Chemical Kinetics. A B. rate =. D [A]. D [B]. rate = . D t. D t. Chemical Kinetics. Thermodynamics – does a reaction take place? Kinetics – how fast does a reaction proceed?. Reaction rate is the change in the concentration of a reactant or a product with time ( M /s).
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rate =
D[A]
D[B]
rate = 
Dt
Dt
Chemical Kinetics
Thermodynamics – does a reaction take place?
Kinetics – how fast does a reaction proceed?
Reaction rate is the change in the concentration of a reactant or a product with time (M/s).
D[A] = change in concentration of A over
time period Dt
D[B] = change in concentration of B over
time period Dt
Because [A] decreases with time, D[A] is negative.
13.1
Br2(aq) + HCOOH (aq) 2Br(aq) + 2H+(aq) + CO2(g)
time
Br2(aq)
393 nm
393 nm
Detector
light
D[Br2] aDAbsorption
13.1
Br2(aq) + HCOOH (aq) 2Br(aq) + 2H+(aq) + CO2(g)
slope of
tangent
slope of
tangent
slope of
tangent
[Br2]final – [Br2]initial
D[Br2]
average rate = 
= 
Dt
tfinal  tinitial
instantaneous rate = rate for specific instance in time
13.1
2H2O2 (aq) 2H2O (l) + O2 (g)
[O2] = P
n
V
1
1
D[O2]
P = RT = [O2]RT
RT
RT
DP
rate =
=
Dt
Dt
measure DP over time
PV = nRT
13.1
2H2O2 (aq) 2H2O (l) + O2 (g)
13.1
aA + bB cC + dD
rate = 
=
=
rate = 
= 
D[D]
D[B]
D[A]
D[B]
D[C]
D[A]
rate =
1
1
1
1
1
Dt
Dt
Dt
Dt
Dt
Dt
c
d
a
2
b
Reaction Rates and Stoichiometry
Two moles of A disappear for each mole of B that is formed.
13.1
Write the rate expression for the following reaction:
CH4(g) + 2O2(g) CO2(g) + 2H2O (g)
D[CO2]
=
Dt
D[CH4]
rate = 
Dt
D[H2O]
=
Dt
D[O2]
= 
1
1
Dt
2
2
13.1
aA + bB cC + dD
The Rate Law
The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers.
Rate = k [A]x[B]y
reaction is xth order in A
reaction is yth order in B
reaction is (x +y)th order overall
13.2
F2(g) + 2ClO2(g) 2FClO2(g)
rate = k [F2]x[ClO2]y
Double [F2] with [ClO2] constant
Rate doubles
x = 1
rate = k [F2][ClO2]
Quadruple [ClO2] with [F2] constant
Rate quadruples
y = 1
13.2
F2(g) + 2ClO2(g) 2FClO2(g)
1
Rate Laws
rate = k [F2][ClO2]
13.2
Determine the rate law and calculate the rate constant for the following reaction from the following data:
S2O82(aq) + 3I(aq) 2SO42(aq) + I3(aq)
rate
k =
2.2 x 104 M/s
=
[S2O82][I]
(0.08 M)(0.034 M)
rate = k [S2O82]x[I]y
y = 1
x = 1
rate = k [S2O82][I]
Double [I], rate doubles (experiment 1 & 2)
Double [S2O82], rate doubles (experiment 2 & 3)
= 0.08/M•s
13.2
A product the following reaction from the following data:
rate
=
[A]
M/s
D[A]

M
= k [A]
Dt
[A] = [A]0exp(kt)
ln[A] = ln[A]0  kt
D[A]
rate = 
Dt
FirstOrder Reactions
rate = k [A]
= 1/s or s1
k =
[A] is the concentration of A at any time t
[A]0 is the concentration of A at time t=0
13.3
Decomposition of N the following reaction from the following data:2O5
13.3
The reaction 2A B is first order in A with a rate constant of 2.8 x 102 s1 at 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ?
0.88 M
ln
0.14 M
=
2.8 x 102 s1
ln
ln[A]0 – ln[A]
=
k
k
[A]0
[A]
[A]0 = 0.88 M
ln[A] = ln[A]0  kt
[A] = 0.14 M
kt = ln[A]0 – ln[A]
= 66 s
t =
13.3
[A] constant of 2.8 x 100
ln
t½
[A]0/2
0.693
=
=
=
=
k
k
What is the halflife of N2O5 if it decomposes with a rate constant of 5.7 x 104 s1?
t½
ln2
ln2
0.693
=
k
k
5.7 x 104 s1
FirstOrder Reactions
The halflife, t½, is the time required for the concentration of a reactant to decrease to half of its initial concentration.
t½ = t when [A] = [A]0/2
= 1200 s = 20 minutes
How do you know decomposition is first order?
units of k (s1)
13.3
A product constant of 2.8 x 10
# of
halflives
[A] = [A]0/n
Firstorder reaction
1
2
2
4
3
8
4
16
13.3
13.3 constant of 2.8 x 10
A product constant of 2.8 x 10
rate
=
[A]2
M/s
D[A]
1
1

M2
= k [A]2
=
+ kt
Dt
[A]
[A]0
t½ =
D[A]
rate = 
Dt
1
k[A]0
SecondOrder Reactions
rate = k [A]2
= 1/M•s
k =
[A] is the concentration of A at any time t
[A]0 is the concentration of A at time t=0
t½ = t when [A] = [A]0/2
13.3
A product constant of 2.8 x 10
rate
[A]0
D[A]

= k
Dt
[A]0
t½ =
D[A]
2k
rate = 
Dt
ZeroOrder Reactions
rate = k [A]0 = k
= M/s
k =
[A] is the concentration of A at any time t
[A] = [A]0  kt
[A]0 is the concentration of A at time t=0
t½ = t when [A] = [A]0/2
13.3
ConcentrationTime Equation constant of 2.8 x 10
Order
Rate Law
HalfLife
1
1
=
+ kt
[A]
[A]0
=
[A]0
t½ =
t½
t½ =
ln2
2k
k
1
k[A]0
Summary of the Kinetics of ZeroOrder, FirstOrder
and SecondOrder Reactions
[A] = [A]0  kt
rate = k
0
ln[A] = ln[A]0  kt
1
rate = k [A]
2
rate = k [A]2
13.3
A + B C + D constant of 2.8 x 10
Endothermic Reaction
Exothermic Reaction
The activation energy (Ea) is the minimum amount of energy required to initiate a chemical reaction.
13.4
ln constant of 2.8 x 10k = 
+ lnA
Ea
1
T
R
Temperature Dependence of the Rate Constant
k = A •exp( Ea/RT )
(Arrhenius equation)
Eais the activation energy (J/mol)
R is the gas constant (8.314 J/K•mol)
T is the absolute temperature
A is the frequency factor
13.4
13.4 constant of 2.8 x 10
2NO ( constant of 2.8 x 10g) + O2 (g) 2NO2 (g)
Elementary step:
NO + NO N2O2
+
Elementary step:
N2O2 + O2 2NO2
Overall reaction:
2NO + O2 2NO2
Reaction Mechanisms
The overall progress of a chemical reaction can be represented at the molecular level by a series of simple elementary steps or elementary reactions.
The sequence of elementary steps that leads to product formation is the reaction mechanism.
N2O2 is detected during the reaction!
13.5
Elementary step: constant of 2.8 x 10
NO + NO N2O2
+
Elementary step:
N2O2 + O2 2NO2
Overall reaction:
2NO + O2 2NO2
Intermediates are species that appear in a reaction mechanism but not in the overall balanced equation.
An intermediate is always formed in an early elementary step and consumed in a later elementary step.
13.5
Unimolecular reaction constant of 2.8 x 10
Bimolecular reaction
Bimolecular reaction
A + B products
A + A products
A products
The ratedetermining step is the sloweststep in the sequence of steps leading to product formation.
Rate Laws and Elementary Steps
rate = k [A]
rate = k [A][B]
rate = k [A]2
13.5
The experimental rate law for the reaction between NO constant of 2.8 x 102 and CO to produce NO and CO2 is rate = k[NO2]2. The reaction is believed to occur via two steps:
Step 1:
Step 2:
NO2 + NO2 NO + NO3
NO2+ CO NO + CO2
NO3 + CO NO2 + CO2
What is the equation for the overall reaction?
What is the intermediate?
NO3
What can you say about the relative rates of steps 1 and 2?
rate = k[NO2]2 is the rate law for step 1 so
step 1 must be slower than step 2
13.5
CH constant of 2.8 x 102
CH2
CH2
CH2
CH2
CH2
2
2
CH2
CH2
Chemistry In Action: Femtochemistry
•
•
CH2
CH2
CH2
CH2
CH2
CH2
CH2
CH2
13.5
uncatalyzed constant of 2.8 x 10
catalyzed
Ea
k
‘
Ea< Ea
A catalyst is a substance that increases the rate of a chemical reaction without itself being consumed.
k = A •exp( Ea/RT )
ratecatalyzed > rateuncatalyzed
13.6
In constant of 2.8 x 10heterogeneous catalysis, the reactants and the catalysts are in different phases.
In homogeneous catalysis, the reactants and the catalysts are dispersed in a single phase, usually liquid.
13.6
4NH constant of 2.8 x 103(g) + 5O2(g) 4NO (g) + 6H2O (g)
2NO (g) + O2(g) 2NO2(g)
2NO2(g) + H2O (l) HNO2(aq) + HNO3(aq)
Hot Pt wire
over NH3 solution
PtRh catalysts used
in Ostwald process
Ostwald Process
Pt catalyst
13.6
catalytic constant of 2.8 x 10
CO + Unburned Hydrocarbons + O2
CO2 + H2O
converter
catalytic
2NO + 2NO2
2N2 + 3O2
converter
Catalytic Converters
13.6
Enzyme Catalysis constant of 2.8 x 10
13.6