Chemical Kinetics Ch 13. We have learned that enthalpy is the sum of the internal energy plus the energy associated with the work done by the system (PV) on the atmosphere In addition, entropy and Gibb’s Free Energy predict whether a reaction will occur or not
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A B
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
A B
time
rate =
D[A]
D[B]
rate = 
Dt
Dt
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
rate
k =
[Br2]
rate a [Br2]
rate = k [Br2]
= rate constant
= 3.50 x 103 s1
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
2A B
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
D[CO2]
=
Dt
D[CH4]
rate = 
Dt
Write the rate expression for the following reaction:
CH4(g) + 2O2(g) CO2(g) + 2H2O (g)
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
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 N2O5
13.3
Ln 1/.75=.287, Div by 42 and k=6.84x103
T1/2 =0.693/k=101 s
0.88 M
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 =
13.3
[A]0
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
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
# of
halflives
[A] = [A]0/n
Firstorder reaction
1
2
2
4
3
8
4
16
13.3
13.3
SecondOrder Reactions ignore
13.3
ConcentrationTime Equation
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
Endothermic Reaction
Exothermic Reaction
The activation energy (Ea) is the minimum amount of energy required to initiate a chemical reaction.
13.4
lnk = 
+ lnA
Ea
1
T
R
Temperature Dependence of the Rate Constant also known as the Arrhenius equation
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
A product
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
lnk = 
+ lnA
Ea
1
T
R
13.4
13.4
uncatalyzed
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
Fe/Al2O3/K2O
N2 (g) + 3H2 (g) 2NH3 (g)
catalyst
Haber Process
13.6
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
13.6
catalytic
CO + Unburned Hydrocarbons + O2
CO2 + H2O
converter
catalytic
2NO + 2NO2
2N2 + 3O2
converter
Catalytic Converters
13.6
Enzyme Catalysis
13.6
enzyme
catalyzed
uncatalyzed
D[P]
rate =
Dt
rate = k [ES]
13.6