2.kinetics homogenous reactions
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KINETICS OF
HOMEGENOUS REACTIONS
A. SARATH BABU
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During a chemical reaction
aA + bB rR + sS
Overall Mass is conserved
Is mass with respect to a species
conserved?
The mass of a reactant depletes /disappears when a reaction is in progress.
The mass of a product increases/appearswhen a reaction is in progress
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Rate of Reaction:
aA + bB rR + sS
Rate of reaction is defined with respect to aspecies participating in the reaction
Rate of formation of species i (ri)
If i is a product, moles of product get formed andhence the rate is +ve
If i is a reactant, moles of reactant get consumedand hence the rate is -ve
))(())(( 3ms
moles
volumeunittimeunit
formediofMolesri ==
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To avoid dealing with both +ve and ve rates
If i is a product, the rate is defined in terms ofrate of appearance (ri)
If i is a reactant, the rate is defined in termsof disappearance (-ri)
dt
d
Vdt
dN
Vvolumeunittimeunit
ddisappeareAofMolesr AAA
===1
))((
dt
dN
Vvolumeunittimeunit
appearedRofMoles
rR
R
1
))(( ==
It may be noted that:rate of disappearance = - (rate of appearance)
i
idnd
=
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For the Reaction: aA + bB rR + sS
Can we have different Rates for the samereaction at the same time
How the change in moles of different speciesrelated at a given time?
How are rates of different species related?
sdN
rdN
bdN
adN SRBA ===
sr
rr
br
ar SRBA ===
Example: A + 2B 2C
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Order of a reaction
...rRb
B
a
AA CCkCr =
Overall Order n = a + b + r + . . .
Order w.r.t. A = a; Order w.r.t. B = b
Without rate law, order cannot be identified
]/[][
]][[
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BrHBrk
BrHkrA
+
= Order n = ??
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Molecularity of a reaction refers to the min.no. of molecules which must combine
Law of mass action: The rate of a reaction isproportional to the product of active massesof the reactants, where the active masses are
raised to the power of their respectivestoichiometric coefficients.
aA + bB rR + sS
b
B
a
A
b
B
a
AA CkCakar ==
The second part is true for ideal solution behavior.
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Liquid phase reactions:
ai = i xi (fi/fi0
)for liquid phase reactions (fi/fi
0) = 1
for ideal liquids i = 1
Gas phase reactions:
ai = yiI P/fi0
= piI /fi0
for ideal gases I = 1 & fi0 = 1 bar
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Elementary reaction ??
AA kCrodAarUnimolecul = .Pr
Order & Molecularity for Elementary reactions
2.Pr2 AA kCrodArBimolecula =
BAA CkCrodBArBimolecula =+ .Pr3
.Pr3AA
kCrodAarTrimolecul =
BAACkCrodBAarTrimolecul
2.Pr2 =+
CBAACCkCrodCBAarTrimolecul =++ .Pr
Order & Molecularity of the forward reaction can bedifferent from those of the backward reaction
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Elementary reaction obeys the law of mass action proceeds in one step
Non-Elementary reaction does not obey the law of mass action
proceeds in more than one step involves the appearance of intermediates
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]][[
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BrHBrk
BrHkrA +
=
Example: H2 + Br22HBr
What is the order & molecularity ??
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Non-Elementary reaction
Non-Elementary reactions involve more than onestep
Involve the formation of intermediates
Intermediates cannot be observed as they arehighly reactive and present in minute quantities
Intermediates could be:
Free radicals: CH3*, C2H5* etc.
Ions & Polar substances: Na+, OH-,NH4+
Highly reactive molecules: A R S Transition State Complexes
h h h f
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Searching the reaction mechanism forNon-Elementary reactions
1. Assume an active intermediate
2.Postulate a mechanism using the experimentalrate law
3.Model each step in the reaction mechanism as
elementary reaction
4. ri, net = ri all elementary steps
5.Use PSSH (SSA): The net rate of all activeintermediates is zero
6.Eliminate the concentration of the intermediates
7.If the derived rate law does not agree withobserved rate law from ex t., oto (2)
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Example: (CH3)2N2 (Azomethane) C2H6 + N2
Mechanism:
A + A A + A*
A*R+ S
Solution:
1. Write the rate law for the desired compoundrS = k3[A*]
2. Write the rate for the intermediate compounds
rA* = k1 [A]2
k2[A*][A] k3[A*] 3. Use PSSH:
rA* = k1[A]2 k2[A*][A] k3[A*]= 0
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k1 [A]2 = (k2[A] + k3)[A*]
][
][
][ 23
2
31*
3 Akk
AkkAkr
s +
==
At low concentrations:k2[A] > k3rS = (k1k3/k2)[A]--- First order
S hi h i h i f
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Searching the reaction mechanism forNon-Elementary reactions Thumb Rules
1. Species having the conc. appearing in thedenominator of the rate law probably collidewith the active intermediate
A + A* . . .
2.If a constant appears in the denominator, one ofthe steps could be the spontaneousdecomposition of the intermediate
A* . . .
3.Species having the conc. appearing in thenumerator of the rate law probably produce theactive intermediate
A A* + . . .
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Rate constant (Specific reaction rate):
nAA ionconcentratk
dt
dN
V
r )(1
==11 )()( = timeionconcentratk n
Example: A + 2B 2C
Write the rate laws for each species ?? Are the rate constants in each case same ?
What is the relation between them??
s
k
r
k
b
k
a
kSCRCBCCA
===
The term reaction rate constant is actually a misnomer, since k may varywith temperature, the solvent for the reaction, and the concentrationsof any catalysts that may be present in the reaction system. The term isin universal use, however, because it implies that the parameter k isindependent of the concentrations of reactant and product species.
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Lec, Stanislaw
Some like to understand what they believe in. Others like to believe in
what they understand.
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Kinetic view of equilibrium for Elementary reactions
A + B C
Forward reaction rate = k1CACB
Backward reaction rate = k2CC
At equilibrium: Forward rate = Backward rate
k1CACB = k2CC
BA
C
C
CC
C
k
kK ==
2
1
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Gas Phase reactions
A Products
ANApACA NkpkCkr ===
What is the relation among different rate constants?
N
n
p
n
C kP
RTkRTk
== )(
N
n
p
n
C KP
RTKRTK
== )(
What is the relation among different Eq. constants?
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Factors affecting the rate of reaction:
The nature of species involved in the reactionConcentration of speciesTemperatureCatalytic activity
Nature of contact of reactantsWavelength of incident radiation
For Homogenous reactions: Rate = f(Concentration, Temperature, Pressure)
The functional form is known as the rate lawand has to be obtained from experiment
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Fractional Conversion (xA):
0
0
A
AAA
N
NN
takenAofmolesInitial
convertedAofmolesx
==
)(0
0 SystemsFlowF
FFx
A
AAA
= )tan(0
0 DensitytConsC
CCx
A
AAA
=
Extent of reaction (): AAAi
i
dxNdn
d /0==
The advantage of using - unique rate of a given reaction.
The major drawback - is an extensive variable and isproportional to the mass of the system.
The fractional conversion is an intensive measure of the
progress of a reaction.
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RELATIONSHIP BETWEEN CONVERSION,
SELECTIVITY, AND YIELD
T t d d f R t
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Temperature dependency of Rate
-rA
T
-rA
T
-rA
T
-rA
T
1 2
3 4
T t d d f R t
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-rA
T
-rA
T
Temperature dependency of Rate
1. Normal behavior simple reactions2. Heterogeneous reactions dominated by resistance to diffusion3. Typical explosions, fuel-air mixtures at ignition temperature4. Catalytic reactions controlled by rate of adsorption, enzymatic
reactions5. Some reactions complicated by side reactions6. Oxygen + Nitric Oxide
5
6
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HR = -ve
E1
E2
E1
E2
HR = E2
- E1
= E1- E2Exothermic Reaction
HR = +ve
E1
E2
E2
E1
HR = E2
- E1
= E1- E2Endothermic Reaction
T t d d f R t
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Temperature dependency of Rate
Effect of temperature on exothermic &
endothermic reactions ??Which reactions are more temperaturesensitive (high E or low E)??
Effect of temperature on exothermic &endothermic reversible reactions ??
Exothermic reaction: EForward < EBackwardEndothermic reaction: EForward > EBackward
Are reactions sensitive at low temperatureranges or high temperature ranges ??
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1/T
ln k
High E
Low E
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1/T
ln k
T = 1000K for doubling the rate
T = 87K fordoubling the rate
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Temperature Rise Needed to Double the Rate of Reactionfor Activation Energies and Average Temperatures
Note that reactions are more sensitive at low temperature Reactions with higher E are more sensitive to temperature
T mp r tur d p nd nc f R t
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Temperature dependency of Rate
1. Arrhenius law: k = A e(-E/RT)
2.Collision Theory: k T1/2 e(-E/RT)
3. Transition State Theory: k Te(-E/RT)
k = k0Tn e(-E/RT)
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RT/E
k/A
0
0.2
0.4
0.6
0.8
1.00
0. 3
0.5
RT/E
k/A
0
1
2
3
4
5
0
0. 5
1
In industrial practice E/R ranges from 5000 to 35000
Therefore RT/E < 0.6 is of practical interest
k approaches A at extreme temperatures
In practice k is several orders of magnitude lower to A
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ANY QUESTIONS ?Chargaff, Erwin
Science is wonderfully equipped to answer the question How? But it
gets terribly confused when you ask it the question Why?