated in Table 2 from (8) and (9) with effective diffusivity Dejf=5.3-10 6 m2/s and intrinsic rate constant =33000 Nm3/h/m3 = 23 s"1 fitted to the measurements. This simple and useful method models the measured influence of particle size satisfactorily for a first optimization of particle size and shape. The 35% higher activity measured for the 9-mm Daisy compared to the 12-mm Daisy, however, exceeds the 25% expected from (8), and this illustrates the importance of measuring the activity of the actual shape. 

A comparative study [10] into the Rh-catalysed carbonylation of ROH (R = Me, Et, Pr) shows that in all cases, the reaction rate is 1st order in both [Rh] and added [HI] and independent of CO pressure. The only Rh species observed by IR under catalytic conditions was 1. The rates of carbonylation decreased in the stated order of R, with relative rates of 21 1 0.47, respectively at 170 °C. This order of the R-groups and the large differences between them is a common feature for organic reactions of this type. All the data are consistent with ratedetermining nucleophilic attack by the Rh complex anion on the corresponding alkyl iodide. 

Fig. 16.1 (A) Calculated 1st order rate constant, and (B) LIOAS frequency in relation to %Ti02 loaded in the zeoliteY/[Ru(bpy)3] VTi02...

A differential virial theorem represents an exact, local (at space point r) relation involving the external potential u(r), the (ee) interaction potential u r,r ), the diagonal elements of the 1st and 2nd order DMs, n(r) and n2(r,r ), and the 1st order DM p(ri r2) close to diagonal , for a particular system. As it will be shown, it is a very useful tool for establishing various exact relations for a many electron systems. The mentioned dependence on p may be written in terms of the kinetic energy density tensor, defined as... 

This equation relates the single-particle external potential slr), the 1st order DMp (ri r2) and its diagonal element n (r) for a noninteracting system. As previously, this matrix can describe a mixed-state system also, thus having the ensemble DM form (143) with (145) in terms of single-particle (e.g. KS) orbitals [Pg.85]

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