Rate law overall

The slopes of the fimctions shown provide the reaction rates according to the various definitions under the reaction conditions specified in the figure caption. These slopes are similar, but not identical (nor exactly proportional), in this simple case. In more complex cases, such as oscillatory reactions (chapter A3.14 and chapter C3.6). the simple definition of an overall rate law tluough equation (A3.4.6) loses its usefiilness, whereas equation (A3.4.1) could still be used for an isolated system. 

Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

To verify that a proposed reaction mechanism agrees with experimental data, we construct the overall rate law implied by the mechanism and check to see whether it is consistent with the experimentally determined rate law. However, although the constructed rate law and the experimental rate law may be the same, the proposed mechanism may still he incorrect because some other mechanism may also lead to the same rate law. Kinetic information can only support a proposed mechanism it can never prove that a mechanism is correct. The acceptance of a suggested mechanism is more like the process of proof in an ideal court of law than a proof in mathematics, with evidence being assembled to give a convincing, consistent picture. 

To construct an overall rate law from a mechanism, write the rate law for each of the elementary reactions that have been proposed then combine them into an overall rate law. First, it is important to realize that the chemical equation for an elementary reaction is different from the balanced chemical equation for the overall reaction. The overall chemical equation gives the overall stoichiometry of the reaction, but tells us nothing about how the reaction occurs and so we must find the rate law experimentally. In contrast, an elementary step shows explicitly which particles and how many of each we propose come together in that step of the reaction. Because the elementary reaction shows how the reaction occurs, the rate of that step depends on the concentrations of those particles. Therefore, we can write the rate law for an elementary reaction (but not for the overall reaction) from its chemical equation, with each exponent in the rate law being the same as the number of particles of a given type participating in the reaction, as summarized in Table 13.3. 

Let s write the rate laws for the steps in a mechanism proposed for the gas-phase oxidation of NO to N02. Its overall rate law has been determined experimentally ... 

To evaluate the plausibility of this mechanism, we need to construct the overall rate law it implies. First, we identify any elementary reaction that results in product and write the equation for the net rate of product formation. In this case, N02 is formed only in step 2, and so... 

The factor of 2 appears in the rate law because two N02 molecules are formed from each N202 molecule consumed. This expression is not yet an acceptable rate law for the overall reaction because it includes the concentration of an intermediate, N202, and intermediates do not appear in the overall rate law for a reaction. 

EXAMPLE 13.7 Setting up an overall rate law from a proposed mechanism... 

STRATEGY Construct the rate laws for the elementary reactions and combine them into the overall rate law for the decomposition of the reactant. If necessary, use the steady-state approximation for any intermediates and simplify it by using arguments based on rapid pre-equilibria and the existence of a rate-determining step. 

When the overall rate law is worked out (see Exercise 13.92), we find that... 

The overall rate law is, however, found to contain a term involving [ketoacid] (47) as well as the term involving [ketoacid anion]. The ready decarboxylation of the (3-ketoacid itself is probably due to incipient proton transfer to 0=0 through hydrogen-bonding in (47) ... 

We now consider the results obtained for the indirect mechanism (for a reminder of this mechanism, see Scheme 4). The overall rate law for this mechanism is given by Eq. (1) ... 

As pH increases over the range studied, H2S(aq) reacts to form HS. The reaction rate observed, and that predicted by Equation 17.29, decreases sharply. Thermodynamics strongly favors forward progress of the reaction, so reverse reaction is insignificant and r r+. The (1 — Q/K) term in the overall rate law (Eqn. 17.9), although formally appended to Equation 17.29 and carried in the calculation, therefore, remains very close to unity and the effect of thermodynamics on the reaction rate in this case is negligible. 

All these features have been initially interpreted102-104 in terms of a molecular mechanism involving two successive alkene-iodine complexes of 1 1 and 1 2 stochiometries the second of which evolves by internal nucleophilic attack of the uncomplexed double bond to the diiodo derivative (equation 87). The intramolecular attack of the second double bond has been regarded as rate determining, owing to the fact that the overall rate law is second order in iodine rather than the usual third order. Nevertheless more... 

Rate-determining steps can occur anywhere in a reaction mechanism. If a slow step is not the first step of the mechanism, however, the overall rate law is more complicated to determine. One reason is that fast reactions occurring early in a mechanism are often reversible—both the forward and reverse reactions take place. (You will learn more about these reactions in Unit 4.)... 

The rate law of the rate-determining step in the proposed mechanism matches the experimentally determined rate law. Since the proposed mechanism is consistent with the overall rate law equation, it is a reasonable mechanism. 

Add the two reactions, and cancel out reaction intermediates. Check the molecularity of the steps. Determine the rate law equation for the rate-determining step, and compare it to the overall rate law equation. 

We will develop an overall rate law considering that each step is rate limiting. Our aim is to eliminate the concentrations of the adsorbed species that cannot be measured during a classical experiment. 

The cubic nature of the empirical rate law discussed in the previous section, and the representation in eqn (1.17), is not at all meant to imply that we are thinking of a single, termolecular, elementary step. There are various ways in which a combination of simple bimolecular steps can combine together to give an overall rate law with this cubic form. For instance, in the two-step mechanism involving an intermediate X... 

C established the rate constants for the proposed mechanisms. With the intermediate N03 in steady state, the overall rate law is... 

The overall rate law of homogeneous acid hydrolysis of glycosides is given by... 

The base-catalysed Aldol reaction is shown in Equation 3.11 [3, 4], and a mechanism to account for the global process in Scheme 3.1. At low concentrations of acetaldehyde, reverse of the proton-abstraction steps is fast compared with the forward bimolecular enolate capture (k [CH3CHO] <rate limiting. Under these conditions, the kinetics are second order in [CH3CHO] and show specific base catalysis, i.e. the reaction is first order in [HCY ] and, even though B is involved in the mechanism, it does not appear in the rate law [5]. According to this mechanism, therefore, the overall rate law is given by Equation 3.12 ... 

Correspondingly, [A] could be in large excess allowing the reaction order with respect to [B] to be isolated, so the overall rate law is established part by part in turn. 

In buffered solutions, the term k2KsKi [S]/[SH+] is constant, so the expected overall rate law is again second order (i.e. pseudo first order in [Y ]) but the correspondence of fcQbs with mechanistic rate constants is different. Of course, if the equilibrium constant Ki is appreciable, the phenolate concentration must be taken into account in the mass balance for the total phenol, i.e. [ArOH]T [ArOH]free + [ArOH- -S] + [ArO-], whereupon the mechanistic rate equation becomes more complicated. 

However, when the reaction proceeds exclusively via the intermediate, and k2 + ki[T] k i, then the overall rate law reduces to the simple form of Equation 9.12 which is clearly distinguishable from both Equation 9.7 and Equation 9.11 ... 

The rate of every chemical reaction depends in one way or another on the concentrations of the chemicals in the system. The overall rate law is often written as the product of the concentrations raised to a power. For example, for the reaction A I B C, the rate law for the disappearance of A may be written as in Eq. (2.7), where the exponents a and p represent the partial reaction order in A and B, respectively, and the overall reaction order is n = a + p. 

The rate laws for the reactions in Eq. 2.5 each have the mathematical form of Eq. 2.4, and the overall rate law for these two parallel reactions is simply the sum of the individual rate laws 10... 

The overall rate law for the oxidation of Fe(II) based on Eq. 4.53 then takes the form... 

The overall rate law for a reaction is determined by the sequence of steps, or the mechanism, by which the reactants are converted into the products of the reaction. 

The mechanism of the deprotonation of esters by LDA has been particularly detailed. A kinetic and IR spectroscopic approach to the deprotonation of f-butyl cyclohexylcar-boxylate by LDA in THF confirmed the formation of a complex between a monomeric LDA and the ester, in fine accord with Ireland s model51. The data suggested that a spectroscopically invisible dimer-monomer pre-equilibrium occurred first, followed by a rate-determining proton transfer, leading to the overall rate laws reported in Scheme 7. 

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