chemical kinetics rates of chemical reaction － definition of reaction rate － integrated and...
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Chemical Kinetics
Rates of chemical reaction
－ definition of reaction rate
－ integrated and differential rate law
－ determination of rate law Mechanism of chemical reaction
－ activated complex theory
－ model for chemical kinetics
－ Arrhenius equation
2 2
2
2
2 2
[ ]Average Rate
[ ]Instantaneous Rate= -
NO NO O
NO
td NO
dt
Rate Law
Rate=k[NO2]n
The concentration of the products do not appear in the rate law.
The value of the exponent n must be determined by experiment; it cannot be written from the balanced equation.
][][
5252 ONk
dt
ONdR
2N2O5→4NO2+O2
Types of Rate Laws Integrated Rate Law: how the concentration
of species in the reaction depend on time Differential Rate Law: how the rate of a
reaction depends on concentrations Determine the differential rate law for a given
reaction, the form of integrated rate law can be automatically known, and vice versa
Initial-Rate method
To determine the instantaneous rate before the initial concentration of reactants have changed significantly.
Several experiments are carried out using different initial concentrations.
The initial rate is determined for each run.
4 2 2 2
44 2
2
[ ][ ] [ ]n m
NH NO N H O
d NHk NH NO
dt
Experiments Initial Rate
1 0.1M 0.005M 1.35X10-7
2 0.1M 0.01M 2.70X10-7
3 0.2M 0.01M 5.40X10-7
4NH 2NO
7
7
7
7
4 2
7
4 1 1
2 2.7 10 (0.1) (0.01)(2) 2 1
1 1.35 10 (0.1) (0.005)
3 5.4 10 (0.2) (0.01)(2) 2 1
2 2.7 10 (0.1) (0.01)
[ ][ ]
1.35 10 (0.1)(0.005)
2.7 10
n mm
n m
n mn
n m
Rate km
Rate k
Rate kn
Rate k
Rate k NH NO
k
k Lmol s
Integrated Rate Law－ first order
2 5 2 2
2 5 2 52 5 2 5
2 5
2 5
22 5
1 02 5
2 52 5 2 5 0
2 5 0
2 5 2 5 0
2 4
[ ] [ ]1[ ] [ ]
22
[ ]
[ ]
[ ]
[ ]
[ ]ln( ) ln[ ] ln[ ]
[ ]
[ ] [ ] a
a
a
a
t
a
a a
k t
N O NO O
d N O d N ORate k N O k N O
dt dtk k
d N Ok dt
N O
d N Ok dt
N O
N Ok t N O N O k t
N O
N O N O e
][][
law rate aldifferenti
5252 ONk
dt
ONdR a
Plot of N2O5 vs. time
Half-Life of a First Order Reaction
The time required for a reaction to reach half of its original concentration is called half-life of a reaction and id designated by t1/2.
2 5 2 5 0
2 5 2 5 0
2 5 0 2 5 0 1/ 2
2 5 0 2 5 0 1/ 2
1/ 2
1/ 2
1 [ ] [ ]
2ln[ ] ln[ ]
1ln( [ ] ) ln[ ]
21
ln( ) ln([ ] ) ln([ ] )2
ln 2
ln 2 0.693
a
a
a
a
a a
when N O N O
N O N O k t
N O N O k t
N O N O k t
k t
tk k
Plot of N2O5 vs. time
Integrated Rate Law－ second order
0
2
[ ]
2 2[ ] 00
0
[ ][ ] ( )
[ ] [ ] 1 1
[ ] [ ] [ ] [ ]
1 1
[ ] [ ]
a a
A t
a a aA
a
aA P
d ARate k A k ak
dtd A d A
k dt k dt k tA A A A
k tA A
Plot of C4H6
Integrated Rate Law－ zero order
0
0
[ ]
[ ]
0
0
[ ][ ] = ( )
[ ]
[ ] [ ]
[ ] [ ]
a a a
A
aA
a
a
aA P
d ARate k A k k ak
dt
d A k dt
A A k dt
A A k dt
Pseudo-Order Reaction Law
3 2 2
233
33 0 0 0
0 0 3 0
' ' 233
5 6 3 3
[ ][ ][ ][ ]
[ ] 1.0 10 [ ] 1.0 [ ] 1.0
[ ] [ ] [ ]
[ ][ ] ( [ ][ ] )
BrO Br H Br H O
d BrORate k BrO Br H
dt
BrO M Br M H M
Br H BrO
d BrOk BrO k k Br H
dt
Arrhenius Postulations Collisions and Rate
－ the rate of reaction is much smaller than
calculated collision frequency. A threshold energy (activation energy)
－ This kinetic energy is changed into potential energy as the molecules are distorted during a collision, breaking bonds and rearranging the atoms into product molecules.
Collisions Frequency and Molecular orientations Experiments show that the observed reaction
rate is considerably smaller than the rate of collisions with enough energy to surmount the barrier.
The collision must involve enough energy to produce the reaction.
The relative orientation of the reactants must allow formation of any new bonds necessary to products.
BrNO collision
Potential energy graph for 2BrNO→2NO+Br2
Temperature Dependence of Rate Constants
The order of each reactant depends on the detailed reaction mechanism.
Chemical reaction speed up when the temperature is increased.
－ molecules must collide to react － an increase in temperature increases the frequency of intermolecular collisions.
T1/T2 graph
T(K) and k
Ea: activation energy
A: pre-exponential factor
Aek
factorp: steric
uencyision freqz:the coll
zpek
RT
E
RT
E
a
a
ln(A))T
1(
R
Eln(k) a
Arrhenius Equation
Plot ln(k) vs. 1/T
Reaction Mechanism
Most chemical reactions occur by a series of steps called the reaction mechanism.
The sum of the elementary steps must give the overall balanced equation for the reaction.
The mechanism must agree with the experimentally determined rate law.
2 2 3
3 2 2
2 2
3
(1) slow
(2) fast
(1) (2)
:
(1) (2) .
NO NO NO NO
NO CO NO CO
NO CO NO CO
NO intermediate
Step and are called elementary setps
Step (1): rate-determining-step
Treatments1. Rate-Determining Step Approximation 2. Steady-State Approximation
2 NO N2O2 fast
N2O2+H2 N2O+H2O slow
Overall: 2NO+H2 N2O+H2O
R=[NO]2[H2]
k1
k-1
k2
Rate-Determining Step Approximation
][][
][][
]][[
][][][][
22
22
1
21
2222
2
1
122221
21
HNOk
HNOk
kk
HONkR
NOk
kONONkNOk
Steady-State Approximation
][
][][
][
][][
0]][[][][][
0][
ON of consumtion of rateON of production of rate
221
22
21
221
21
22
22222212
122
22
2222
Hkk
HNOkkR
Hkk
NOkON
HONkONkNOkdt
ONddt
ONd
][][][][][
][][
][][][
][
][][
22
22
1
21221
21
22
22
21221
221
22
21
HNOkHNOk
kkRHkkif
NOkHk
HNOkkRHkkif
Hkk
HNOkkR
Overall reaction
H++HNO2+C6H5NH2→C6H5N2++2H2O
Proposed mechanism
H++HNO2 H2NO2+ rapid equilib.
H2NO2++Br-→ONBr+H2O slow
ONBr+C6H5NH2 →C6H5N2++H2O+ Br- fast
k1
k-1
k2
k3
][Br
]][Br][HNO[H
]][Br][HNO[H
21
221
21
21
kk
kkte:rsteady sta
k
kkrds:r
Activated Complex Theory
The arrangement of atoms found at the top of potential energy hill or barrier is called the activated complex or transition state.
△E has no effect on the rate of reaction. The rate depends on the size of the activation
energy Ea
Catalysis
A substance can speed up a reaction without being consumed itself.
The catalyst is to provide a new pathway for the reaction and to decrease activation energy.
Effect of a catalyst
Heterogeneous Catalysis
Adsorption and activation of the reactants Migration of the adsorbed reactants on the
surface Reaction among the adsorbed substances Escape, or desorption, of the products.
Hydrogenation of ethylene
Exhaust gases