Meaning of Reaction Rate

To discuss reaction rate meaningfully, it must be defined precisely. The rate of reaction is a positive quantity that expresses how the concentration of a reactant or product changes with time. To illustrate what this means, consider the reaction 

Changes in reactant and product concentrations with time. For the reaction NA(9) — ZNO g) + yg). the concentrations of NO2 and O2 increase with time, whereas that of N2O5 decreases. The reaction rate is defined as -A[NA1/Af= AINOJ/2 At= AIOJ/ At 

To Dlustrate the use of this expression, suppose that for the formation of ammonia, Na(j) + 3Ha(j)----------------------------- 2NH3(tf) 

By defining rate this way, it is independent of which species we focus on N2, H2, or NH3. 

Notice that reaction rate has the units of concentration divided by time. We will always express concentration in moles per liter. Time, on the other hand, can be expressed in seconds, minutes, hours.A rate of 0.10 mol/L - min corresponds to 

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Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

Although the mean relative speed of the molecules increases with temperature, and the collision frequency therefore increases as well, Eq. 16 shows that the mean relative speed increases only as the square root of the temperature. This dependence is far too weak to account for observation. If we used Eq. 16 to predict the temperature dependence of reaction rates, we would conclude that an increase in temperature of 10°C at about room temperature (from 273 K to 283 K) increases the collision frequency by a factor of only 1.02, whereas experiments show that many reaction rates double over that range. Another factor must be affecting the rate. 

Experimental methods for the measurement of reaction rate are discussed further in Chapter 3, and are implicitly introduced in many problems at the ends of other chapters. By these means, we emphasize that chemical kinetics is an experimental science, and we attempt to develop the ability to devise appropriate methods for particular cases. 

A remark would be in order at this point concerning the calculation of the dissociation rate coefficient by means of the rate coefficient for recombination of H and OH and the equilibrium constant K = [H20]/[H][OH]. Getzinger5 determined the rate coefficient for the recombination reaction H+OH+Ar - ... 

Fluidized beds provide many features not available in the fixed-bed types, including high rates of heat and mass transfer and good mixing of the solid phase, which means that reaction rates are high and the temperature is more or less... 

Another simple reaction with a complicated reaction rate law is Reaction 1-5, 203(gas) 302(gas), which may be accomplished thermally or by photochemical means. The reaction rate law for the thermal decomposition of ozone is d /df= c5[03] /[02] when [O2] is very high, and is d /dt=ks [O3] when [O2] is low. 

For overall reactions, the reaction rate law cannot be written down by simply looking at the reaction, but has to be determined from experimental studies. (Whether a reaction is elementary must be determined experimentally, which means that reaction rate laws for all chemical reactions must be experimentally determined.) The reaction rate law may take complicated forms, which might mean that the order of the reaction is not defined. 

The Arrhenius relation means that the rate constant or the diffusivity increases with temperature. Typically, at low temperatures (0-60°C), a 10-degree increase in temperature results in a doubling of reaction rates. In this section, two theories are introduced to account for the Arrhenius relation and reaction rate laws. Collision theory is a classical theory, whereas transition state theory is related to quantum chemistry and is often referred to as one of the most significant advances in chemistry. 

Heat increases reaction rates. It is common knowledge that chemical reaction rates double whenever the temperature of a system increases by 18°F (10°C). This also means that reaction rates can slow by one-half whenever the temperature decreases by the same amount. 

Remarkable tuning of reaction rates has been achieved for the isomerization of several dye molecules in supercritical fluid solvents using both small pressure changes and small additions of cosolvents. Rates of the thermal cis-trans relaxation were measured spectroscopically following irradiation for three dyes in supercritical carbon dioxide and ethane, pure and with several polar and protic cosolvents. These results demonstrate the versatility of supercritical fluid solvents, both to examine reaction mechanisms and as a means to tune rates (DiUow et al., 1998). 

The observation that reaction (13) is the slowest step, and that the organochromium complexes are highly colored with peak maxima at 300 (2500) and —400 (—300), provides a means of determining rate constants for (13) (18). 

What is the physical meaning of the rate constant of a chemical reaction What is the dimension of the rate constant of a first-(second-) order chemical reaction How does the rate constant depend on the temperature Write the Arrhenius equation. What is called the activation energy What substances are called catalysts and inhibitors ... 

Another consequence of the solvent s presence on the rate of reactant diffusion towards (and away from) each other is that solvent has to be squeezed out of ( sucked into ) the intervening space between the reactants. Because this takes time, the approach (or separation) of reactants is slowed. Effectively, the solvent diffusion coefficient is reduced at distances of separation between reactants from one to several solvent diameters. Figure 38 (p. 216) shows the diffusion coefficient as a function of reactant separation distances. This effect is known as hydrodynamic repulsion and it more than cancels the net increase of reaction rate due to the potential of mean force. It is discussed further in Chap. 8 Sect. 2.5 and Chap. 9 Sect. 3. Both the steady-state and transient terms in the rate coefficient depend on these effects. 

When more satisfactory forms of diffusion coefficient for the hydro-dynamic repulsion effect become available, these should be incorporated into the diffusion equation analysis. The effect of competitive reaction processes on the overall rate of reaction only becomes important when the concentration of both reactants is so large that it would require exceptional means to generate such concentrations of reactants and a solvent of extremely low diffusion coefficient to observe such effects. This effect has been the subject of much rather repetitive effort recently (see Chap. 9, Sect. 5.5). By contrast, the recent numerical studies of reactions between uncharged species is a most welcome study of the effect of this competition in various small clusters of reactants (see Chap. 7, Sect. 4.4). It is to be hoped that this work can be extended to reactions between ions in order to model spur decay processes in solvents less polar than water. One other area where research on the diffusion equation analysis of reaction rates would be very welcome is in the application of the variational principle (see Chap. 10). 

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