Concentration dependence of reaction rates

Harcourt Esson Systematic study on concentration dependence of reaction rate... 

The temperature and concentration dependencies of reaction rates can usually be expressed as separate functions, for example... 

In this section we will introduce a model that can be used to account for the observed characteristics of reaction rates. This model, the collision model, is built around the central idea that molecules must collide to react. We have already seen that this assumption can explain the concentration dependence of reaction rates. Now we need to consider whether this model can also account for the observed temperature dependence of reaction rates. 

The interpretation of measured flame profiles by means of the continuity equations may be approached in one of two ways. The direct experimental approach involves the use of the measured profiles to calculate overall fluxes, reaction rates, and hence rate coefficients. Its successful application depends on the ability to measure the relevant profiles, including concentrations of intermediate products. This is not always possible. In addition, the overall fluxes in the early part of the reaction zone may involve large diffusion contributions, and these depend in turn on the slopes of the measured profiles. Thus accuracy may suffer. The lining up on the distance axis of profiles measured by different methods is also a problem, and, in quantitative terms, factor-of-two accuracy is probably about the best that may normally be expected from this approach at the position of maximum rate. Nevertheless, examination of the concentration dependence of reaction rates in flames may still provide useful preliminary information about the nature of the controlling elementary processes [119—121]. Some problems associated with flame profile measurements and their interpretation have been discussed by Dixon-Lewis and Isles [124]. Radical recombination rates in the immediate post-combustion zones of flames are capable of measurement with somewhat h her precision than above. 

Ai = concentration, mols i/kg of gas f(pAi) = concentration dependence of reaction rate G = mass velocity, kg gas/m2-hour kj = rate constant of jth reaction first order kj [=] m3 gas/kg catalyst-hour L = reactor length, m X = reactor length, dimensionless p = gas density, kg/m3 pB = catalyst density, kg/m3 of reactor... 

Detailed studies of the concentration dependence of reaction rates are necessary to distinguish between the two mechanisms. 

The concentration dependence of reaction rate shows two regions, the region of the first order dependence in substrate concentrations at low values of S (below Km) (Figure 6.3)... 

Now we switch attention from the concentration dependence of reaction rates to the temperature dependence of rate coefficients. This, too, can give insights into the mechanism of the reaction. 

Go to http //now.brookscole.com/ cracolice3e and dick Chemistry Interactive for the module Concentration Dependence of Reaction Rate. 

Ammonia decomposition over Fe, Cu, Ag, Au, and Pt Hydrolysis of starch to glucose catalyzed by acids Mixture of coal gas and air makes a platinum wire white hot Measurements on the rate of H2O2 decomposition Selective oxidation of ethanol to acetic acid over platinum Comprehensive paper on the H2 + O2 reaction on platinum foils, including reaction rates, deactivation, reactivation, and poisoning Definition of catalysis, catalyst, and catalytic force First quantitative analysis of reaction rates Systematic studies on the concentration dependence of reaction rates First concise monograph on chemical kinetics Definition of order of reaction Arrhenius equation k = u exp (-Ea/RT)... 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

The dependence of reaction rates on pH and on the relative and absolute concentrations of reacting species, coupled with the possibility of autocatalysis and induction periods, has led to the discovery of some spectacular kinetic effects such as H. Landolt s chemical clock (1885) an acidified solution of Na2S03 is reacted with an excess of iodic acid solution in the presence of starch indicator — the induction period before the appearance of the deep-blue starch-iodine colour can be increased systematically from seconds to minutes by appropriate dilution of the solutions before mixing. With an excess of sulfite, free iodine may appear and then disappear as a single pulse due to the following sequence of reactions ... 

The dependence of reaction rate on concentration is readily explained. Ordinarily, reactions occur as the result of collisions between reactant molecules. The higher the concentration of molecules, the greater the number of collisions in unit time and hence the faster the reaction. As reactants are consumed, their concentrations drop, collisions occur less frequently, and reaction rate decreases. This explains the common observation that reaction rate drops off with time, eventually going to zero when the limiting reactant is consumed. 

In the search for a better approach, investigators realized that the ignition of a combustible material requires the initiation of exothermic chemical reactions such that the rate of heat generation exceeds the rate of energy loss from the ignition reaction zone. Once this condition is achieved, the reaction rates will continue to accelerate because of the exponential dependence of reaction rate on temperature. The basic problem is then one of critical reaction rates which are determined by local reactant concentrations and local temperatures. This approach is essentially an outgrowth of the bulk thermal-explosion theory reported by Fra nk-Kamenetskii (F2). 

B. U. Felderhof and J. M. Deutch, Concentration dependence of the rate of diffusion-controlled reactions, J. Chem. Phys. 64, 4551 (1976). 

Since data are almost invariably taken under isothermal conditions to eliminate the temperature dependence of reaction rate constants, one is primarily concerned with determining the concentration dependence of the rate expression [0(Ct)] and the rate constant at the temperature in question. We will now consider two differential methods that can be used in data analysis. 

When multiple reactions are possible, certain of the products have greater economic value than others, and one must select the type of reactor and the operating conditions so as to optimize the product distribution and yield. In this subsection we examine how the temperature can be manipulated with these ends in mind. In our treatment we will ignore the effect of concentration levels on the product distribution by assuming that the concentration dependence of the rate expressions for the competing reactions is the same in all cases. The concentration effects were treated in detail in Chapter 9. 

If the two competing reactions have the same concentration dependence, then the catalyst pore structure does not influence the selectivity because at each point within the pore structure the two reactions will proceed at the same relative rate, independent of the reactant concentration. However, if the two competing reactions differ in the concentration dependence of their rate expressions, the pore structure may have a significant effect on the product distribution. For example, if V is formed by a first-order reaction and IF by a second-order reaction, the observed yield of V will increase as the catalyst effectiveness factor decreases. At low effectiveness factors there will be a significant gradient in the reactant concentration as one moves radially inward. The lower reactant concentration within the pore structure would then... 

Studies of the reaction kinetics at low concentrations of dibutylmagnesium (<0.35 M) reveal a first-order dependence of reaction rate on both zirconocene and dibutylmagnesium concentration, which is consistent with ratedetermining transmetallation. At higher concentration of dibutylmagnesium (>0.35 M), the reaction is first order in... 

Reaction weight is a reaction rate calculated at unit concentrations of intermediates, i.e. it is either the reaction constant or the reaction constant multiplied by power product corresponding to the "slow" components (either reagents or products). Thus, the dependencies of reaction rate on temperature and concentrations are "hidden" in reaction weights. 

Another factor that affects the rate of a chemical reaction is the concentration of reactants. As noted, most reactions take place in solutions. It is expected that as the concentration of reactants increases more collisions occur. Therefore, increasing the concentrations of one or more reactants generally leads to an increase in reaction rate. The dependence of reaction rate on concentration of a reactant is determined experimentally. A series of experiments is usually conducted in which the concentration of one reactant is changed while the other reactant is held constant. By noting how fast the reaction takes place with different concentrations of a reactant, it is often possible to derive an expression relating reaction rate to concentration. This expression is known as the rate law for the reaction. 

The decomposition of hydrogen peroxide illustrates the dependence of reaction rate on concentration. One way to determine how fast hydrogen decomposes is to measure the amount of oxygen generated. By performing a series of trials using different concentrations of hydrogen peroxide, it is found that the reaction rate increases in... 

Scheme (254) does not predict explicitly any dependence of reaction rates r(1), r 2), and r 3) on the concentration of H2S04 and product salts. It is... 

Note that careful evaluation and minimization of uncertainties and errors in CTMs is requested to enable the application of these CTMs to the study of observed changes in 03 as small as < 1.5 %/yr. However, actually 03 concentrations are simulated by the models within 20-50%. Chemical reaction rates are also uncertain, for instance in the 90 s determinations of the rates of CH4 and CH3CC13 reactions with OH suggested that these reactions are about 20% slower than believed. Similarly OH reaction with N02 which is an important sink for NOx in the troposphere is measured to be 10-30% lower than earlier estimates [23]. Thus, the past years a number of studies (mainly based on Monte Carlo simulations) focused on the identification and evaluation of the importance of various chemical reactions on oxidant levels to highlight topics crucial for error minimization. Temperature dependence of reaction rates can also introduce a 20-40% uncertainty in 03 and H20 computations in the upper troposphere. It has been also shown that 03 simulations are particularly sensitive to the photolysis rates of N02 and 03 and to PAN chemistry. 

Note that both 9.50 and 9.55 show the characteristic dependence of reaction rate on first power of substrate concentration and square root of the ratio of initiation rate to termination rate. 

The simplest way to determine a rate law is the method of initial rates. If a reaction is slow enough, it can be allowed to proceed for a short time, At, and the change in a reactant or product concentration measured. Repeating the experiment for different concentrations, the concentration-dependence of the rate can be deduced. 

An aim of the model is to determine the influence of the various mass transport parameters and show how they influence the polarization behavior of three-dimensional electrodes. In the model we have adopted relatively simple electrode kinetics, i.e., Tafel type, The approach can also be applied to more complicated electrode kinetics which exhibit non-linear dependency of reaction rate (current density) on reactant concentration. 

Dependence of reaction rates on the concentrations of the reactants (and the products in certain cases) can be very useful in understanding the mechanism of catalysis. Some of the ubiquitous mechanistic steps reveal themselves in empirically derived rate expressions. In other words, such rate expressions, once established by experiments, are characteristic signs of such steps. 

When UV irradiated, an octane solution of 1 (R = H, Aik) changes its color from yellowish to deep blue. The initial spectrum is slowly restored at room temperature (the effective lifetime of the colored form at room temperature is about 104s). No concentration dependence of the rate of the dark reaction was observed, which agrees with the intramolecular nature of the reaction. Figure 8.1 portrays the evolution of the absorption spectrum of a perimidinespirocyclohex-adienone 1 (R = Me) during UV irradiation of its hexane solution (Scheme 1). 

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