KineticsHow fast does a reaction (event) occur?

Reaction rates are controlled by:

•Nature of reactants

•Ability of reactants to meet

•Concentration of reactants

•Temperature

•Presence of a catalyst

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UNITS: mol/L x 1/s =mol.L-1.s-1 or M.s-1

dt

Ad ][

in time) (change

ion)concentratin (change

KineticsChange of reaction rate with time

Concentration and rate

A + B products

In general it is found that:

rate[A]m[B]n

The values of the exponents, m and n, must be determined empirically

(by experiment).

We can replace by = if we introduce a rate constant, k.

Rate = k [A]m[B]n

This expression is the rate law

Rate LawsExample: H2SeO3 + 6I- + 4H+ Se + 2I3

- + 3H2O

Rate = k[H2SeO3]x[I-]y[H+]z

Experimentally found that x=1, y=3, z=2

Rate = k[H2SeO3][I-]3[H+]2

At 0C, k=5.0 x 105 L5 mol-5 s-1

(units of rate constant are such that the rate has units of mol.L-1.s-1)

Notice that exponents in rate law frequently are unrelated to reaction stoichiometry.

Sometimes they are the same, but we cannot predict this without experimental data!

Exponents in the rate law are used to describe the order of the reaction with respect to each reactant. The overall order of a reaction is the sum of the orders with respect to each reactant (6th order in example above).

Determining exponents in a rate lawOne way to do this is to study how changes in initial concentrations

affect the initial rate of the reaction

Initial Concs

[A] [B]

Initial rate

(mol L-1 s-1)

0.10 0.10 0.20

0.20 0.10 0.40

0.30 0.10 0.60

0.30 0.20 2.40

0.30 0.30 5.40

A + B products

Rate = k [A]m[B]n

1-3: [B] is constant.

Rate changes due only to [A]

m must be 1

3-5: [A] is constant. When [B] is doubled, rate increases by factor of 4 (=22). When [B] is tripled, rate increases by factor of 9 (=32).

n must be 2

Concentration and Time-1st order reactions

0AlnAln ktt

Rate = k[A]

Integrated rate law

ktA

A

t

0ln

We can show that

A plot of ln[A]t versus t is a straight line y = mx + c

with slope -k and y intercept ln[A]0.

Concentration and Time-1st order reactions 0AlnAln ktt

Half-life: time required for half of initial concentration of reactant to disappear.

Set [A]t = ½[A]0

t1/2 = ln2/k

A plot of ln[A]t versus t is a straight line with slope -k and y intercept ln[A]0.

Concentration and Time-2nd order reactions

Simplest 2nd order: 2A B

Rate = k[A]2

Integrated rate law

ktAA t

0

11

Half-life

t1/2 = 1/k[A]0

Half-life depends on initial concentration

Temperature dependence of reaction rates

Activation EnergyIn order to form products, bonds must be

broken in the reactants.Bond breakage requires energy.

The Arrhenius equation relates the activation energy to the rate constant

Activation EnergyActivation Energy• Consider the reaction between Cl and NOCl:

– If the Cl collides with the Cl of NOCl then the products are Cl2 and NO.

– If the Cl collided with the O of NOCl then no products are formed.

ArrheniusArrhenius discovered most reaction-rate data obeyed the equation

RTEAk

Aek

a

RTaE

/lnln

/

k is the rate constant, Ea is the activation energy, R is the gas

constant (8.314 J/mol-K) and T is the temperature in K.

A is called the frequency factor.A is a measure of the probability of a

favorable collision.Both A and Ea are specific to a given

reaction.

Catalysis

A catalyst provides a reaction with an alternate pathway that has a lower energy

of activation.A catalyst is not consumed in a reaction.

Enzymes are biological catalysts.

Nerve Agents-Inhibition of Acetylcholinesterase

F P

O

CH3

O

CH CH3

CH3

Sarin

CH2

OH ..:

P

O

CH3

O

CH CH3

CH3

CH2 O

Inactivated Enzyme

ActiveSite

ser ser + HF

O C CH3

O

N+

CH2 CH2

CH3

CH3

CH3

H2O

ON+

CH2 CH2

CH3

CH3

CH3

C CH3

O

OH+

+

H

Acetylcholine

Ozone depletion

Radio-activity

Unstable atomic nuclei may decay by emitting particles that are detected with special counters. Alpha, beta, and gamma emission are common types of radioactivity. In beta decay the emitted particles are electrons; in alpha decay they are helium nuclei, and in gamma decay they are high energy photons.

Counters can be sensitive to either alpha, beta, or gamma-ray particles. The rubidium isotope 37Rb87 decays by beta emission to 38Sr87, a stable strontium nucleus:

37Rb87 38Sr87 + .

From the following experimental data, calculate (a) the rate constant and (b) the half-life of the rubidium isotope. From a 1.00 g sample of RbCl which is 27.85% 37Rb87, an activity of 478 beta counts per second was found. The molecular weight of RbCl is 120.9 g mole-1.

Summary Of Decay Types

94Pu244

• 94Pu239 is used for nuclear weapons and for energy

Radiological Properties of Important Plutonium Isotopes

Pu-238 Pu-239 Pu-240 Pu-241 Pu-242

Half-life(in years) 87.74 24,110 6537 14.4 376,000

Specific activity(curies/gram) 17.3 0.063 0.23 104 0.004

Principal decay mode alpha alpha alpha beta alpha

some spontaneous fission(a)

Decay energy(MeV) 5.593 5.244 5.255 0.021 4.983

Radiological hazards

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