atkins & de paula: atkins physical chemistry 9e chapter 21: the rates of chemical reactions

Atkins & de Paula:

Atkins’ Physical Chemistry 9e

Chapter 21: The Rates of Chemical Reactions


chemical kinetics, the study of reaction rates. mechanism of reaction, the sequence of elementary steps involved in a reaction.

CHEMICAL KINETICS21.1 Experimental techniques real-time analysis, a procedure in which the composition of a system is analysed

while the reaction is in progress.(1)flow method, a procedure in which the composition of a system is analysed as the

reactants flow into a mixing chamber. (2)stopped-flow technique, a procedure in which the reagents are mixed very quickly in

a small chamber fitted with a syringe instead of an outlet tube.


(3) flash photolysis, a procedure in which the reaction is initiated by a brief flash of light.

quenching methods, techniques based on stopping the reaction after it has been allowed to proceed for a certain time.

(1)chemical quench flow method, a technique in which the reactants are mixed as in the flow method but the reaction is quenched by another reagent.

(2)freeze quench method, a technique in which the reaction is quenched by cooling the mixture.

Chapter 21: The Rates of Chemical Reactions21.2 The rates of reactions21.2(a) The definition of rate rate of consumption of a reactant R, –d[R]/dt. rate of formation of a product P, d[P]/dt. rate of reaction, v = (1/V)dξ/dt where ξ is the extent of reaction. rate of homogeneous reaction, v = (1/vJ)d[J]/dt. rate of heterogeneous reaction, v = (1/vJ)dσJ/dt. 21.2(b) Rate laws and rate constants rate law, the rate as a function of concentration, v = f([A],[B], ...). rate constant, the constant k in a rate law. hydrogen–bromine reaction: the observed rate law is d[HBr]/dt = kr[H2][Br2]3/2/([Br2] +

kr[HBr]).21.2(c) Reaction order reaction order, the power to which the concentration of a species is raised in a rate law of

the form v = [A]a[B]b... . first-order reaction, a reaction with a rate law of the form v = kr[A]. second-order reaction, a reaction with a rate law of the form v = kr[A]2. overall order, the sum of the orders a + b +..., in a rate law of the form v = kr[A]a[B]b.... zero-order rate law, a rate law of the form v = kr.


21.2(d) The determination of the rate law isolation method, a procedure in which the concentrations of all the reactants except one

are in large excess. Pseudo first-order rate law, v = kr[A] with kr = kr[B]0 by maintaining B in large excess.

S. W. Han et al., Chem. Lett., 2007, 36, 1350.

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method of initial rates, a procedure in which the rate is measured at the beginning of the reaction for several different initial concentrations of reactants; v0 = kr [A]0

a

log v0 = log kr + a log [A]0.

Example 21.2

Chapter 21: The Rates of Chemical Reactions21.3 Integrated rate laws integrated rate law, the integrated form of a rate law for concentration as a function

of time. 21.3(a) First-order reactions first-order integrated rate law, -d[A]/dt= kr[A] ln([A]/[A]0) = –krt, [A] = [A]0e–krt. half life, t1/2 = (ln 2)/kr. time constant, the time required for the concentration of a reactant to fall to 1/e of its

initial value,τ = 1/kr.

Example 21.3

Chapter 21: The Rates of Chemical Reactions21.3(c) Second-order reactions second-order integrated rate law, -d[A]/dt= kr[A]2 1/[A] – 1/[A]0 = krt [A] = [A]0/(1 + krt[A]0). half life, t1/2 = 1/kr[A]0. half life for nth-order reaction (n>1), t1/2 = 2n-1-1/(n-1)kr[A]0

n-1.

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21.4(b) Relaxation methods relaxation, the return to equilibrium. temperature jump, a procedure in which a sudden temperature rise is imposed and

the system returns to equilibrium. pressure-jump techniques, as for temperature jump, but with a sudden change in

pressure.

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Chapter 21: The Rates of Chemical Reactions21.5 The temperature dependence of reaction rates Arrhenius equation, ln k = ln A – Ea/RT. pre-exponential factor (frequency factor), the parameter A in the Arrhenius equation. activation energy, the parameter Ea in the Arrhenius equation; the minimum kinetic

energy for reaction during a molecular encounter. Arrhenius parameters, the parameters A and Ea. generalized activation energy, Ea = RT2(d ln k/dT). activated complex, the cluster of atoms that corresponds to the region close to the

maximum potential energy along the reaction coordinate. transition state, a configuration of atoms in the activated complex which, if attained,

leads to products.


ACCOUNTING FOR THE RATE LAWS21.6 Elementary reactions elementary reaction, a single step in a reaction mechanism.

H + Br2 HBr + Br molecularity, the number of molecules coming together to react in an elementary

reaction. reaction order, the power to which the concentration of a species is raised in a rate

law of the form v = [A]a[B]b... ; an empirical quantity, and obtained from the experimental rate law.

unimolecular reaction, an elementary reaction involving a single reactant molecule. bimolecular reaction, an elementary reaction involving the encounter of two reactant

molecules.

CH3I(alc) + CH3CH2O-(alc) CH3OCH2CH3(alc) + I-(alc)Mechanism: CH3I + CH3CH2O- CH3OCH2CH3 + I-, a single elementary stepRate law: v=kr[CH3I][CH3CH2O-]


21.7 Consecutive elementary reactions consecutive first-order reactions, a sequence of first-order reactions.

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induction period, the initial stage of a reaction during which reaction intermediates are formed.

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rate-determining step, the step in a mechanism that controls the overall rate of the reaction; commonly but not necessarily the slowest step.


pre-equilibrium, a state in which an intermediate is in equilibrium with the reactants and which arises when the rates of formation of the intermediate and its decay back into reactants are much faster than its rate of formation of products.

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21.9 POLYMERIZATION KINETICS stepwise polymerization, a polymerization reaction in which any two monomers present

in the reaction mixture can link together at any time and the growth of the polymer is not confined to chains that are already forming.

chain polymerization, a polymerization reaction in which an activated monomer attacks another monomer, links to it, then that unit attacks another monomer, and so on.

stepwise polymerization

chain polymerization


21.9(a) Stepwise polymerization degree of polymerization, the average number of monomer residues per polymer

molecule, n = 1/(1 – p), where p is the average number of monomers per polymer molecule; n = 1 + krt[A]0.

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21.10 PHOTOCHEMISTRY primary process, a process in which products are formed directly from the excited

state of a reactant. secondary process, a process in which products originate from intermediates formed

directly from the excited state of a reactant.


21.10(a) The primary quantum yield primary quantum yield, ϕ, the number of photophysical or photochemical events that

lead to primary products divided by the number of photons absorbed by the molecule in the same interval, ϕ = v/Iabs.

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21.10(c) Quenching quenching, shortening of the lifetime of an excited state. Stern–Volmer equation, φf,0/φf = 1 + τ0kQ[Q].

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Q: Fe(OH2)63+


Three common mechanism of quenching

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:ondeactivati lCollisiona

21.10(d) Resonance energy transfer Förster theory, a theory of resonance energy transfer, - efficiency (ηT =1-φf,0/φf); ηT 1/R6 [ηT = R0

6/(R06 + R6)].

- hdonor h acceptor


fluorescence resonance energy transfer (FRET), a technique used to measure distances in biological systems.

ηT = R06/(R0

6 + R6)

7.9 nm

Protein rhodopsin

ηT =1-φf,0/φf