Calculation of product distribution

J. Troe Let me point out that the ab initio calculations of the HO2 surface still must be in error in their long-range part. High-pressure H + O2 recombination experiments clearly show that the potential is completely loose and not semirigid like the potential you used for illustration. For loose potentials SACM and classical trajectory calculations of product distributions (in the classical range) nicely agree. 

Calculation of Product Distribution from X. The kinetic equations of the network allow YQ, YE, and YQ to be calculated versus XA (= 1 - YA) or versus riser height. 

C. C. Marston, G. G. Balint-Kurti, and R. N. Dixon, Theor. Chim. Acta, 79, 313 (1991). Time-Dependent Quantum Dynamics of Reactive Scattering and the Calculation of Product Distributions—A Study of the Collinear F -I- H, (v = 0) — HF (v ) -I- FI Reaction. 

Baltanas, M. A., and G. F. Froment, Computer generation of reaction networks and calculation of product distributions in the hydroisomerization and hydrocracking of paraffins on Pt-containing bifunctional catalysts, Comput. Chem. Eng., 9. 71-81 (1985). 

Calculation of Product Distribution. Problem. Assume a process is to produce the hypothetical compound R from the raw materials A and B. It is a liquid-phase reaction, and the equations of the reaction are... 

Baltanas M.A. and Froment G.F. (1985) Computer Generation of Reaction Networks and Calculation of Product Distribution in the Hydroisomerization and Hydrocracking of Paraffins on Pt-Containing Bi-ftmctional Catalysts , Comp. Chem. Eng. 9, 1, 71-81. 

Two different and possibly complementary approaches have been explored. One utilizes a panel of quantifiable internal reference standards (QIRS), which are common proteins present widely in tissues in relatively consistent amounts.11,22 In this instance because the reference proteins are intrinsic to the tissue they are necessarily subjected to identical fixation and processing, and incur no additional handling or cost, other than synchronous performance of a second IHC assay (stain), such that the intensity of reaction for the QIRS and the test analyte can be compared by IA, allowing calculation of the amount of test analyte (protein) present on a formulaic standard curve basis. The other approach seeks to identify external reference materials and to introduce these into each step of tissue preparation for cases where IHC studies are anticipated in this instance the logistical issues of production, distribution, and inclusion of the reference standard into all phases of tissue processing also must be considered, along with attendant costs. 

Notably, with a single set of rate parameter estimates, the present model can also correctly describe the effects of all the investigated process conditions on product distribution. Figure 16.10 compares experimental and calculated ASF product distributions in five of the investigated process conditions. It is worth noticing also that the model predicts the hydrocarbons selectivity up to n = 49,... 

FIGURE 16.10 Experimental and calculated ASF product distributions in terms of total hydrocarbons at five different process conditions. 

These rate laws are coupled through the concentrations. When combined with the material-balance equations in the context of a particular reactor, they lead to uncoupled equations for calculating the product distribution. For a constant-density system in a CSTR operated at steady-state, they lead to algebraic equations, and in a BR or a PFR at steady-state, to simultaneous nonlinear ordinary differential equations. We demonstrate here the results for the CSTR case. 

Distribution planning including transports and inventories are also investigated in the context of production-distribution systems providing methods for material balances or inventory calculations... 

Another area to which the MM method can be advantageously applied is the prediction of product distribution under thermodynamic control, where the errors in energy calculations tend to cancel if structurally related products are compared (120). A remarkable example is the dodecahydrogenation of phenanthrene, in which 25 structural isomer products are possible, each having one to four stable... 

The polynomial approach is the logical expansion of the binomial approach. It is useful for the calculation of isotopic distributions of polyisotopic elements or for formulas composed of several non-monoisotopic elements. [2,14] In general, the isotopic distribution of a molecule can be described by a product of polynominals... 

The n-hexane (Fluka), n-heptane (Prolabo) and n-octane (Fluka) were all used as received with purities of >99.5%, >99.5% and >99.0%, respectively. The major organic impurities were subtracted from the exit gas analysis before calculating the product distribution. The hydrogen was obtained from Air Liquide (Grade U). 

Fig. 1. Relation of product distribution to calculated contact time in propylene disproportionation. Data obtained in tests at 163 C and 450 p.s.i.g. with C0O-M0O3-AI2O3 catalyst and 60 propylene-40 propane feed (Ref. 1)...

Essentially, the problem falls into two parts. Firstly, the calculation of the multi-body reaction potential surface and secondly, the determination of the properties of the reaction products from the knowledge of the potential surface. The reverse process of inverting experimental data to yield a potential energy surface is more complicated and has rarely been attempted. The calculation of potential surfaces and of product distributions may be carried out at various levels of sophistication using classical, semi-classical or full quantum mechanical treatments. Gross features of the reaction potential surfaces may be related to various product properties by simplistic model calculations. Statistical theories may also be used in cases where the lifetime of the collision is long enough to justify their use. 

The rational design of a reaction system to produce a polymer with desired molecular parameters is more feasible today by virtue of mathematical tools which permit prediction of product distribution. New analytical tools such as gel permeation chromatography are being used to check theoretical predictions and to help define molecular parameters as they affect product properties. There is a laudable trend away from arbitrary rate constants, but systems other than styrene need to be treated in depth. A critical review of available rate constants would be useful. Theory might be applied more broadly if it were more generally recognized that molecular weight distributions as well as rates can be calculated from combinations of constants based on the pseudo-steady-st te assumption. These are more easily determined than the individual constants in chain reactions. 

In such a simplified approach the basic question is the "char partitioning" with all existing and competitive reactants. Since each reaction, eqns. 4a to 4d, has different reactants and products, to calculate the product distribution after the b.2 step, the fractions of char reacting with Oj, with CO , with H2O and with H would need to be known. Since there are not good kinetic equations that would provide a scientific answer to this question, the problem remains open. Another empirical approach (one more ) has to be used for this step. It will be shown later. 

To calculate the product distribution for Grignard reagent formation from 5-hexenyl bromide. Garst et al. [93b,c] used the following equations and compared the results with the experimental data of Bodewitz et al. [76] for the reaction of 5-hexenyl bromide with magnesium (see Sec. III.E.2). 

More recently, the authors of the D-model investigated the reaction of bromocyclopropane 133 with magnesium [93e], using again the equations V=l4kJ3(kfD) ]v, A = (D//cJ mentioned earlier to calculate the product distribution, but substituting another composite parameter F for A and using the same values, questioned earlier for 5-hexenyl bromide, now for cyclopropyl... 

Hankel, M., Balint-Kurti, G.G., and Gray, S.K. (2000) Quantum mechanical calculation of product state distributions for the 0( D)- -H2 —t OH H reaction on the ground electronic state surface. J. Cham. Phys. 113, 9658-9667. 

In a typical experiment, styrene (180 mg, 1.74 mmol) was admixed with clayfen or clayan (300 mg) in a glass tube. The reaction mixture was placed in an oil bath for 15 min or irradiated for 3 min in an alumina bath inside an unmodified household microwave oven (900 W) at its medium power. On completion of the reaction, followed by TLC examination (hexane-EtOAc, 4 1, v/v), the product was extracted into dichloromethane (45 mL), the combined organic extract dried with anhydrous sodium sulfate and solvent removed under reduced pressure. The relative amounts of product distribution were calculated from GC-MS analysis. Alternatively, the crude material was chromatographed on a silica gel column and eluted with hexane-EtOAc (4 1, v/v) to afford the pure product (147 mg, 57%). 

EXPERIMENTAL FISCHER TROPSCH DISTRIBUTIONS AS COMPARED WITH THE IDEAL MODEL Calculated ideal product distributions as defined by the chain prolongation probabilities pq = 0.6 0.7 0.8 and 0.9 are shown in the upper part of Fig. 10 on a molar carbon basis, a molar product basis and on a molar logarithmic product basis. Obviously the Anderson plot, the logarithmic molar product representation is suited best to observe deviations from ideality because the ideal distribution is just a straight line. The experimental distributions shown in the lower part of Fig. 10 follow the ideal model fairly Deviations are (1) the... 

In general, except when the transition state is loose, the calculation of the distribution function EJn, of excess energy among the quantum states of the reaction products involves an additional approximation over and above those needed to calculate kEJ. Examples are given in Section III. 

A calculation of the distribution function PEJnt for the quantum states of the reaction products requires an additional approximation over and above that needed for kEJ. One approximation is to assume an adiabaticity in the exit channel, wherein the lowest states in correlate adiabatically with the lowest states in the products.2 The relative probability 1°EJn, that the quantum state of the ith coordinate is n, is then given by2... 

The most recent attempt to extend xenon-nitrogen chemistry has been an investigation of the reactions of XeF2 with HN3, NaN J, and NaOCN in solution in H20, anhydrous HF, or S02C1F. Although no stable xenon—nitrogen compounds were obtained, on the basis of product distribution, FXe(N3) and FXe(NCO) have been postulated as intermediates and ab initio calculations have shown that both possess stable minima (163). 

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