Rate equation concentration effects

Problem 6.20 For each rate equation, what effect does the indicated concentration change have on the overall rate of the reaction ... 

Nitric acid being the solvent, terms involving its concentration cannot enter the rate equation. This form of the rate equation is consistent with reaction via molecular nitric acid, or any species whose concentration throughout the reaction bears a constant ratio to the stoichiometric concentration of nitric acid. In the latter case the nitrating agent may account for any fraction of the total concentration of acid, provided that it is formed quickly relative to the speed of nitration. More detailed information about the mechanism was obtained from the effects of certain added species on the rate of reaction. 

Rate equations 28 and 30 combine the advantages of concentration-independent mass transfer coefficients, even in situations of multicomponent diffusion, and a familiar mathematical form involving concentration driving forces. The main inconvenience is the use of an effective diffusivity which may itself depend somewhat on the mixture composition and in certain cases even on the diffusion rates. This advantage can be eliminated by working with a different form of the MaxweU-Stefan equation (30—32). One thus obtains a set of rate equations of an unconventional form having concentration-independent mass transfer coefficients that are defined for each binary pair directiy based on the MaxweU-Stefan diffusivities. 

Equation 39 can often be simplified by adopting the concept of a mass transfer unit. As explained in the film theory discussion eadier, the purpose of selecting equation 27 as a rate equation is that is independent of concentration. This is also tme for the Gj /k aP term in equation 39. In many practical instances, this expression is fairly independent of both pressure and Gj as increases through the tower, increases also, nearly compensating for the variations in Gj. Thus this term is often effectively constant and can be removed from the integral ... 

The effectiveness is known from experiment for important industrial catalysts and is correlated, in general, in terms of pore characteristics, concentrations, and specific rate equations. 

A brief overview of the form for rate equations reveals that temperature and concentration e Tects are strongly interwoven. This is so even if all four basic steps in the rules of Boudart (1968) are obeyed for the elementary steps. The expectations of simple unchanging temperature effects and strict even-numbered gas concentration dependencies of rate are not justified. 

If the rate equation contains the concentration of a species involved in a preequilibrium step (often an acid-base species), then this concentration may be a function of ionic strength via the ionic strength dependence of the equilibrium constant controlling the concentration. Therefore, the rate constant may vary with ionic strength through this dependence this is called a secondary salt effect. This effect is an artifact in a sense, because its source is independent of the rate process, and it can be completely accounted for by evaluating the rate constant on the basis of the actual species concentration, calculated by means of the equilibrium constant appropriate to the ionic strength in the rate study. 

The effect of substrate concentration on specific growth rate (/i) in a batch culture is related to the time and p,max the relation is known as the Monod rate equation. The cell density (pcell) increases linearly in the exponential phase. When substrate (S) is depleted, the specific growth rate (/a) decreases. The Monod equation is described in the following equation ... 

The most extensive study of the effect of conditions upon the kinetics of bromination was made by Robertson et al.23l 279, who measured the rates of bromination of alkylbenzenes, acetanilide, aceto-p-toluidide, mesitylene, anisole and p-tolyl methyl ether in acetic acid at 24 °C. They found that at relatively high concentrations of bromine (A//40-M/100) the reaction is second-order in bromine, i.e. the rate equation is... 

For example, imagine that the reaction between BrOj and Br in acidic solutions, Eq. (1-11), is conducted with [H+]0 = 910 X [BrOj ]0 and [Br-]0 = 280 x [BrOj ]0. The effective concentrations of H+ and Br- being nearly constant, the rate equation would become... 

The route from kinetic data to reaction mechanism entails several steps. The first step is to convert the concentration-time measurements to a differential rate equation that gives the rate as a function of one or more concentrations. Chapters 2 through 4 have dealt with this aspect of the problem. Once the concentration dependences are defined, one interprets the rate law to reveal the family of reactions that constitute the reaction scheme. This is the subject of this chapter. Finally, one seeks a chemical interpretation of the steps in the scheme, to understand each contributing step in as much detail as possible. The effects of the solvent and other constituents (Chapter 9) the effects of substituents, isotopic substitution, and others (Chapter 10) and the effects of pressure and temperature (Chapter 7) all aid in the resolution. 

So far, what has been examined is the effect of the concentrations of the reactants and the products on the reaction rate at a given temperature. That temperature also has a strong influence on reaction rates can be very effectively conveyed by considering the experimentally found data on the formation of water from a mixture of hydrogen and oxygen. At room temperature the reaction will not take place hence the reaction rate is zero. At 400 °C it is completed in 1920 h, at 500 °C in 2 h, and at 600 °C the reaction takes place with explosive rapidity. In order to obtain the complete rate equation, it is also necessary to know the role of temperature on the reaction rate. It will be recalled that a typical rate equation has the following form ... 

Operation with an excess of ammonia in the reactor has the effect of increasing the rate due to the C fHl term. However, operation with excess ammonia decreases the concentration of ethylene oxide, and the effect is to decrease the rate due to the CEO term. Whether the overall effect is a slight increase or decrease in reaction rate depends on the relative magnitude of a and b. Consider now the rate equations for the by product reactions ... 

A kinetic distinction between the operation of the SN1 and SN2 modes can often be made by observing the effect on the overall reaction rate of adding a competing nucleophile, e.g. azide anion, N3e. The total nucleophile concentration is thus increased, and for the SN2 mode where [Nu ] appears in the rate equation, this will result in an increased reaction rate due to the increased [Nut]. By contrast, for the Stfl mode [Nut] does not appear in the rate equation, i.e. is not involved in the rate-limiting step, and addition of N3e will thus be without significant effect on the observed reaction rate, though it will naturally influence the composition of the product. 

This relation is the broadly known Michaelis-Menten equation. The effect of substrate concentration ni on the rate predicted by this equation follows a characteristic pattern. Where substrate concentration is considerably smaller than the half saturation constant (ni <reactive intermediate EA depends on the availability of the substrate A. In this case, (mA + K A ) and reaction rate r+ given by 17.18 is proportional to mA. For the opposite case, (mA K ), little free enzyme E is available to complex with A. Now, (mA + mA and reaction... 

Raising a mixture of fuel and oxidizer to a given temperature might result in a combustion reaction according to the Arrhenius rate equation, Equation (4.1). This will depend on the ability to sustain a critical temperature and on the concentration of fuel and oxidizer. As the reaction proceeds, we use up both fuel and oxidizer, so the rate will slow down according to Arrhenius. Consequently, at some point, combustion will cease. Let us ignore the effect of concentration, i.e. we will take a zeroth-order reaction, and examine the concept of a critical temperature for combustion. We follow an approach due to Semenov [3],... 

The stability constants of the mono- and bis-complexes between Cu(II) and catecholate were determined under anaerobic conditions and were found to be the same as reported earlier, i.e. log p1 = 13.64 (CuC) and log p2 24.92 (CuC2+) (36,39). A comparison of the speciation and oxidation rate as a function of pH clearly indicated that the mono-catechol complex is the main catalytic species, though the effect of other complexes could not be fully excluded. The rate of the oxidation reaction was half-order in [02] and showed rather complex concentration dependencies in [H2C]0, [Cu(II)]0 and pH. The experimental data were consistent with the following rate equation ... 

The rate equation of a reaction with an immobilized enzyme is r = 5tjC/(0.05+C). The inlet concentration to a three-stage CSTR is 1.2 and 80% conversion is required. Find the required residence time per stage when the effectiveness is 60% or 100%. 

Now, let us discuss the rate equations embodied in eq.(74). To do this, there is need of a statistical analysis. If the system is kept coupled to a thermostat at absolute temperature T, and assuming that w(i - >if) contains effects to all orders in perturbation theory, the rate of this unimolecular process per unit (state) reactant concentration k + is obtained after summation over the if-index is carried out with Boltzman weight factors p(if,T) ... 

The rate of reaction may depend upon reactant concentration, product concentration, and temperature. Cases in which the product concentration affects the rate of reaction are rare and are not covered on the AP exam. Therefore, we will not address those reactions. We will discuss temperature effects on the reaction later in this chapter. For the time being, let s just consider those cases in which the reactant concentration may affect the speed of reaction. For the general reaction aA + bB+...->c C + dD +. . . where the lower-case letters are the coefficients in the balanced chemical equation the upper-case letters stand for the reactant and product chemical species and initial rates are used, the rate equation (rate law) is written ... 

In this expression, k is the rate constant—a constant for each chemical reaction at a given temperature. The exponents m and n, called the orders of reaction, indicate what effect a change in concentration of that reactant species will have on the reaction rate. Say, for example, m = 1 and n = 2. That means that if the concentration of reactant A is doubled, then the rate will also double ([2]1 = 2), and if the concentration of reactant B is doubled, then the rate will increase fourfold ([2]2 = 4). We say that it is first order with respect to A and second order with respect to B. If the concentration of a reactant is doubled and that has no effect on the rate of reaction, then the reaction is zero order with respect to that reactant ([2]° = 1). Many times the overall order of reaction is calculated it is simply the sum of the individual coefficients, third order in this example. The rate equation would then be shown as ... 

Unfortunately, OH and O concentrations in flames are determined by detailed chemical kinetics and cannot be accurately predicted from simple equilibrium at the local temperature and stoichiometry. This is particularly true when active soot oxidation is occurring and the local temperature is decreasing with flame residence time [59], As a consequence, most attempts to model soot oxidation in flames have by necessity used a relation based on oxidation by 02 and then applied a correction factor to augment the rate to approximate the effect of oxidation by radicals. The two most commonly applied rate equations for soot oxidation by 02 are those developed by Lee el al. [61] and Nagle and Strickland-Constable [62],... 

The value of A i oep was evaluated from results of separate experiments in which GR catalyzes the reduction of GSSG by NADPH in the presence of various concentrations of G6P as inhibitor. The procedure employed is described in Section 3.3.2, and the pertinent results, plotted as 1/T versus 1/[GSSG], are presented in Figure 4.60. It can be seen that whenever the inhibitor G6P is present, the lines bend upward as they approach the /V axis. This bend becomes more pronounced as the concentration of G6P increases. This behavior is usually associated with substrate inhibition [149] and perhaps the inhibitor G6P affects the substrate GSSG and the latter becomes inhibitory to the enzyme GR. However, this effect was not considered in the rate equations used in the experimental system. 

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