High-pressure limit

Figure A3.4.9. Pressure dependence of the effective unimolecular rate constant. Schematic fall-off curve for the Lindemaim-FIinshelwood mechanism. A is the (constant) high-pressure limit of the effective rate constant...

Quack M 1984 On the mechanism of reversible unimolecular reactions and the canonical ( high pressure ) limit of the rate coefficient at low pressures Ber. Bunsenges. Phys. Chem. 88 94-100... 

From stochastic molecnlar dynamics calcnlations on the same system, in the viscosity regime covered by the experiment, it appears that intra- and intennolecnlar energy flow occur on comparable time scales, which leads to the conclnsion that cyclohexane isomerization in liquid CS2 is an activated process [99]. Classical molecnlar dynamics calcnlations [104] also reprodnce the observed non-monotonic viscosity dependence of ic. Furthennore, they also yield a solvent contribntion to the free energy of activation for tlie isomerization reaction which in liquid CS, increases by abont 0.4 kJ moC when the solvent density is increased from 1.3 to 1.5 g cm T Tims the molecnlar dynamics calcnlations support the conclnsion that the high-pressure limit of this unimolecular reaction is not attained in liquid solntion at ambient pressure. It has to be remembered, though, that the analysis of the measnred isomerization rates depends critically on the estimated valne of... 

Figure B2.5.3. The fall-off curve of reaction (B2.5.14) with M = He between 0.3 bar and 200 bar. The dashed lines represent the extrapolated low- and high-pressure limits, /r r, = (2.1 0.2) x [He] cm moU s ...

Finally, before leaving our exploration of the dusty gas model, we must compare the large pore (or high pressure) limiting form of its flux relations with the corresponding results derived in Chapter 4 by detailed solution of the continuum equations in a long capillary. The relevant equations are (4,23) and (4,25), to be compared with the corresponding scalar forms of equations (5.23) and (5.24). Equations (4.25) and (5.24).are seen to be identical, while (4,23) and (5.23) differ only in the pressure diffusion term, which takes the form... 

If the pressure for the process is lowered, the reaction (R3) will shift from a first-order reaction (high-pressure limit) to a second-order reaction (low-pressure limit). If (R3) is now considered a second-order reaction and assuming that the other pressure dependent reactions do not shift regime, determine expressions for d[C2H6]/dt, d[CH3]/dt, d[C2Hs]/dt and d[H]/dt. 

The reverse of reactions (3) and (4) in the high pressure limit is the desorption process described by... 

The activation energy at the high pressure limit, Em, should be 3-5 kcal.mole-1 greater than Ei 8 torr. The value of 48.8 kcal.mole-1 from the benzene flow system... 

Fig. 3. Arrhenius plots for the decomposition of dimethyl mercury. All rate coefficients are at or near the high-pressure limit. If a radical scavenger has been used it is shown in brackets following the authors names. 1, Krech and Price (benzene) 2, Kallend and Purnell (propene) 3, Russell and Bernstein (cyclopentane) 4, Russell and Bernstein 5, Laurie and Long 6, Kominar and Price (toluene) O, Weston and Seltzer (cyclopentane) , point calculated from the steady-state equation of Kallend and Purnell.

The mechanism proposed by Kallend and Purnell explains many features of the dimethyl mercury pyrolysis but two difficulties arise. Their explanations are valid only if addition of NO does, in fact, increase the methyl radical concentration. The process by which this occurs has not been specified and none comes readily to mind. In fact, the equilibrium CH3+NO CH3NO might reasonably be expected to lower the methyl radical concentration. The second difficulty arises when high pressure limiting values of calculated from Kallend and Purnell s steady-state equation... 

In the high pressure limit, the denominator of Equation 14.13 approaches unity (k2[M] ka(E)) and kun becomes a truly first order rate constant. After substituting the appropriate expressions for ka and dki /k2 into the expression for ku i, one obtains (for details see Holbrook et al., reading list)... 

The formalism for treating primary isotope effects on unimolecular processes follows analogously to the development above, once due account is taken of the difference in zero point energies on isotope substitution at the reaction site (which is reflected in an isotopic difference in the threshold energy Eo). For thermal activation the rate ratio in the high pressure limit is straightforwardly obtained from Equation 14.25. For H/D effects... 

It is also necessary to explain why there are parentheses around the collision partner M in reactions (3.94), (3.95), and (3.99). When RH in reactions (3.94) and (3.95) is ethane and R in reaction (3.99) is the ethyl radical, the reaction order depends on the temperature and pressure range. Reactions (3.94), (3.95), and (3.99) for the ethane system are in the fall-off regime for most typical combustion conditions. Reactions (3.94) and (3.95) for propane may lie in the fall-off regime for some combustion conditions however, around 1 atm, butane and larger molecules pyrolyze near their high-pressure limits [34] and essentially follow first-order kinetics. Furthermore, for the formation of the olefin, an ethyl radical in reaction (3.99) must compete with the abstraction reaction. 

The thermal isomerization of cyclopropane to propylene is perhaps the most important single example of a unimolecular reaction. This system has been studied by numerous workers. Following the work of Trautz and Winkler (1922), who showed that the reaction was first order and had an energy of activation of about 63,900 cal mole measured in the temperature range 550-650° C, Chambers and Kistiakowsky (1934) studied the reaction in greater detail and with higher precision from 469-519° C. They confirmed that it was first order and, for the reaction at its high-pressure limit, obtained the Arrhenius equation... 

At 5 mm the rate constant has already begun to decrease from the high-pressure value, and at 0-15 mm it is only about 13 % of the high-pressure value. Addition of inert gases in the fall-off region increases the value of the rate constant towards the high pressure limiting value. 

The optimum choice of operating conditions are around a steam to methanol ratio of 1.5 and a temperature range of 250°C to 399°C. Pressure does not influence the reaction rate, but very high pressures limit the equilibrium conversion, which otherwise is better than 99% at the preferred range of 5 to 15 bars. The CU/Zn/Al and Cu/Zn/Cr based catalysts have been used in large units in industry for many years (12). 

Figure 6.7 shows the average correlation g(PQ) as a function of oxygen partial pressure. At the low-pressure limit (determined by the pair correlation only) there is no clear-cut monotonic dependence on temperature. At the high-pressure limit (as determined by the quadruplet correlations, see Section 5.8), we see that the... 

Figure 6.7. Average correlation s(Pq ) as a function of the partial pressure of oxygen Pq (in torrs), for the same system as in Fig. 6.5. (a) Low-pressure limit (b) high-pressure limit. The temperatures are indicated next to each curve.

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