Chapter 12 1
Chapter 12: Kinetics; Outline1. Introduction2. macroscopic determination of rate (experimental)•define rate •define rate law, rate constant, reaction order •rate determination via expt: initial rate •integrated rate laws
first order; half-lives second order; half-lives
•rate & temperature: the Arrhenius equation
Chapter 12 2
Arrhenius equation:•from observation, reaction rates and rate constants increase with temperature
examples: food decays faster at higher temperature; cooking; fireflies;
•from observation, a graph of log(k) vs. 1/T gives a straight line•the slope of the log(k) vs. 1/T graph is related to the activation energy
Chapter 12 3
)ln(1
303.2)log( A
TR
Ek A
A graph of ln(k) vs. 1/T gives a straight line with a slope of -EA/Rand an intercept of ln(A)
where k is rate constant, EA is the activation energy, R is the gas constant in J K-1mol-1, T is temperature in Kelvin, and A is the “steric factor”
Chapter 12 4
Example: The rate constant for a certain reaction is measured at four temperatures (see the data below). What is the activation energy for the reaction? What is the value of the rate constant at 400°C?
T(C) k
330 0.77
354 1.8
378 4.1
383 4.7
Chapter 12 5
k T(K) 1/T log(k)0.77 603 0.001658 -0.11351.8 627 0.001595 0.25534.1 651 0.001536 0.61284.7 656 0.001524 0.6721
Chapter 12 6
Arrhenius Plot
y = -5904.6x + 9.6756
R2 = 0.9998
-0.5
0
0.5
1
1.520E-031.590E-03
1.660E-031/T (1/K)
log(
k)
activation energy = slope ·2.303·(-R) = +1.13x105 J mol-1
Chapter 12 7
3. molecular view of kinetics•mechanisms•relationship to rate laws•Arrhenius equation4. Catalysis, Factors affecting rates3. Molecular View of Kinetics
Chapter 12 8
•MechanismsA mechanism is a series of elementary reactions, or steps, that describe what happens as a reaction proceeds.
Elementary reactions are not overall reactions: overall reactions summarize the products and reactants and give the stoichiometry.
Elementary reactions may have intermediates: short-lived (<1 second) species that are formed and then react away as the reaction proceeds.
An elementary reaction often involves a collision between two species (a bimolecular step or reaction).
Chapter 12 9
example: NO2+CONO+CO2
rate=k[NO2]2 [2nd order]
NO2+NO2 NO3+NO
NO3+CO NO2+CO2
possible mechanism:
Chapter 12 10
A few comments on the mechanism and its relation to the rate law:
•NO and NO3 are intermediates. They don’t appear as
reactants or products and they are very reactive (unstable).•Each of these steps is bimolecular: involves 2 molecules.•The individual reactions add up to give the overall
reaction with the correct stoichiometry.•The order and the rate equation of an elementary reaction is determined by its stoichiometry
step 1: rate(1)=k1[NO2]2 bimolecularstep 2: rate(2)=k2[NO][NO3] bimolecular
Chapter 12 11
•If one step is much slower than the others, the rate of that slow step is the rate of the overall reaction
step 1: slow (forms two unstable intermediates)step 2: FAST (two unstable, reactive intermediates react)
overall rate predicted by the mechanism: k1[NO2]2
rate determined by experiment: k[NO2]2
Therefore, we say that the proposed mechanism is REASONABLE.
Chapter 12 12
example: devise a plausible mechanism consistent with the overall reaction and the overall reaction rates for each of the following
Co(CN)5H2O-2(aq)+I-1(aq) Co(CN)5I-3(aq)+H2O(l)rate=k[Co(CN)5H2O-2]1(aq)
Co(CN)5H2O-2 Co(CN)5-2+H2O k[Co(CN)5H2O-2]
Co(CN)5-2+I1- Co(CN)5I-3 k[Co(CN)5
-2][I1-]
slow
fast
Chapter 12 13
2NO2(g)+F2(g)2NO2F(g) rate=k[NO2][F]
[HINT: consider a slow step and a fast step.]
Chapter 12 14
•Collision Theory From observation, we know
1. reaction rates and rate constants increase with temperature
2. a graph of ln(k) versus 1/T gives a straight line with a negative slope
3. rate constants are relatively slow considering the HUGE number of collisions that occur at room temperature (around 1025 in a cm3 at 1 atm and 298 K)
Develop a theory that accounts for these observations
Chapter 12 15
•reactions occurs as the result of a collision
•only collisions above some minimum energy (the ACTIVATION ENERGY)will result in product formation
•only collisions of the correct geometry (orientation) will result in product formation
Chapter 12 16
So, we can write an equation based on theory that gives the reaction rate;
this equation is based on molecular parameters.
rate=(collision rate)x (fraction molecules with EA)x (fraction molecules with correct geometry)
collision rate=Z[A][B] where Z depends on temperature and [A], [B] are concentrations
fraction molecules with EA=f
fraction molecules with correct geometry=P
Chapter 12 17
combineZPfk
definitionBAkrate
theoryPfBAZrate
]][[
]][[
Chapter 12 18
fraction of molecules with enough energy to react: Activation Energy
0.00
0.01
0.02
0.03
0.04
0 20 40 60 80 100 120 140 160
energies
fraction
activation energy
lower temperature
highertemperature
more particles have energy>EA at higher T
113145.8
molJKRef RTEA
fraction of particles withenergy >EA
Chapter 12 20
ZPfk from before
we have 113145.8
molJKRef RTEA
RTEA
eAk
line form of Arrhenius equationbmxy
ART
Ek A
)ln()ln(
combining
rearranging
Chapter 12 21
•Catalysis
1. definition: a catalyst is a chemical substance that increases the rate of a chemical reaction but is not consumed in the reaction (does not appear as a reactant or product).
catalysts work by
2. providing an alternate, lower energy reaction pathway to product formation
or
3. stabilizing the activated complex (transition state) and thus lowering the activation energy
Chapter 12 22
Chapter 12 23
3 examples
1. HOMOGENEOUS CATALYSIS: ozone depletion
depletiongOgOgO
formationgOgOgO
)(2)()(
)()()(
23
32
Cl· catalyzes the depletion reaction through a series of reactions:
)()()()(
)()()()(
)()()(
2
23
222
gOgClgOgClO
npropagatiogOgClOgClgO
formationgClgClCFgClCF
Cl· acts as a catalyst in the second two steps
Chapter 12 24
2. HETEROGENEOUS CATALYSIS catalytic converterCO(g)+1/2O2(g)CO2(g)
reactant molecules adsorb (by intermolecular forces or by chemical bonding) to the metal surface in the converter bonds in reactants weaken activated complex energy is reduced reaction goes faster
Chapter 12 25
3. enzymes: large molecules that act as catalysts in biological reactions
•enzymes are specific: they work with only 1 substrate
•reaction rates are increased by factors of 108 to 1020
•the “turnover number” of number of reaction events per second is large:
103 to 107 s-1
link to www: http://wizard.pharm.wayne.edu/biochem/enz.html
