Simplified reactions

There is another difficulty with exact solutions of complex sets of reactions. We frequently don t want to know all the C (t), just the important reactants and products. In many chemical reaction systems there are many intermediates and minor species whose concentrations are very small and unmeasured. 

Therefore, we need to find approximate methods for simultaneous reaction systems that will permit finding analytical solutions for reactants and products in simple and usable form. We use two approximations that were developed by chemists to simplify simultaneous reaction systems (1) the equilibrium step approximation and (2) the pseudo-steady-state approximation 

Here we assume simply that some reaction steps remain in thermodynamic chemical equilibrium throughout the process. The validity of the approximation rehes on the fact that both the forward and the reverse reaction steps for the reaction assumed to be in equilibrium are very fast compared to others. 

We will work out these approximations for the series reactions 

Thus we search for the approximate solution for the single nonelementary reaction A — C, which proceeds through the reaction intermediate B in the two preceding reactions. We of course know the exact solution in batch, PFTR, and CSTR This will allow us to test 

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The development of selective extractants for copper has made extraction from dilute solutions (1—5 kg/m ) economically feasible. Transfer of the copper by stripping to a more concentrated sulfuric acid solution, ie, 30—40 kg/m for Cu " and 150—170 kg/m for H2SO4, from which the copper is recovered by electrowinning. The simplified reaction,... 

During superchlorination or shock treatment, ammonium ion is oxidized to nitrogen by breakpoint chlorination which is represented by the simplified reaction sequence... 

A simplified reaction scheme is shown in Fig. 26.5 Again, the ability of rhodium to change its coordination number and oxidation state is crucial, and this catalyst has the great advantage over the conventional cobalt carbonyl catalyst that it operates efficiently at much lower temperatures and pressures and produces straight-chain as opposed to branched-chain products. 

In order to define the raLe and efficiency of photoinitiation, consider the simplified reaction Scheme 3.12. 

Another common deposition system is based on the reaction of silane with a hydrocarbon such as propane or benzene in the following simplified reactions ... 

Titanium Carbonitride. Titanium carbonitride (TiCJSfi.x) combines the wear properties of TiC with the low friction and oxidation and chemical resistance of TiN. It is obtained in a hydrogen atmosphere and at a temperature of approximately 1000°C by the following simplified reaction ... 

CVD Reactions. MoSi2 is usually deposited by the reaction of a molybdenum halide with silane. The simplified reactions are as... 

This corresponds with MacDiarmid s observations which show that the second redox step is strongly pH-dependent. MacDiarmid further differentiated his redox model to take account of the fact that pure leucoemaraldine with its amine-N is already protonated at pH values 2, and that the totally oxidized pemigraniline with its less basic imine-N can also be protonated. This gives the following (simplified) reaction scheme ... 

Chemical kinetic analysis of these simplified reactions allows net ozone formation to be directly related to hydrocarbon consumption by HO on a time-independent basis... 

Because of the variety of ionic species present in the melt, the reactions that take place at the electrodes are considerably more complex than the simple representations given here. Nevertheless, the net reaction is the one given by these simplified reactions 4 e I f) + 6 0 m slt) + 3 (. ) -> 3 C02(g) + 4 Al(/)... 

CDj a The simplified reaction scheme for the enantioselective hydrogenation of a-keto esters over cinchona-Pt/Al203 catalyst can be written as follows ... 

There are four species containing Rh in the reaction scheme in Figure 3.2B Xo, Xi, Xi and X2. Since quasi-equilibrium between Xj and Xj is assumed, these two can be lumped into one pseudo-component X, thereby reducing the total number of intermediates containing Rh from 4 to 3. This results in a simplified reaction network as shown in Figure 3.2C. However, the mathematical expressions for [XJ, Kqs, and s2need to be established the detailed derivation is described below. 

In a number of publications, Rostrup-Nielsen discusses different mechanism of methane steam reforming over Ni catalysts [17]. The proposed simplified reaction sequence for reforming of methane is as follows ... 

In an electrolysis cell, the following simplified reactions take place ... 

Fig. 1 Simplified reaction network for the Fischer-Tropsch synthesis. C represents the growing chain on the catalyst surface.

Thus, two following simplified reaction mechanisms appear possible, viz. 

Ninhydrin Amino acid Ruhemann s purple Simplified reaction between ninhydrin and primary amino acids... 

Ninhydrin Proline Yellow chromophore Simplified reaction between ninhydrin and secondary amino adds... 

PITC Amino acid PTC-amino acid Simplified reaction between PITC and amino acids... 

The fact that water often permits, as noted above, a simplified reaction or work-up procedure made Organic Chemistry in Water an active field of research9,12 14. This might sound quite surprising due to (a) the limited solubility of non-polar organic molecules in water and (b) the danger of hydrolysis. Nevertheless, many organic reactions can be carried out in water, often with improved results. 

Salen stands for the tetradentate, dianionic ligands bis(salicylidene)-ethylenediamines (not the formal name either ), which form extremely stable complexes with a large variety of metals. Their basic structure and the simplified reaction equation for epoxidation is given in Figure 14.9. 

Fig. 8.11. Simplified reaction mechanism of intramolecular cyclization-elimination of anthra-nilamide phenylcarbamates (8.135) [173]...

Fig. 9.1. Simplified reaction mechanisms in the hydrolytic decomposition of organic nitrates. Pathway a Solvolytic reaction (Reaction a) with formation of a carbonium ion, which subsequently undergoes SN1 addition of a nucleophile (e.g., HO ) (Reaction b) or proton E1 elimination to form an olefin (Reaction c). Pathway b HO -catalyzed hydrolysis (,SN2). Pathway c The bimolecular carbonyl-elimination reaction, as catalyzed by a strong base (e.g., HO or RO ), which forms a carbonyl derivative and nitrite.

Fig. 9.2. Simplified reaction mechanisms in the hydrolytic decomposition of organic nitrites. Pathway a Base-catalyzed hydrolysis with liberation of nitrite. Pathway b Reversible nitro-syl exchange between organic nitrites and alcohols. Pathway c General acid catalysis with concerted mechanism in the acid hydrolysis of organic nitrites.

Fig. 4.9 Simplified reaction profiles for various situations in the associative mechanism for substitution in square planar complexes, focusing attention on the replacement M-X-l-Y —> M-Y + X(4.93).

This chapter will focus exclusively on cross-linked vinyl polymer supports either in a spherical bead or resin form, or in some other macroscopic format. These essentially insoluble materials lead to considerably simplified reaction work-up and product isolation procedures when used e.g. in solid phase synthesis or as catalyst or... 

Hydrogenolysis tests have been carried out with dodecane at very low conversions (Figure 3.24). Following the simplified reaction model, Cj, should be strictly equal to Cu-p- There is indisputably an excess of C1-C4 over Cn-Cg, respectively- the greatest excess concerns C2/C10 with a molar ratio of 2 1. 

The time-series array of catalytic spectral data Af-xy can be processed in order to remove the reference spectra, and thereby simplify the reaction spectra. For infrared spectroscopy, this requires proper subtraction of the background moisture and carbon dioxide, the solvent, and some of the reagents. This process can be done manually by trial and error, or it can automated for optimal subtraction. The output is a set of k simplified reaction spectra, Eq. (10). 

First, a simplified reaction for the gunpowder decomposition can be written as in reaction (7.1) ... 

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