Extent reaction

Eor production use, once an accurate determination of monomeric, dimeric, and higher oligomeric dimer acids has been estabHshed for a specific process and feedstock s oligomerization, subsequent reaction extent can be estimated rapidly by a viscometric method (80). 

The glycolysis of PETP was studied in a batch reactor at 265C. The reaction extent in the initial period was determined as a function of reaction time using a thermogravimetric technique. The rate data were shown to fit a second order kinetic model at small reaction times. An initial glycolysis rate was calculated from the model and was found to be over four times greater than the initial rate of hydrolysis under the same reaction conditions. 4 refs. 

The basic expression used in the procedure for identification of stoichiometry is the one defining reaction extents, i.e. 

In order indicate the contribution of each reaction to the overall model more clearly, the matrix of reaction extents is differenced, giving the reaction extents in each interval ... 

Stoichiometry matrix Af—. i is then plotted as shown in Fig. A-2. The matrix of reaction extents is scaled by dividing by the maximum value (104.3) and plotted as shown in Fig. A-3. The stoichiometric interpretation of the data given in, i is as follows ... 

The task now is to select the linear combinations that will most probably correspond to independent parts of the reaction network with easily interpretable stoichiometry. A simplification of the data in the matrix can be achieved by such a rotation that the axes go through the points in Fig. A-2 (this is equivalent to some zero-stoichiometric coefficients) and that the points of Fig. A-3 are in the first quadrant (this corresponds to positive reaction extents) if possible. Rotations of the abscissa through 220° and the ordinate through 240° lead to attaining both objectives. The associated rotation matrix is ... 

After rotating and scaling to make the largest stoichiometric coefficients unity, the matrices of stoichiometry and reaction extents are ... 

The kinetics of the gas-phase reaction between nitrogen dioxide (A) and trichloroethene (B) have been investigated by Czamowski (1992) over the range 303-362.2 K. The reaction extent, with the reaction carried out in a constant-volume BR, was determined from measurements of infrared absorption intensities, which were converted into corresponding pressures by calibration. The products of the reaction are nitrosyl chloride, NOC1 (C), and glyoxyloxyl chloride, HC(0)C(0)C1. 

In complex systems, fA is not a unique parameter for following the course of a reaction, unlike in simple systems. For both kinetics and reactor considerations (Chapter 18), this means that rate laws and design equations cannot be uniquely expressed in terms of /A, and are usually written in terms of molar concentrations, or molar flow rates or extents of reaction. Nevertheless, fA may still be used to characterize the overall reaction extent with respect to reactant A. 

The yield of a product is a measure of the reaction extent at some point (time or position) in terms of a specified product and reactant. The most direct way of calculating the yield of a product in a complex system from experimental data is by means of a stoichiometric model in canonical form, with the product as a noncomponent. This is because that product appears only once in the set of equations, as illustrated for each of CO, CO and HCHO in Example 5-1. 

The are stoichiometric coefficients in the R independent reactions. The progress of each of the independent reactions is indicated by a reaction extent ej, j = l, R. The mole number of species in a reacting mixture is given by... 

The reaction extents, ej, are dimensionless numbers in this formulation. They are restricted to values such that all the n are non-negative. 

As this reaction proceeds, beginning with some initial mixture, each of the four mole fractions can be represented as a function of a single reaction extent, e. 

For every initial H20/C0 ratio, the mixture mole fractions, hence the critical temperature and volume, are determined by the reaction extent e. The equilibrium constant is calculated at the critical temperature. The fugacities are calculated also at the critical condition for the given e. The function F, defined as... 

Although it has been shown that thermodynamic models which imply phase separations can create difficulties with uniqueness in solving the reaction equilibrium equations (10, 25, 24), there proved to be only one solution to equation (26) under the conditions studied. It is conceivable that more than one critical point could be found for some reacting mixtures at certain reaction extents (two critical points are indeed indicated in Figure 1 for some C02 - CO mixtures), in which case F(e) will not be a single-valued function. This possibility was not explored. 

The study described above for the water-gas shift reaction employed computational methods that could be used for other synthesis gas operations. The critical point calculation procedure of Heidemann and Khalil (14) proved to be adaptable to the mixtures involved. In the case of one reaction, it was possible to find conditions under which a critical mixture was at chemical reaction equilibrium by using a one dimensional Newton-Raphson procedures along the critical line defined by varying reaction extents. In the case of more than one independent chemical reaction, a Newton-Raphson procedure in the several reaction extents would be a candidate as an approach to satisfying the several equilibrium constant equations, (25). 

O Dormell, J., Adverse dmg reactions extent of the problem and causality assessment, in O Donnell, J.T., Ed., Drug Injury Liability, Analysis, and Prevention, L J Publishers, Tucson, AZ,... 

Figure 4.1S Representation of the three primary steps for the generic inverse problem in chemical kinetics including homogeneous catalysis. In situ spectroscopic data is represented by 4kexv Tbe inverse spectroscopic problem (Eq. (2)), which is the focus of this chapter, is represented by S [,s, Ojxv The inverse problem associated with stoichiometries and reaction topology is represented by r rxs moles, reactions, extents of reaction and reaction stoi-...

The goals of geochemical kinetics are to understand (i) the reaction rate and how long it would take to reach equilibrium for a specific reaction or system, (ii) atoministic mechanisms for a reaction to proceed, and (iii) the history (such as age and cooling rate) of rocks based on reaction extents. 

A reaction vessel consisting of phenol (1040 ppw), water (226 ppw), and sodium sulfite (305 ppw) was warned to 57°C and treated with 50% aqueous formaldehyde (532 ppw) over 25 minutes where the mixture exothermed to 80°C. After the addition the mixture was warmed to 100°C for 60 minutes and then cooled to 80°C and additional 50% formaldehyde (1094 ppw) added to the reaction mixture over 30 minutes. The reaction extent was monitored by determining the concentration of free phenol in the mixture. When the free phenol content was about 0.7% by weight the mixture was cooled to ambient temperature and a third quantity of formaldehyde (850 ppw) added. The isolated resin had a total solids content of 47 wt%, a free formaldehyde content of 12.6 wt%, and a free phenol content of 0.3 wt%. 

The step 1 product was transesterified to form linear poly(propylene fumarate) containing hydroxyl groups on the termini. The polymerization was performed using propylene glycol under vacuum at 100°C and then at 130°C for 3 hours where the molecular weight was modulated by the reaction extent. The product was then isolated and used without further purification. 

Starting at line 900 you find the user subroutine. In this routine the mole numbers occupy the array elements NW(1), NW(2),. .., NW(5) and the scalar variable NW stores the total mole number. At the current value X(l) and X(2) of the reaction extents we first calculate tine mole numbers. If any of them is negative or zero, the error flag ER is set to a nonzero value. If the mole numbers are feasible, the values computed according to (2.31) will occupy the array elements G(l) and G(2). The initial estimates are X(1) = 1 and X(2) = 0.1, the first corrections are D(l) = D(2) = 0.01. The following output shows some of the iterations. 

Other forms Heat of energy Reaction direction Reaction extent ... 

Calculation of Equilibrium Constant, K for Dissociation Reactions. Extent or Degree of Dissociation, a... 

Application to Simultaneous Phase and Chemical Equilibrium. The single-stage process with simultaneous phase and chemical equilibrium is another application of the inside-out concept where the Newton-Raphson method has been employed in a judicious way in the inside loop. There would appear to be no reaction parameter having characteristics that make it suitable as an outside loop iteration variable in the spirit of the inside-out concept. On the other hand, the chemical equilibrium relationships are simple in form, and do not introduce new thermophysical properties that depend in a complicated way on other variables. Thus it makes sense to include them in the inside loop, and to introduce the reaction extents as a new set of inside loop variables. 

The reaction extent is governed by the mass balance equation... 

Neglecting the light byproducts, and assimilating all the heavy byproducts with dodecane, the input-output mass balance can be written using the reaction extents (kmol/h) ... 

At this design stage, the mole balance model of the plant is given by the following equations, where the reactor and separation performances are described by the reaction extents and ( 2 and the recoveries pP and pl respectively. 

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