Reaction Mechanisms and the Rate-Law Expression

Some reactions take place in a single step, but most reactions occur in a series of elementary or fundamental steps. The step-by-step pathway by which a reaction occurs is called the reaction mechanism. 

Unless otheiwise noted, all content on this page is Cengage Learning. 

The reaction o cAs cs for any single elementary step are equal to the coefficients for that step. 

In many mechanisms, however, one step is much slower than the others. 

An overall reaction can never occur faster than its slowest elementary reaction step. 

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Time The Integrated Rate Equation 16-5 Collision Theory of Reaction Rates 16-6 Transition State Theory 16-7 Reaction Mechanisms and the Rate-Law Expression... 

The coefficients of the balanced overall equation bear no necessary relationship to the exponents to which the concentrations are raised in the rate law expression. The exponents are determined experimentally and describe how the concentrations of each reactant affect the reaction rate. The exponents are related to the ratedetermining (slow) step in a sequence of mainly unimolecular and bimolecular reactions called the mechanism of the reaction. It is the mechanism which lays out exactly the order in which bonds are broken and made as the reactants are transformed into the products of the reaction. 

Boreskov assumed the power law dependence for reaction rate, which is mathematically incorrect. Thus, strictly speaking, he did not prove Equations (13) and (14). Authors performed the analysis of the model corresponding to the single-route reaction mechanism with the rate-limiting step and proved these relations rigorously (see Lazman and Yablonskii, 1988 Lazman and Yablonskii, 1991). Mathematically, expression (12) is the first term of infinite power series by powers kinetic parameters of rate-limiting step. 

The rates of the overall reactions can be related to the rate law expressions of the individual steps by using the steady state approximation. However simple kinetic data alone may not distinguish a mechanism where, for example, a metal and an olefin form a small amount of complex at equilibrium that then goes on to react, from one in which the initial complex undergoes dissociation of a ligand and then reacts with the olefin. As a reaction scheme becomes more complex such steady state approximations become more complicated, but numerical methods are now available which can simulate these even for complex mixtures of reactants. 

An alternative mechanism invoking an ion-pair transition state assembly has been proposed to account for the enantioselectivity of the asymmetric epoxidation process. In this proposal, two additional alcohol species are required in the transition state complex. This requirement is inconsistent with the kinetic studies of this reaction which have led to the rate law expressed in equation (5) and, therefore, this proposal must be considered incorrect. 

Rate laws of chemical reactions have a great practical value, as they provide a concise expression for the progress of reaction and, also, serve for the c culation of time and the yield of reaction. Very often, the rate laws provide an insight into the mechanism of chemical reactions. 

Analyze and Plan The rate law of the slow elementary step in a mechanism determines the rate law foimd experimentally for the overall reaction. Thus, we first write the rate law based on the molecularity of the slow step. In this case the slow step involves the intermediate N2O2 as a reactant. Experimental rate laws, however, do not contain the concentrations of intermediates, but are expressed in terms of the concentrations of starting substances. Thus, we must relate the concentration of N2O2 to the concentration of NO by assuming that an equilibrium is established in the first step. 

Bonding and molecular considerations presented in prior chapters allow student understanding of reaction mechanisms and their influence on the rate-law expression. 

The major problem in describing the FT reaction kinetics is the complexity of its reaction mechanism and the large number of species involved. As discussed above, the mechanistic proposals for the FTS used a variety of surface species and different elementary reaction steps, resulting in empirical power law expressions for the kinetics. However, the rate equations of Langmuir—Hinshelwood—Hougen—Watson (LHHW) have been applied based on a reaction mechanism for the hydrocarbon-forming reactions. In most cases, the rate-determining step was assumed to be the formation of the monomer. 

Depending upon the concentration of A, the predicted rate law varies between first and second order. At very low pressure ka k [A] and the rate law is second order with an apparent rate constant k. However, when the pressure is high and A [A] k the reaction is first order with an apparent rate constant k = k K, where K is the equilibrium constant for the activation process. To test the Lindemann mechanism express the data in first-order form... 

If the rate-determining step is the first step in the mechanism, then the rate law for the overall reaction is simply the rate law from the elementary process. (And because the first step does not have any intermediates as reactants, by definition the rate law can be expressed in terms of measurable quantities of chemical species.) Suppose, however, that the rate-determining step is the second step. Consider the following hypothetical two steps ... 

If mechanism (a) were correct, the rate law would be rate = [N02 [C0]. But this expression does not agree with the experimental result and can be eliminated as a possibility. Mechanism (b) has rate = NO,]2 from the slow step. Step 2 does not influence the overall rate, but it is necessary to achieve the correct overall reaction thus this mechanism agrees with the experimental data. Mechanism (c) is not correct, which can be seen from the rate expression for the slow step, rate = [NO ][CO]. [COJ cannot be eliminated from this expression to yield the experimental result, which does not contain [CO. ... 

And so, this cannot be a mechanism for this reaction, since it doesn t match the experimentally-derived rate law expression. 

The obvious challenge in the interpretation of the data is to find a suitable explanation for the independence of the third term of the rate law, Eq. (102), on the concentrations of HSO3 and 02. The rate expression determined experimentally could be modeled quantitatively by combining the following propagation steps with the uncatalyzed reaction mechanism ... 

The rate of a reaction is usually measured in terms of the change of concentration, with time, of one of the reactants or products, - d [reactant]/clt or +r/ [products]/r/t, and is usually expressed as moles per liter per second, or M s . We have already seen how this information might be used to derive the rate law and mechanism of the reaction. Now we are concerned, as kineticists, with measuring experimentally the concentration change as a function of the time that has elapsed since the initiation of the reaction. In principle, any property of the reactants or products that is related to its concentration can be used. A large number of properties have been tried. 

An early paper reported that reaction of PtCll- and 1 obeyed the rate law (30) expressed in Eq. (1) through the formation of a methylplatinum intermediate that decomposed in the presence of excess chloride to form chloromethane. Fanchiangef al. made a more detailed study of this reaction and proposed the reaction mechanism shown in Fig. 2, from which... 

In the broadest sense, I found the analogy with fluid mechanics to be very helpful. Just as kinematics provides the geometrical framework of fluid mechanics by exploring the motions that are possible, so also stoicheiometry defines the possible reactions and the restrictions on them without saying whether or at what rate they may take place. When dynamic laws are imposed on kinematic principles, we arrive at equations of motion so, also, when chemical kinetics is added to stoicheiometry, we can speak about reaction rates. In fluid mechanics different materials are distinguished by their constitutive relations and allow equations for the density and velocity to be formulated thence, various flow situations are examined by adding appropriate boundary conditions. Similarly, the chemical kinetics of the reaction system allow the rates of reaction to be expressed in terms of concentrations, and the reactor is brought into the picture as these rates are incorporated into appropriate equations and their boundary conditions. 

The rate constants kt and k2 were found to be 0.5 M 1 min-1 and 29.0 M-1 min-1 respectively at pH 5.05 and 25 C. The rate law and other data suggest a nucleophilic displacement by the bisulfide ion (HS ) on H202 as the rate-determining step with subsequent formation of polysulfide as intermediates. The rate of the reaction was found to decrease as HS ion in solution decreases and hence the optimal pH for oxidation was determined to be 7. They postulated the following mechanism for the second term in the rate expression ... 

However, N202 is a reaction intermediate, which is not allowed in the rate law. In order to solve the problem, we will have to use the first step in the mechanism and find a suitable substitution for N2Oz. In the first step, which is an equilibrium step, the rates of the forward and reverse reactions are identical. Therefore, we can set up an expression such that kx = k x. In this expression, we obtain the following equality ... 

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