rate-determining step

Examples of rate-determining step in the following topics:

• Rate-Determining Steps

  • The rate of a multi-step reaction is determined by the slowest elementary step, which is known as the rate-determining step.
  • In kinetics, the rate of a reaction with several steps is determined by the slowest step, which is known as the rate-determining, or rate-limiting, step.
  • Since the first step is the slowest, and the entire reaction must wait for it, it is the rate-determining step.
  • If the second or a later step is rate-determining, determining the rate law is slightly more complicated.
  • Describe the relationship between the rate determining step and the rate law for chemical reactions

• Molecularity

  • If a chemical reaction proceeds by more than one step or stage, its overall velocity or rate is limited by the slowest step, the rate-determining step.
  • Once a group gathers at the door, the speed at which other people leave their seats and move along the aisles has no influence on the overall exit rate.
  • When we describe the mechanism of a chemical reaction, it is important to identify the rate-determining step and to determine its "molecularity".
  • The molecularity of a reaction is defined as the number of molecules or ions that participate in the rate determining step.
  • A mechanism in which two reacting species combine in the transition state of the rate-determining step is called bimolecular.

• Overall Reaction Rate Laws

  • Rate laws for reactions are affected by the position of the rate-determining step in the overall reaction mechanism.
  • Since the first step is the rate-determining step, the overall reaction rate for this reaction is given by this step: $\text{rate}=k[H_2][ICl]$.
  • Step two is the slow, rate-determining step, so it might seem reasonable to assume that the rate law for this step should be the overall rate law for the reaction.
  • We can now substitute this expression into the rate law for the second, rate-determining step.
  • How to determine the rate law for a mechanism with a fast initial step.

• Steady-State Approximation

  • The steady state approximation can be used to determine the overall rate law when the rate-determining step is unknown.
  • This slowest step determines the rate of the entire reaction, and as such, it is called the rate-determining step.
  • We will now consider cases in which the rate-determining step is either unknown or when more than one step in the mechanism is slow, which affects the overall reaction rate.
  • Before, we assumed that the first step was fast, and that the second step was slow, thereby making it rate-determining.
  • We will now proceed as if we had no such prior knowledge, and we do not know which, if either, of these steps is rate-determining.

• Rate Laws for Elementary Steps

  • The rate law of the rate-determining step must agree with the experimentally determined rate law.
  • The rate-determining step is the slowest step in a reaction mechanism.
  • The molecularity of the elementary step, and the reactants involved, will determine what the rate law will be for that particular step in the mechanism.
  • For now, just keep in mind that the rate laws for each elementary step are determined by the molecularity of each step only.
  • The molecularity of an elementary step in a reaction mechanism determines the form of its rate law.

• A Mechanism for Electrophilic Substitution Reactions of Benzene

  • A two-step mechanism has been proposed for these electrophilic substitution reactions.
  • In the first, slow or rate-determining, step the electrophile forms a sigma-bond to the benzene ring, generating a positively charged benzenonium intermediate.
  • In the second, fast step, a proton is removed from this intermediate, yielding a substituted benzene ring.
  • The second step of alkene addition reactions proceeds by the first mode, and any of these three reactions may exhibit molecular rearrangement if an initial unstable carbocation is formed.

• Kinetics

  • One way of investigating the molecularity of a given reaction is to measure changes in the rate at which products are formed or reactants are lost, as reactant concentrations are varied in a systematic fashion.
  • Such an equation is termed a kinetic expression, and for a reaction of the type: A + B –> C + D it takes the form: Reaction Rate = k[A] n[B] m, where the rate constant k is a proportionality constant that reflects the nature of the reaction, [A] is the concentration of reactant A, [B] is the concentration of reactant B, and n & m are exponential numbers used to fit the rate equation to the experimental data.
  • In a simple bimolecular reaction n & m would both be 1, and the reaction would be termed second order, supporting a mechanism in which a molecule of reactant A and one of B are incorporated in the transition state of the rate-determining step.
  • Each different reaction has its own distinct rate constant, k#.
  • It not only shows first order kinetics (only the alkyl halide concentration influences the rate), but the chiral 3º-alkyl bromide reactant undergoes substitution by the modest nucleophile water with extensive racemization.

• Addition of Strong Brønsted Acids

  • This two-step mechanism is illustrated for the reaction of ethene with hydrogen chloride by the following equations.
  • An energy diagram for this two-step addition mechanism is shown below.
  • From this diagram we see that the slow or rate-determining step (the first step) is also the product determining step (the anion will necessarily bond to the carbocation site).
  • Evidently, alkyl substituents act to increase the rate of addition by lowering the activation energy, ΔE‡1 of the rate determining step, and it is here we should look for a rationalization of Markovnikov's rule.
  • The carbocation intermediate formed in the first step of the addition reaction now assumes a key role, in that it directly influences the activation energy for this step.

• Anchimeric Assistance

  • In this manner a neighboring aromatic ring accelerates the rate-determining (endothermic) ionization step, an influence called anchimeric assistance (Greek: anchi = neighbor).
  • Both reactions begin by an initial rate-determining ionization step, the transition state of which is colored pink.
  • The activation energy for this step is larger for neopentyl chloride because it leads to a discrete 1º-carbocation.
  • The second step in the neopentyl chloride solvolysis is a rapid rearrangement of the 1º-carbocation to an isomeric 3º-carbocation.
  • These isomers were solvolyzed in hot acetic acid solution, buffered with sodium acetate, and the configurations of the resulting acetate esters were determined.

• The Rate Law

  • For the general reaction$aA + bB \rightarrow C$ with no intermediate steps in its reaction mechanism, meaning that it is an elementary reaction, the rate law is given by:
  • The exponents x and y vary for each reaction, and they must be determined experimentally; they are not related to the stoichiometric coefficients of the chemical equation.
  • To reiterate, the exponents x and y are not derived from the balanced chemical equation, and the rate law of a reaction must be determined experimentally.
  • A certain rate law is given as $Rate=k[H_2][Br_2]^\frac{1}{2}$.
  • Note that the reaction order is unrelated to the stoichiometry of the reactions; it must be determined experimentally.