Integrated rate laws

1
Integrated rate laws
1st order
lnA -kt lnA0
rate kA
2nd order
1/A kt 1/A0
rate kA2
2
Reaction mechanism
reaction
? Elementary steps
Elementary step
Molecularity
rate law
unimolecular
A ? product
kA
A B ? product
bimolecular
kAB
ABC ? product
kABC
termolecular
AAA ? product
kA3
chemical reaction
sum of elementary steps
rate law
and stoichiometry
3
Reaction mechanism
2H2O2 (aq) ? 2H2O(l) O2(g)
?Gorxn
2(-237.9)
- 2(-131.67)
-212.46 kJ
spontaneous reaction
experimental rate law
rate kH2O2
I-
I-
catalyst
increase rate of reaction not consumed in
the overall reaction
reactant in early elementary step
product in later elementary step
4
Reaction mechanism
2H2O2 (aq) ? 2H2O(l) O2(g)
rate kH2O2 I-
k1
step 1
H2O2
? H2O
OI-
I-
k2
step 2
H2O2
OI- ?
H2O
O2
I-
2H2O2 (aq)
?
2H2O(l)
O2(g)
step 1
rate
k1
H2O2
I-
5
Reaction mechanism
k1
step 1
H2O2 I- ? H2O OI-
k2
step 2
H2O2 OI- ? H2O O2 I-
what about step 2 ?
assume k2
gtgt
k1
step 1
rate determining step
I- catalyst
consumed in rate determining step regenerated in
later elementary step
intermediate
OI-
formed in early step, consumed in later step
6
Rate determining step on Labor Day weekend
Big Mac bridge
7
Reaction Mechanism
H2(g) I2(g) ? 2HI(g)
rate k H2 I2
reaction faster in light
free radical
unpaired electron
8
Reaction Mechanism
H2(g) I2(g) ? 2HI(g)
rate k H2 I2
?
I2
2I.
step 1
?
forward rate
kf I2
kr I.2
reverse rate
kfI2
krI.2
equilibrium
kf
I.2
Keq
I2
kr
9
Reaction Mechanism
H2(g) I2(g) ? 2HI(g)
rate k H2 I2
step 1
step 2
H2
2I.?
2HI
?
2HI
H2
I2
need H2 in the rate determining step
rate
k H2 I.2
from step 2
I.
intermediate
10
Reaction Mechanism
H2(g) I2(g) ? 2HI(g)
rate k H2 I2
step 1
step 2 H2 2I.? 2HI
kf
rate k H2 I.2
Keq
I.2
I2
kr
rate
k H2
Keq I2
I.2
Keq I2
rate k H2 I2
11
Reaction Mechanism
2NO O2 ? 2NO2
rate kNO2
step 1
step 2
N2O2 O2 ? 2NO2
2NO O2 ? 2NO2
overall reaction
intermediates
N2O2
relative rates of steps 1 and 2
12
2NO O2 ? 2NO2
rate kNO2
step 1
slow
N2O2 O2 ? 2NO2
step 2
NO
step 1
rate
k1
2
step 1 is rate determining step
N2O2
O2
step 2
rate
k2