Reactions, independent simultaneous

Over the years many blends of polyurethanes with other polymers have been prepared. One recent example is the blending of polyurethane intermediates with methyl methacrylate monomer and some unsaturated polyester resin. With a suitable balance of catalysts and initiators, addition and rearrangement reactions occur simultaneously but independently to give interpenetrating polymer networks. The use of the acrylic monomer lowers cost and viscosity whilst blends with 20% (MMA + polyester) have a superior impact strength. 

The principle of independent electrochemical reactions applies when several reactions occur simultaneously. It says that each reaction follows its own quantitative laws, irrespective of other reactions. At a given potential, the rates of the different reactions are not at all interrelated, and at a given CD they are merely tied together by relation (13.53). This does not mean that the reactions have no influence on each other at all. One of the reactions may produce changes in the external conditions for other reactions (e.g., in the temperature or solution pH, the amount of impurities adsorbed on the electrode). However, the form of the kinetic equation of each reaction is not affected by these changes. The principle of independent electrochemical reactions is quite general, and rarely violated (we discuss an instance of such a departure in Section 22.2). 

When the effectiveness factors for both reactions approach unity, the selectivity for two independent simultaneous reactions is the ratio of the two intrinsic reaction-rate constants. However, at low values of both effectiveness factors, the selectivity of a porous catalyst may be greater than or less than that for a plane-catalyst surface. For a porous spherical catalyst at large values of the Thiele modulus s, the effectiveness factor becomes inversely proportional to (j>S9 as indicated by equation 12.3.68. In this situation, equation 12.3.133 becomes... 

Traud1 [26], The latter reported that Zn dissolution from Zn/Hg amalgam was dependent on the amalgam electrochemical potential, but independent of the accompanying H2 evolution partial reaction. In Paunovic s and Saito s adaptation of this model, the partial electroless reactions occur simultaneously on the plating surface, resulting in the development of an equilibrium potential intermediate in value between the reversible potentials, in practice the experimentally-determined open circuit potential values, of the anodic and cathodic partial reactions. 

When several reactions occur simultaneously a degree of advancement is associated with each stoichiometric equation. Problem P4.01.26 is a application of this point. Some processes, for instance cracking of petroleum fractions, involve many substances. Then a correct number of independent stoichiometric equations must be formulated before equilibrium can be calculated. Another technique is to apply the principle that equilibrium is at a minimum of Gibbs free energy. This problem, however, is beyond the scope of this book. 

A similar analysis can be made for many reactions occurring simultaneously. If we have r independent reactions with n species, their stoichiometric coefficients can be termed Vij, with i = 1, 2,..., n species and j = I,... 

Equation 3.39 holds valid for the system in which only a single process or reaction is occurring. In a system in which multiple chemical reactions are simultaneously occurring, Eq. 3.27 for the uncompensated heat can be expressed by the sum of the products of all independent affinities and their conjugated reaction rates as given in Eq. 3.40 ... 

The reactivity of the molecular fullerene solid resembles the expected pattern for a homogeneous material. Only a small prereactivity at 700 K indicates that a fullcrcne-oxygen complex [12] is formed as an intermediate stoichiometric compound [15, 105], At 723 K the formation of this compound and the complete oxidation are in a steady state [12, 106, 107] with the consequence of a stable rate of oxidation which is nearly independent of the bum-off of the fullerene solid. This solid transforms prior to oxidation into a disordered polymeric material. The process is an example of the alternative reaction scenario sketched above for the graphite oxidation reaction. The simultaneous oxidation of many individual fullerene molecules. leaving behind open cages with radical centers, is the reason for the polymerization. 

We see from Eq. (15.3) that either the v, s or e must be expressed in molest and that the other quantity must be a pure number. As a matter of convenience we choose to express the reaction coordinate e in moles. This allows one to speak of a mole of reaction, meaning that e has changed by a unit amount, i.e., by one, mole. When Ae = 1 mol, the reaction proceeds to such an extent that the chaise in mole number of each reactant artd product is equal to its stoichiometric number. When two or more independent reactions proceed simultaneously, we let subscript j be the reaction index, and associate a separate reaction coordinate with each reaction. The stoichiometric numbers are doubly subscripted to identify , their association with both a species and a reaction. Thus designates th stoichiometric number of species i in reaction j. Since the number of moles of i species n,- may change because of several reactions, the general equation analogous to Eq. (15.3) includes a sum ... 

Provided the sample is large enough for statistics to be reliable, the rate equations in Table 2.1 are valid under all circumstances, regardless of the presence or absence of other molecules not involved in the respective step, and regardless of whether other reactions occur simultaneously in the same volume element. However, these "ideal" rate equations in terms of concentrations and with concentration-independent coefficients are only approximations. Deviations must be expected, but are relatively minor in most cases of practical interest and will be disregarded in this book, except for a brief discussion of nonideality in the next section. 

Wlien two or more independent reactions proceed simultaneously, subscript j serves as the reaction index. A separate reaction coordinate j then applies to each reaction. The stoichiometric numbers are doubly subscripted to identify their association with botli a species and a reaction. Thus vij designates the stoichiometric number of species / in reaction j. Since the number of moles of a species n, may change because of several reactions, tlie general equation analogous to Eq. (13.3) includes a sum ... 

As shown previously, it is uncommon that the side chain reactions will take place independently from any chain scission. Heating at relatively low temperatures between 100° C to 300° C (known as thermal degradation) may lead in some polymers to side chain reactions with elimination of small molecules (such as H2O, HCI), while the polymer backbone still remains intact. At typical pyrolysis temperatures (500-800° C) both types of reactions occur simultaneously or very rapidly one after the other, as combined reactions. Combined reactions may take place either with a cyclic transition state or with free radical formation. The free radicals formed during polymeric chain scission or during the side chain reactions can interact with any other part of the molecule. 

If an incomplete reaction occurs, you should calculate the standard heat of reaction only for the products which are actually formed from the reactants that actually react. In other words, only the portion of the reactants that actually undergo some change and liberate or absorb some energy are to be considered in calculating the overall standard heat of the reaction. If some material passes through the reactor unchanged, it can contribute nothing to the standard heat of reaction calculations (however, when the reactants or products are at conditions other than 25°C and 1 atm, whether they react or not, you must include them in the enthalpy calculations as explained in Sec. 4.7-5). If several reactions occur simultaneously, your material balance must reflect what enters the reactor and is produced via the independent reactions. 

If this is summed, the last term will give AH)r, by definition of the heat of reaction. For simultaneous reactions, Eq. (7.1.25) shows that the last term would have a similar sum for each independent reaction ... 

For investigation of the kinetics of p)Tolysis and oxidation reactions a Simultaneous Thermal Analyzer is preferred, provided that the incorporated software permits the evaluation according both to ASTME 689-79 and Flynn and Wall. In this way the kinetic parameters can be obtained and at the same time the peak maxima (minima) of the curves of energy against temperature can be examined to decide whether they really appear at equal conversion levels independent of the heating rates. All the requirements for the thermoanalysis of petroleum and its products would be fulfilled if such an instrument could... 

When diffusion and chemical reaction occur simultaneously i.e. at the same time in the same space, both effects usually cannot be separated experimentally. With the appropiate models, however, the combined effect can be described effectively, so that from a series of experiments the influence of the separate elementary processes can be evaluated. A very important simplification can be made in many practical situations since the characteristic length scale in this situation is often independent of the scale of operation (the film thickness in gas/liquid reactions, or the particle size in heterogeneous catalysis) scaling up is often quite simple. There is one important exception to this the case of diffusion and reaction around bubbles in fluidized beds, since the sizes of the bubbles are generally scale dependent. 

Reaction (2) is simply the sum of reactions (1) and (3), so even though all reactions progress simultaneously, only reactions (1) and (3) are considered independently, with maximum conversion of syngas to methanol limited by thermodynamic equilibrium. 

In 1997 the application of two different chiral ytterbium catalysts, 55 and 56 for the 1,3-dipolar cycloaddition reaction was reported almost simultaneously by two independent research groups [82, 83], In both works it was observed that the achiral Yb(OTf)3 and Sc(OTf)3 salts catalyze the 1,3-dipolar cycloaddition between nitrones 1 and alkenoyloxazolidinones 19 with endo selectivity. In the first study 20 mol% of the Yb(OTf)2-pyridine-bisoxazoline complex 55 was applied as the catalyst for reactions of a number of derivatives of 1 and 19. The reactions led to endo-selective 1,3-dipolar cycloadditions giving products with enantioselectivities of up to 73% ee (Scheme 6.38) [82]. In the other report Kobayashi et al. described a... 

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