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
[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
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
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
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
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
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
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
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
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
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
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
Endothermic Reaction
Exothermic Reaction
The activation energy (Ea) is the minimum amount of energy required to initiate a chemical reaction.
13.4
+ 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
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
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
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 NO2 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
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 heterogeneous 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
4NH3(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
CO + Unburned Hydrocarbons + O2
CO2 + H2O
converter
catalytic
2NO + 2NO2
2N2 + 3O2
converter
Catalytic Converters
13.6
13.6