Rate laws substitution

The value of the rate constant can be determined by substituting the rate, the [C3H5O], and the [H+] for an experiment into the rate law and solving for k. Using the data from experiment 1, for example, gives a rate constant of 3.31 X 10 s h The average rate constant for the eight experiments is 3.49 X 10-5 M-i s-i ... 

Substituting Equation 1-154 into the predieted rate law allows the temperature dependenee of the overall reaetion to be predieted. In the deeomposition of aeetaldehyde, it follows that... 

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. 

Substitution of the second form of each of these equations into the rate law, imposition of the equilibrium condition i[A]"[B] = -i [P] [R] , and the dropping of quadratic terms give this expression for the relaxation time ... 

STRATEGY The level of mercury(II) in the urine can be predicted by using the integrated first-order rate law, Eq. 5b. To use this equation, we need the rate constant. Therefore, start by calculating the rate constant from the half-life (Eq. 7) and substitute the result into Eq. 5b. 

Now that we have an expression for fN202J, we can substitute that expression into the rate law ... 

When we substitute this expression into the rate law for net rate of decomposition of ozone, we get... 

Substituting in our proposed rate law, we have rate = ,( ,/ , )[NC>l2fH2 = [NO]2 H2] where k = ,<, /, ) The assumptions made above reproduce the observed rate law therefore, step 2 is the slow step. 

No matter how produced, RN2 are usually too unstable to be isolable, reacting presumably by the SnI or Sn2 mechanism. Actually, the exact mechanisms are in doubt because the rate laws, stereochemistry, and products have proved difficult to interpret. If there are free carbocations, they should give the same ratio of substitution to elimination to rearrangements, and so on, as carbocations generated in other SnI reactions, but they often do not. Hot carbocations (unsolvated and/or chemically activated) that can hold their configuration have been postulated, as have ion pairs, in which OH (or OAc , etc., depending on how the diazonium ion is generated) is the coun-... 

A good starting place for discussion is the rate law for substitution reactions in acidic aqueous solutions. One typical reaction is... 

It is pertinent, then, to seek a dependence of substitution rates on (/) leaving group, (ii) solvent, Hi) steric crowding, iv) charge, v) nature of non-labile substituents including stereochemistry, consistent with this picture of the activation mode. If these tests generally support d modes it will be desirable to examine rate laws closely to attempt a distinction between D and 7j stoichiometric pathways. 

The ki term in the rate law for square planar substitution is very clearly connected with an associative mechanism. The k term may be also. Consider the pathway (S = solvent)... 

The two-term rate law for substitution reactions of the group VI hexacar-bonyls has been previously mentioned (see p. 29) and it will be useful to summarize the evidence for associative activation in this case. i. There is reasonably good agreement between the rate of exchange in the gas phase and the first-ot tv rate of substitution in decalin, suggesting that this term represents a dissociative reaction. 

In the above case both the reaction steps 1 and 2 are virtually at equilibrium so that the concentration of YXY present may be expressed in terms of the concentrations of the reactants and the rate constants in these previous steps, i.e., [YXY] = K2 [XY] [Y] = K2 [X [Y]2. Thus substituting for [YXY] the rate law for the reaction step 3 is given by... 

Thus, although the rate of substitution should be very dependent on the nature of Lx, distinguishing the operation of an A mechanism according to Eq. (8) from ligand substitution proceeding through an outer-sphere complex on the basis of rate laws is usually not feasible. This does not, however, preclude the operation of an A mechanism within an outer-sphere complex. 

The rate law for the substitution reaction was proven to be expressed in the presence of a large excess of EDTA as... 

According to this mechanism, there is a first-order dependence on both the concentration of [ A B] and B, and the reaction is called an SN2 process (substitution, nucleophilic, second-order). Although many nucleophilic substitution reactions follow one of these simple rate laws, many others do not. More complex rate laws such as... 

Because it is the rate of dissociation of the M-X bond that determines the rate of substitution, the rate law involves only the concentration of the starting complex, ML X. 

The simplest approach to this problem is to assume that the initial concentrations of NO and 02 for the first experiment are each 1 M Then for the second experiment, the initial concentration of NO is 1/2 Mand that of 02 is 2 M Let us substitute these values into the rate-law expression, rate = [N0]2[02]... 

Method 2 A mathematical solution is obtained by substituting the experimental values of Experiments 1 and 3 into rate-law expressions and dividing the latter by the former. Note the calculations are easier when the experiment with the larger rate is in the numerator. 

Substitute the given values into the complete rate-law expression to determine the reaction rate. 

Substituting into the rate law expression obtained in the slow, rate-determining step ... 

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