Chemical Kinetics�Lecture 5

CML101

August 06, 2024

This is a plot of Δ[B] versus time for a typical temperature-jump experiment. From Δ[B] = Δ[B]₀exp(-t/τ) (as per expression derived), we see that a plot of ln(Δ[B]/Δ[B]₀) versus t is linear and has a slope of -(k₁ + k_-1), which is the negative of the sum of the forward and reverse rate constants for the reaction at T₂. If we know the equilibrium constant at T₂ and the rate laws for the forward and reverse reactions, then the rate constants k₁ and k_-1 can be independently determined.

We now consider this chemical reaction and assume that both the forward and reverse reactions are first order in their respective reactants

Derive expression for τ,

the relaxation time!

Reaction Mechanisms

The study of reaction rates leads to an understanding of the mechanism of a reaction, its analysis into a sequence of elementary steps.

Many reactions occur in a sequence of steps called elementary reactions, each of which involves only a small number of molecules or ions. A typical elementary reaction is

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H + Br₂ → HBr + Br

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Note that the phase of the species is not specified in the chemical equation for an elementary reaction and the equation represents the specific process occurring to individual molecules. This equation, for instance, signifies that an H atom attacks a Br₂ molecule to produce an HBr molecule and a Br atom.

The molecularity of an elementary reaction is the number of molecules coming together to react in an elementary reaction. In a unimolecular reaction, a single molecule shakes itself apart or its atoms into a new arrangement, as in the isomerization of cyclopropane to propene. In a bimolecular reaction, a pair of molecules collide and exchange energy, atoms, or groups of atoms, or undergo some other kind of change.

It is important to distinguish molecularity from order:

• reaction order is an empirical quantity, and obtained from the experimentally determined rate law;

• molecularity refers to an elementary reaction proposed as an individual step in a mechanism.

The molecularity of an elementary reaction is defined to be the number of reactant molecules involved in the chemical reaction. Elementary reactions that involve one, two, and three molecules are termed unimolecular, bimolecular, and termolecular reactions,

respectively. These terms should be used to describe only elementary reactions.

Consecutive Elementary Reactions

Examine the shapes of curves

k₁ > k₂

k₁ < k₂

A → I → P

k₁

k₂

[A]

[P]

[I]

k₂ is constant

k₁ is constant

Problem:

This plot shows the concentrations of ²¹⁰Bi, ²¹⁰Po, and ²⁰⁶Pb over time. Note the “temporary” buildup of ²¹⁰Po, which does start at 0. Note that the x-axis is in units of seconds, but in this example the right side of the plot is equivalent to a time of 1.9 years.

Can you distinguish between single step and a two-step reaction mechanism?

k₂ >> k₁

k₁ >> k₂

For a single-step reaction, the kinetics of A and P depend upon the same rate constant.

For the two-step mechanism in which the second step is rate determining, the kinetics of A depend upon k₁ and the kinetics of P depend upon k₂ .

Therefore, if we measure both the decay kinetics of A and the formation kinetics of P, we can distinguish between a single-step and two-step mechanism when the second step of the two-step reaction scheme is rate determining

The Steady-State Approximation

The basis of the steady‑state approximation: It is supposed that the concentrations of intermediates remain small and hardly change during most of the course of the reaction

Imagine the intermediate being so reactive that it does not accumulate at an appreciable level compared to concentration of reactants or products!

There is a considerable increase in mathematical complexity as soon as the reaction mechanism has more than a couple of steps or reverse reactions are taken into account.

Need to make an approximation

Steady-state Approximation

Steady-state approximation assumes that the intermediate, I, is in a low, constant concentration. More specifically, after an initial induction period, an interval during which the concentrations of intermediates rise from zero, the rates of change of the concentrations of all reaction intermediates are negligibly small during the major part of the reaction.

Now complete this! Express as d[HCl]/dt