Reactants and Products

When a material is heated to a certain temperature level, the chemical bonds between the atoms of the material are broken and then thermal decomposition occurs. The molecules and atoms produced by the decomposition react to form different molecules through many steps. For example, the reaction process may be represented by  

Though the molecular structures of the intermediate products are different from those of the reactants, and heat is released or absorbed at each reaction step, the energy of the initial reactant remains unchanged at each reaction step, and hence the energy of the initial reactant is equivalent to that of the final reaction product. Thus, the energy conservation is represented by Eq. (2.14), as described in Section 2.2, and the final reaction products and the adiabatic flame temperature are determined. 

Since pyrolants are mixtures of various chemicals, such as crystalline particles, metal particles, metal oxide particles, and/or polymeric materials, the physico- 

---

For gas reactions where the gases are assumed to follow ideal behaviour this equation becomes AG° = RT]n Kp, where Kp is defined in terms of the partial pressures of reactants and products. Thus for the general reaction above,... 

U is essential to specify the physical states of the reactants and products, since there may t>e additional heat changes associated with changes in state. 

Nernst equation This equation relates the e.m.f. of a cell to the concentrations or, more accurately, the activities of the reactants and products of the cell reaction. For a reaction... 

Table 5.1 gives a sample calculation of the NHVj for toluene, starting from the molar enthalpies of formation of the reactants and products and the enthalpies of changes in state as the case requires. 

Reactions in which a product remains in the him (as above) are complicated by the fact that the areas of reactant and product are not additive, that is, a nonideal mixed him is formed. Thus Gilby and Alexander [310], in some further studies of the oxidation of unsaturated acids on permanganate substrates, found that mixed hlms of unsaturated acid and dihydroxy acid (the immediate oxidation product) were indeed far from ideal. They were, however, able to ht their data for oleic and erucic acids fairly well by taking into account the separately determined departures from ideality in the mixed hlms. 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

In the case of reaction VII-28, the reactant and product are mutually soluble. Langmuir argued that in this case, escape of oxygen is easier from bulk Fe203... 

The course of a surface reaction can in principle be followed directly with the use of various surface spectroscopic techniques plus equipment allowing the rapid transfer of the surface from reaction to high-vacuum conditions see Campbell [232]. More often, however, the experimental observables are the changes with time of the concentrations of reactants and products in the gas phase. The rate law in terms of surface concentrations might be called the true rate law and the one analogous to that for a homogeneous system. What is observed, however, is an apparent rate law giving the dependence of the rate on the various gas pressures. The true and the apparent rate laws can be related if one assumes that adsorption equilibrium is rapid compared to the surface reaction. 

It is convenient to define a relative activity a. in tenns of the standard states of the reactants and products at the same temperature and pressure, where Aj = fi, =... 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

In principle, the reaction cross section not only depends on the relative translational energy, but also on individual reactant and product quantum states. Its sole dependence on E in the simplified effective expression (equation (A3.4.82)) already implies unspecified averages over reactant states and sums over product states. For practical purposes it is therefore appropriate to consider simplified models for tire energy dependence of the effective reaction cross section. They often fonn the basis for the interpretation of the temperature dependence of thennal cross sections. Figure A3.4.5 illustrates several cross section models. 

The solution to the usual macroscopic kinetic rate equations for the reactant and product concentrations yields... 

As a result of possible recrossings of the transition state, the classical RRKM lc(E) is an upper bound to the correct classical microcanonical rate constant. The transition state should serve as a bottleneck between reactants and products, and in variational RRKM theory [22] the position of the transition state along q is varied to minimize k E). This minimum k E) is expected to be the closest to the truth. The quantity actually minimized is N (E - E ) in equation (A3.12.15). so the operational equation in variational RRKM theory is... 

Utilizing FT-EPR teclmiques, van Willigen and co-workers have studied the photoinduced electron transfer from zinc tetrakis(4-sulfonatophenyl)porphyrin (ZnTPPS) to duroquinone (DQ) to fonn ZnTPPS and DQ in different micellar solutions [34, 63]. Spin-correlated radical pairs [ZnTPPS. . . DQ ] are fomied initially, and the SCRP lifetime depends upon the solution enviromnent. The ZnTPPS is not observed due to its short T2 relaxation time, but the spectra of DQ allow for the detemiination of the location and stability of reactant and product species in the various micellar solutions. While DQ is always located within the micelle, tire... 

In this approach one uses narrow-band continuous wave (cw) lasers for continuous spectroscopic detection of reactant and product species with high time and frequency resolution. Figure B2.5.11 shows an experimental scheme using detection lasers with a 1 MFIz bandwidth. Thus, one can measure the energy spectrum of reaction products with very high energy resolution. In practice, today one can achieve an uncertainty-limited resolution given by... 

Here the transition state is approximated by the lowest crossing pomt on the seam intersecting the diabatic (non-interacting) potential energy surfaces of the reactant and product. The method was originally developed... 

Catalyst particles are usually cylindrical in shape because it is convenient and economical to fonii tliem by extmsion—like spaghetti. Otlier shapes may be dictated by tlie need to minimize tlie resistance to transport of reactants and products in tlie pores tlius, tlie goal may be to have a high ratio of external (peripheral) surface area to particle volume and to minimize the average distance from tlie outside surface to tlie particle centre, witliout having particles tliat are so small tliat tlie pressure drop of reactants flowing tlirough tlie reactor will be excessive. 

In tire preceding example, tire stmcture of tire catalyst combined witli reactants and products was detennined and tire data were used to infer a cycle. Stmctures of tire highly reactive intennediates in catalysis are generally elusive and infonnation about tliem based only on inference. In prospect, tire most incisive infonnation about tire workings of a catalyst can be obtained by observations of tire catalyst in action. The following example illustrates this... 

How does one monitor a chemical reaction tliat occurs on a time scale faster tlian milliseconds The two approaches introduced above, relaxation spectroscopy and flash photolysis, are typically used for fast kinetic studies. Relaxation metliods may be applied to reactions in which finite amounts of botli reactants and products are present at final equilibrium. The time course of relaxation is monitored after application of a rapid perturbation to tire equilibrium mixture. An important feature of relaxation approaches to kinetic studies is that tire changes are always observed as first order kinetics (as long as tire perturbation is relatively small). This linearization of tire observed kinetics means... 

Here X is tire reorganization energy associated witli the curvature of tire reactant and product free energy wells and tlieir displacement witli respect to one another. Assuming a stmctureless polarizable medium, Marcus computed the solvent or outer-sphere component of tire reorganization energy to be... 

Electron transfer reaction rates can depend strongly on tire polarity or dielectric properties of tire solvent. This is because (a) a polar solvent serves to stabilize botli tire initial and final states, tluis altering tire driving force of tire ET reaction, and (b) in a reaction coordinate system where the distance between reactants and products (DA and... 

Development of laser technology over the last decade or so has permitted spectroscopy to probe short-time events. Instead of having to resort to the study of reactants and products and their energetics and shuctures, one is now able to follow reactants as they travel toward products. Fast pulsed lasers provide snapshots of entire molecular processes [5] demanding similar capabilities of the theory. Thus, explicitly time-dependent methods become suitable theoretical tools. 

---