Chemical Kinetics. Chapter 15. A B. ___ = . D [A]. D [B]. ___ = . D t. D t. Chemical Kinetics. ____________________ – does a reaction take place? ____________________– how fast does a reaction proceed?.
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Chapter 15
___ =
D[A]
D[B]
___ = 
Dt
Dt
Chemical Kinetics
____________________ – does a reaction take place?
____________________– how fast does a reaction proceed?
____________ ____________ 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 __________ .
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.
Br2(aq) + HCOOH (aq) 2Br(aq) + 2H+(aq) + CO2(g)
time
Br2(aq)
393 nm
393 nm
Detector
light
D[Br2] aDAbsorption
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]
_________________ = 
= 
Dt
tfinal  tinitial
_________________ = rate for specific instance in time
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
k =
[Br2]
Rates of the Reaction Between Molecular Bromine and Formic Acid at 25ºC
rate a [Br2]
rate = k [Br2]
= ____ _________
= 3.50 x 103 s1
k =
[Br2]
Rates of the Reaction Between Molecular Bromine and Formic Acid at 25ºC
rate a [Br2]
rate = k [Br2]
= Rate Constant
= 3.50 x 103 s1
[O2] = P
n
V
1
1
D[O2]
P = RT = [O2]RT
RT
RT
DP
rate =
=
Dt
Dt
measure DP over time
PV = nRT
aA + bB cC + dD
rate = 
=
=
rate = 
= 
D[C]
D[B]
D[A]
D[B]
D[D]
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.
Write the rate expression for the following reaction:
CH4(g) + 2O2(g) CO2(g) + 2H2O (g)
D[CH4]
D[CO2]
D[O2]
D[H2O]
rate = 
=
=
=
Dt
Dt
Dt
Dt
Which relationship correctly compares the rates of the following reactants and products?
C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(l)
a)
b)
c)
d)
e)
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 =
reaction is _______ order in A
reaction is _______ order in B
reaction is _______________ order overall
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]m [B]n
reaction is mth order in A
reaction is nth order in B
reaction is (m + n)th order overall
Rate Data for the Reaction between F2 and ClO2
rate =
Double [F2] with [ClO2] constant
Rate _____________
x = 1
Quadruple [ClO2] with [F2] constant
Rate ______________
y = 1
rate =
Rate Data for the Reaction between F2 and ClO2
rate = k [F2]m[ClO2]n
Double [F2] with [ClO2] constant
Rate doubles
m = 1
Quadruple [ClO2] with [F2] constant
Rate quadruples
n = 1
rate = k [F2]1[ClO2]1
1
Rate Laws
rate = k [F2][ClO2]
1
Rate Laws
rate = k [F2][ClO2]
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 =
M/s
=
[S2O82][I]
( M)( M)
rate =
y =
x =
rate =
Double [I], rate ___________ (experiment 1 & 2)
Double [S2O82], rate ___________ (experiment 2 & 3)
= ______ /M•s
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 =
1.1 x 104 M/s
=
[S2O82][I]
( 0.08 M)( 0.017 M)
rate=k[S2O82]m[I]n
m = 1
n = 1
rate=k[S2O82][I]
Double [I], rate doubles (experiment 1 & 2)
Double [S2O82], rate doubles (experiment 2 & 3)
= 0.081 /M•s
rate
=
[A]
M/s
D[A]

M
= k [A]
Dt
[A] = [A]0exp(kt)
ln[A] = ln[A]0  kt
D[A]
rate = 
Dt
First  Order 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
ln
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 ?
0.14 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 =
What is the halflife of N2O5 if it decomposes with a rate constant of 5.7 x 104 s1?
ln
t½
[A]0/2
0.693
=
=
=
=
k
k
t½
ln2
ln2
0.693
=
k
k
5.7 x 104 s1
First  Order 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
= 1216 s = 20 minutes
How do you know decomposition is first order?
units of k (s1)
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
Second  Order 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
rate
[A]0
D[A]

= k
Dt
[A]0
t½ =
D[A]
2k
rate = 
Dt
Zeroth  Order Reactions
rate = k [A]0 = k
Reminder: what is the value of any number raised to the zero power? x0= ??
= 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
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
Implications of the Collision Theory of Chemical Kinetics
Rate
The ____________ ____________ (Ea ) is the minimum amount of energy required to initiate a chemical reaction.
Implications of the Collision Theory of Chemical Kinetics
Rate 1/Ea
The Activation Energy (Ea ) is the minimum amount of energy required to initiate a chemical reaction.
__________ Reaction
__________ Reaction
The __________ __________ (___)is the minimum amount of energy required to initiate a chemical reaction.
Endothermic Reaction
Exothermic Reaction
The Activation Energy (Ea) is the minimum amount of energy required to initiate a chemical reaction.
The Rate Constant Depends on Temperature
What happens to the rate of a chemical reaction as the temperature increases?
Why does this happen?
Explain this observation in terms of the Collision Theory of Kinetics.
We express this dependence of rate on temperature in the ___________ equation.
The Rate Constant Depends on Temperature
What happens to the rate of a chemical reaction as the temperature increases?
Why does this happen?
Explain this observation in terms of the Collision Theory of Kinetics.
We express this dependence of rate on temperature in the Arrhenius Equation.
+ lnA
Ea
1
T
R
The Rate Constant Depends on Temperature
Arrhenius equation
k =
Ea= the activation energy (J/mol)
R = the gas constant (8.314 J/K•mol)
T = the absolute temperature
A = frequency factor/collision frequency
e = the base of the natural log scale
Why do we write it in this form?
+ lnA
Ea
1
T
R
Why do we rewrite the equation in this form?
y = m x + b
slope
Now a plot of lnkversus 1/T is a __________ line,Ea/R is the _________, and the _____________________is lnA.
+ lnA
Ea
1
T
R
Why do we rewrite the equation in this form?
y = m x + b
slope
Now a plot of lnkversus 1/T is a straight line,Ea/R is the slope, and the yintercept is lnA.
A balanced chemical equation does not tell us how the reaction actually takes place.
Usually it just represents the sum of a series of simpler elementary steps or elementary reactions.
We try to deduce these steps and propose a _______________ _______________ .
A balanced chemical equation does not tell us how the reaction actually takes place.
Usually it just represents the sum of a series of simpler elementary steps or elementary reactions.
We try to deduce these steps and propose a reaction mechanism.
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!
NO + NO N2O2
+
Elementary step:
N2O2 + O2 2NO2
Overall reaction:
2NO + O2 2NO2
Species that appear in a reaction mechanism but not in the overall balanced equation are called ___________.
An ___________ is always formed in an early elementary step and consumed in a later elementary step.
Bimolecular reaction
Bimolecular reaction
A + B products
A + A products
A products
Rate Laws and Elementary Steps
rate = k [A]
rate = k [A][B]
rate = k [A]2
The ratedetermining step is the __________step in the sequence of steps leading to product formation
Step 2:
NO2 + NO2 NO + NO3
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:
NO3 + CO NO2 + CO2
What is the equation for the overall reaction?
What is the intermediate?
What can you say about the relative rates of steps 1 and 2?
rate = is the rate law for step 1 so
step 1 must be ___________ than step 2
catalyzed
Ea
k
'
Ea< Ea
A _____________ is a substance that increases the rate of a chemical reaction without itself being consumed.
k = A •exp( Ea/RT )
ratecatalyzed > rateuncatalyzed
In ____________________________________ catalysis, the reactants and the catalysts are in different phases.
In ________________________ catalysis, the reactants and the catalysts are dispersed in a single phase, usually liquid.
4NH3(g) + 5O2(g) 4NO (g) + 6H2O (g)
2NO (g) + O2(g) 2NO2(g)
2NO2(g) + H2O (l) HNO2(aq) + HNO3(aq)
PtRh catalysts used
in Ostwald process
Hot Pt wire
over NH3 solution
Ostwald Process
Pt catalyst
CO + Unburned Hydrocarbons + O2
CO2 + H2O
converter
catalytic
NO + NO2
N2 + O2
converter
Catalytic Converters