Rate-determining-step

Consider the correlation between the kinetic parameters of the overall reaction and those of its individnal steps in the instance of a very simple, invertible two-step chemical reaction  

The direction of the reaction will depend on the relative concentrations of reactants and products the reaction will go from left to right when k k2Cf k i 2Cd and in the opposite direction, o 0, when the opposite inequality holds. 

When we consider the overall reaction while disregarding the formation of intermediates, we can write its rate as 

A quantity of great importance in these equations is the ratio of parameters k 1 and 2 (i.e., of the constants in the expressions for the rate of reconversion of the intermediates to original reactants and for the rate of conversion of the intermediates to final products), hi the particular case of 1 k, it follows from Eq. (13.5) that 

One of constituent steps of a steady reaction of single route is called rate-determining or its rate-determining step, if its stoichiometric number is not zero and all constituent steps but the latter are, respectively, in partial equilibria i.e., the forward rate of each is practically balanced with its backward rate. 

by the reversal of step 2 followed by step 3, i.e., by the scheme, H2 2H(a), H(a) + H -f e H2. The initial system of the former elementary reaction of the sequence is hence the product itself of the steady reaction. 

Ratio of the Forward Unidirectional Rate of Steady Reaction with Rate-Determining Step to the Backward Unidirectional Rate 18) 

Now let —AG be the affinity, i.e., the decrease of Helmholtz (Gibbs) energy of the assembly per one completion of the steady reaction. Since the completion per one constituent step s is associated with the decrease of Helmholtz (Gibbs) energy of the assembly of the amount the affinity is expressed in terms of the latter and v/s as 

It follows on the other hand from Eqs. (II.3) and (II.9), inasmuch as the vfa are individually positive exclusively for v, 0 as mentioned in Section III,D,3, that 

To use these expressions in formulating LHHW rate models, an understanding of the slowest or the rate-determining step is necessary. 

We now develop rate equations by assuming any one of several steps involved in a given reaction as the rate-determining step. 

To study reaction mechanisms, we first do a series of experiments to establish initial rates at various reactant concentrations. We then analyze the data to determine the rate constant and overall order of the reaction, and we write the rate law. Finally, we propose a plausible mechanism for the reaction in terms of logical elementary steps. The steps of the proposed meehanism must satisfy two requirements  

The sum of the elementary reactions must be the overall balanced equation for the reaction. 

The rate-determining step must have the same rate law as that determined from the experimental data. 

It is important to remember that this is not the case in general. It only applies to elementary reactions—anti whether or not a reaction is elementary must be determined experimentally. 

the reaction is first order with respect to both H2O2 and I . 

The decomposition of H2O2 is not an elementary reaction, because it does not occur in a single step. If it did, the reaction would be second order in H2O2 (as a result of the colhsion of two H2O2 molecules). What s more, the F ion, which is not even part of the overall equation, would not appear in the rate law expression. How can we reconcile these facts First, we can account for the observed rate law by assuming that the reaction takes place in two separate elementary steps, each of which is bimolecular. 

Many ion-transfer reactions involve two or more steps. Often one of these steps proceeds more slowly than the others, and if the reaction proceeds under stationary conditions, this step determines the overall rate. We will elaborate this concept of a rate-determining step further. For this purpose consider a reaction taking place according to the general scheme  

This is a series of reactions, and the substances X (i = 2. n — 1) are intermediates that are generated in one step and consumed in the next. The individual steps can be electrochemical or chemical reactions, or even mass-transport steps like the diffusion of a species from the bulk of the solution to the interface. The overall reaction is  

When the reaction is stationary, all steps proceed at the same rate v, which is also the rate of the overall reaction. We denote by Vi and v-i the rates at which the forward and backward reactions proceed. Then  

Let step number j be rate determining-, that is, its forward and backward rates are much smaller than those of the other steps  

In systems of consecutive reactions it may sometimes occur that there is one step which is very much slower than all the subsequent steps leading to product. Then the rate of production of product may depend on the rates of all the steps preceding the last slow step but will not depend on any of the subsequent steps, all of which are rapid compared to the last slow step. Such a last slow step has been called, somewhat misleadingly, the rate-determining step of the reaction. 

For illustration let us consider the following complex sequence of stoichiometric reactions as representing the reaction path for the over-all change A + C — P  

We can apply the stationary-state technique if both the in xxxc viiates B and D are small at all times compared to A and C. Their stationary-state concentrations will then be given by 

In case 1 step 3 is the slow step and in case 2 step 1 is the slow step. It can be seen that in each of these extreme cases, the form of the over-all rate law is independent of the rates of all the much faster steps following the rate-determining steps. Note also that the steps leading up to the rate-determining step do appear. 

The principle behind such terminology lies in the following method of analysis. In a system of consecutive reaction steps where reactant passes through a number of intermediate stages, the total time to produce a molecule of product is simply the sums of the discrete times necessary to pass through each consecutive stage of the reaction. The mean reaction time tp is thus  

The pre-equilibrium approximation (PEA also called the partial equilibrium approximation or fast-equilibrium approximation) is applicable when the species participating in a pair of fast-equilibrium reactions are consumed by slow reactions. After the onset of an equilibrium, the rates of the, forward and backward reactions become equal to each other, and therefore the ratios of the concentrations of the participating species can be calculated from the stoichiometry of the reaction steps and the equilibrium constant. According to the pre-equilibrium approximation, if the rates of the equilibrium reactions are much higher than the rates of the other reactions consuming the species participating in the equilibrium reactions, then the concentrations of these species are determined, with good approximation, by the equilibrium reactions only. 

As an example, let us consider the equilibrium reaction A B. The corresponding rate coefficients are ki and k2, and the equilibrium constant is denoted by K=kilk2- In the case of an onset of equilibrium, the rates of the opposing reactions are identical kia = k2b, and therefore, b = ki/k2a = Ka. Now consider the reaction system A B C, where species B is consumed by a slow reaction with a small rate coefficient k compared to ki and 2- In this case, we can still assume that b = Ka is a good approximation, and thus, dc/df = 3h, dc/ dt = k2,Ka. Therefore, the concentration of B is not required in order to calculate the rate of production of C as long as the rate coefficients are known. 

A common example of such a situation is the enzyme-substrate reaction involved in biochemical pathways. In this type of reaction, an enzyme E binds to a substrate S to produce an enzyme-substrate intermediate ES, which then forms the final product P  

Here the rate of production of the final product (usually an essential biomolecule) can be derived using the pre-equilibrium approximation to be 

Another common situation is when a large organic molecule isomerises in a fast-equilibrium reaction to a low-concentration, more reactive form, and this more reactive species is consumed by a slow reaction. Using the equation dc/dt = k3Ka means that the rate equation contains the less reactive organic species that is present in higher concentration and therefore can be measured more easily. 

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The treatment may be made more detailed by supposing that the rate-determining step is actually from species O in the OHP (at potential relative to the solution) to species R similarly located. The effect is to make fi dependent on the value of 2 and hence on any changes in the electrical double layer. This type of analysis has permitted some detailed interpretations to be made of kinetic schemes for electrode reactions and also connects that subject to the general one of this chapter. 

The measurement of a from the experimental slope of the Tafel equation may help to decide between rate-determining steps in an electrode process. Thus in the reduction water to evolve H2 gas, if the slow step is the reaction of with the metal M to form surface hydrogen atoms, M—H, a is expected to be about If, on the other hand, the slow step is the surface combination of two hydrogen atoms to form H2, a second-order process, then a should be 2 (see Ref. 150). 

B. Reaction within the Adsorbed Film as the Rate-Determining Step... 

The above equations can apply when the rate-determining step is first order even though the complete reaction mechanism is complicated. Thus for the reac-... 

Some early observations on the catalytic oxidation of SO2 to SO3 on platinized asbestos catalysts led to the following observations (1) the rate was proportional to the SO2 pressure and was inversely proportional to the SO3 pressure (2) the apparent activation energy was 30 kcal/mol (3) the heats of adsorption for SO2, SO3, and O2 were 20, 25, and 30 kcal/mol, respectively. By using appropriate Langmuir equations, show that a possible explanation of the rate data is that there are two kinds of surfaces present, 5 and S2, and that the rate-determining step is... 

Fig. 1. The rate-determining step in the neutral hydrolysis of paramethoxy-phenyl dichloroacetate. In the reactant state (a) a water molecule is in proximity of the carbonyl carbon after concerted proton transfer to a second water molecule and electron redistribution, a tetrahedral intermediate (b) is formed.

Melander first sought for a kinetic isotope effect in aromatic nitration he nitrated tritiobenzene, and several other compounds, in mixed acid and found the tritium to be replaced at the same rate as protium (table 6.1). Whilst the result shows only that the hydrogen is not appreciably loosened in the transition state of the rate-determining step, it is most easily understood in terms of the S 2 mechanism with... 

A primary isotope effect /ch/ d of 6.4 (extrapolated for 35 C) is observed for the metalation and the methylation of 171b when the C-5 position is deuterated. This value is in excellent agreement with the primary isotope effect of 6.6 reported for the metalation of thiophene (392) and it confirms that the rate-determining step is the abstraction by the base of the acidic proton. 

With the potential energies shown on a common scale we see that the transition state for formation of (CH3)3C is the highest energy point on the diagram A reaction can proceed no faster than its slowest step which is referred to as the rate determining step In the reaction of tert butyl alcohol with hydrogen chloride formation of the... 

The rate determining step m the S l mechanism is dissociation of the alkyloxo mum ion to the carbocation... 

Bromide ion forms a bond to the primary carbon by pushing off a water molecule This step IS bimolecular because it involves both bromide and heptyloxonium ion Step 2 IS slower than the proton transfer m step 1 so it is rate determining Using Ingold s ter mmology we classify nucleophilic substitutions that have a bimolecular rate determining step by the mechanistic symbol Sn2... 

Secondary and tertiary alcohols react with hydrogen halides by a mech anism that involves formation of a carbocation intermediate m the rate determining step... 

Assuming that the rate determining step in the reaction of cyclohexanol with hydrogen bro mide to give cyclohexyl bromide is unimolecular write an equation for this step Use curved arrows to show the flow of electrons... 

Like the reaction of tert butyl alcohol with hydrogen chloride step 2 m which tert butyloxonium ion dissociates to (CH3)3C and water is rate determining Because the rate determining step is ummolecular the overall dehydration process is referred to as a ummolecular elimination and given the symbol El... 

Because the rate determining step involves two molecules—the alkyloxonium ion and water—the overall reaction is classified as a bimolecular elimination and given the sym bol E2... 

What are the implications of the effects of the various halide leaving groups Because the halogen with the weakest bond to carbon reacts fastest Ingold concluded that the carbon-halogen bond breaks m the rate determining step The weaker the carbon-halogen bond the easier it breaks... 

The alkyl halide m this case 2 bromo 2 methylbutane ionizes to a carbocation and a halide anion by a heterolytic cleavage of the carbon-halogen bond Like the dissoci ation of an aUcyloxonmm ion to a carbocation this step is rate determining Because the rate determining step is ummolecular—it involves only the alkyl halide and not the base—It is a type of El mechanism... 

Both steps m this general mechanism are based on precedent It is called elec trophilic addition because the reaction is triggered by the attack of an acid acting as an electrophile on the rr electrons of the double bond Using the two rr electrons to form a bond to an electrophile generates a carbocation as a reactive intermediate normally this IS the rate determining step... 

Table 6 3 shows that the effect of substituents on the rate of addition of bromine to alkenes is substantial and consistent with a rate determining step m which electrons flow from the alkene to the halogen Alkyl groups on the carbon-carbon double bond release electrons stabilize the transition state for bromonium ion formation and increase the reaction rate... 

Hughes and Ingold interpreted second order kinetic behavior to mean that the rate determining step is bimolecular that is that both hydroxide ion and methyl bromide are involved at the transition state The symbol given to the detailed description of the mech anism that they developed is 8 2 standing for substitution nucleophilic bimolecular... 

As we have seen the nucleophile attacks the substrate m the rate determining step of the Sn2 mechanism it therefore follows that the rate of substitution may vary from nucleophile to nucleophile Just as some alkyl halides are more reactive than others some nucleophiles are more reactive than others Nucleophilic strength or nucleophilicity, is a measure of how fast a Lewis base displaces a leaving group from a suitable substrate By measuring the rate at which various Lewis bases react with methyl iodide m methanol a list of then nucleophihcities relative to methanol as the standard nucleophile has been compiled It is presented m Table 8 4... 

The Stvfl mechanism is an ionization mechanism The nucleophile does not participate until after the rate determining step has taken place Thus the effects of nucleophile and alkyl halide structure are expected to be different from those observed for reactions pro ceedmg by the 8 2 pathway How the structure of the alkyl halide affects the rate of Stvfl reactions is the topic of the next section... 

How does the rate determining step of the mechanism respond to this property of the solvent ... 

Rate of substitution is independent of both concentration and nature of nucleophile Nucleophile does not participate until after rate determining step (Section 8 8) Rate depends on both nature of nucleophile and its concentration (Sections 8 3 and 8 7)... 

Step 1 Sulfur tnoxide attacks benzene m the rate determining step... 

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