reaction kinetics - marmara Üniversitesimimoza.marmara.edu.tr/~zehra.can/chem209/03. reaction...
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REACTION KINETICS
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Chemical Kinetics
Kinetics – how fast does a reaction proceed?
Will the reaction produce significant change within milliseconds or thousands of years?
Reaction rate is the change in the concentration of a reactant or a product with time (M/s).
A B
rate = - Δ[A]
Δ t
rate = Δ[B]
Δ t
Δ[A] = change in concentration of A over time period Δ t
Δ[B] = change in concentration of B over time period Δ t
Because [A] decreases with time, Δ[A] is negative. 2
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A B
rate = - D[A]
Dt
rate = D[B]
Dt
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Reaction Rates and Stoichiometry
4
2 N2O5 (g) 4 NO2 + O2
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Reactants decrease
with time
Time Concentration (M)
(s) N2O5 NO2 O2 0 0,02 0 0
100 0,0169 0,0063 0,0016 200 0,0142 0,0115 0,0029 300 0,0120 0,0160 0,0040 400 0,0101 0,0197 0,0049 500 0,0086 0,0229 0,0057 600 0,0072 0,0256 0,0064 700 0,0061 0,0278 0,0070
Products increase
with time
Consider the decomposition of N2O5 to give NO2 and O2:
2 N2O5 (g) 4 NO2 + O2
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0
0,01
0,02
0,03
0 100 200 300 400 500 600 700 800
Con
cen
tra
tio
n (
M)
Time (sec)
N2O5
NO2
O2
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From the graph looking at t = 300 to 400 sec
Rate O2 = 0.0009 M
100 s = 9 x 10−6 M𝑠−1
Rate NO2 = 0.0037 M
100 s = 3.7 x 10−5 M𝑠−1
Rate N2O5 = −0,0019 M
100 s = -1.9 x 10−5 M𝑠−1
Why do they differ?
Recall :
2 N2O5 (g) 4 NO2 + O2
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Rate O2 = 1
1 x 9 x 10−6 M𝑠−1 = 9 x 10−6 M𝑠−1
Rate NO2 = 1
4 x 3.7 x 10−5 M𝑠−1 = 9.2 x 10−6 M𝑠−1
Rate N2O5 = - 1
2 x 1.9 x 10−5 M𝑠−1 = 9.5 x 10−6 M𝑠−1
To compare the rates one must account for the stoichiometry.
Now they
agree !
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Reaction Rates and Stoichiometry
2A B
Two moles of A disappear for each mole of B that is formed.
rate = D[B]
Dt rate = -
D[A]
Dt 1
2
aA + bB cC + dD
rate = - D[A]
Dt 1
a = -
D[B]
Dt 1
b =
D[C]
Dt 1
c =
D[D]
Dt 1
d
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aA + bB cC + dD
d
r
c
r
b
r
a
r DCBA
10
3A 2B + C If the overall rate of rxn is 1st order wrt to A , then r = k [A] rate =
rA = rxn. rate wrt to rA = -3 k [A]
rB = rxn. rate wrt to rB = 2 k [A]
rC = rxn. rate wrt to rC = k [A]
123
cba rrr
Rate =
Example :
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The Rate Law and Reaction Order
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.
aA + bB cC + dD
Rate = k [A]x[B]y
reaction is xth order with respect to reactant A
reaction is yth order with respect to reactant B
reaction is (x +y)th order overall
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@ constant temperature, the rate of rxn. (disappearance of a reactant or formation of a product) is some function of the concentration of the reactants
aA + bB cC + dD
Overall order of rxn = r= k [A]α [B]β Overall order of rxn = α+β Order of rxn with respect to reactant A =α Order of rxn with respect to reactant B = β
(mol/L.t)
reaction rate constant
order of the rxn. respect to individual reactants A and B (0, 1, 2 may be fractional)
molar concentrations of reactants (mol/ L)
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F2 (g) + 2ClO2 (g) 2FClO2 (g)
rate = k [F2]x[ClO2]
y
Double [F2] with [ClO2] constant
Rate doubles
x = 1
Quadruple [ClO2] with [F2] constant
Rate quadruples
y = 1
rate = k [F2][ClO2]
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F2 (g) + 2ClO2 (g) 2FClO2 (g)
rate = k [F2][ClO2]
Rate Laws
• Rate laws are always determined experimentally.
• Reaction order is always defined in terms of reactant (not
product) concentrations.
• The order of a reactant is not related to the stoichiometric
coefficient of the reactant in the balanced chemical
equation.
1
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Unit of k (reaction rate constant)
For 0 order rxn. k =
r = k[A]⁰ r = k
For 1st order rxn. k = =
r = k [A]
For 2nd order rxn. k = =
r = k *A+²
15
t.L
molrate
L
molt.L
mol
L
molrate
t
1
t.mol
L22
L
molt.L
mol
L
mol
rate
k = M1-n t-1
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Example :
r = k *A+² *B+
Order of overall rxn. = 2 + 1 = 3
Order of rxn. with respect to reactant A = 2
Order of rxn. with respect to reactant B = 1
Unit of k = M-2 t-1 =
16
tmol
L 12
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Classes of Reactions That Occur In Nature
Homogenous Reactions
Reactants and products are in the same phase.
(i.e., liquid, solid or gas)
Reactants are distributed continuously(but
not necessarily uniformly) throughout the
fluid.
1a. Single irreversible reaction:
A B A+A B aA + bB C
1b. Multiple irreversible reaction:
A (Parallel reaction) A B C
(consecutive or series reaction)
1c. Reversible reaction:
A B A+B C+D
Heterogenous Reactions
Reactions that occur at surfaces between
phases.
Examples:
Reactions on the surface of ion exchange resin
Reactions that require the presence of a solid
phase catalyst
C
B
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Types of Reactions and Reaction Rates
→ irreversible rxns
→ reversible rxns
→ saturation rxns
→ autocatalytic rxns
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Irreversible Reactions
a)Single Irreversible Rxns:
A P A + A P aA + bB P
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Example:
aA pP (Rxn. rate 1st order)
r = k [A] rA = r x (-a) rA = -a k [A] rP = p k [A]
Irreversible Reactions
a)Single Irreversible Rxns:
PBA rb
r
a
rr
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b)Multiple Irreversible Rxns:
b-1) Parallel rxns:
k1 bB
aA
k2 cC
Overall rate of rxn: r1 + r2
Rate of rxn with respect to A = rA = -ar1 – ar2
Rate of rxn with respect to B = rB = b r1
Rate of rxn with respect to C = rC = cr2
bB
r
aA
rr 1
cCr
aA
rr 2
aA
r2
cCr
bB
r
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If both of the rates of rxn 1st order
r1= k1[A] r2= k2[A]
rA= -ak1[A] - ak2[A]
rB= bk1[A] rC= ck2[A]
k1 bB aA k2 cC
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b-2) Consequtive rxns
rA = - a r1
rB = b r1 – b r2
rC = c r2
bBr
aAr
1r
cCr
bBr
2r
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k1
cCbB
bBaA
cCbBaA
k1
k2
k2
If both of the rates of rxn 1st order
r1= k1[A] r2= k2[A]
rA= -ak1[A]
rB= bk1[A] - bk2[B]
rC= ck2[A]
Slowest step limits the overall rxn. rate
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Reversible Reactions aA bB
aA bB rA = ar1 + ar2 bB aA rB = br1 + br2
bBr
aAr
1r
aAr
bBr
2r
k1
k2
k1
k2
Note: for reversible rxns signs of stoichiometric coefficients (both reactants & products) are always positive (+)
If both of the rates of rxn 1st order
r1= k1[A] r2= k2[A]
ra= ak1[A] + ak2[B] rb= bk1[A]+ bk2[B]
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Saturation Type Reactions
Saturation type reactions have a maximum rate that is a point at which
the rate becomes independent of concentration A.
For the reaction aA bB
r = rate of rxn, mol /L.t
[A] = conc. of reactant, mol / L
k = rxn rate constant, mol/ L.t
K = half saturation constant, mol/ L
Fig.1.Graphical representation of Saturation –Type Reaction
Ref: Tchobanoglous and Schroeder, 1985, Addison-Wesley Publishing Company
[A]K
[A]k r
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Saturation Type Reactions (continue)
• When K << [A] r = k [A] ≈ k (zero order)
K + [A]
Negligible
• When K >> [A] r = k [A] ≈ k [A] (first order)
K + [A] K
Negligible
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[A]K
k[A]r
Ref: Tchobanoglous and Scroeder, 1985, Addison-Wesley Publishing Company
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For the reaction A + B P = k
[A]K
[B][A]kr
[B]2
K
[B]
[A]1K
[A]
k
Saturation Type Reactions (continued)
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Autocatalytic Reactions
Example: Bacterial growth
(rate of increase in bacterial number is proportional to the number present)
Autocatalytic rxns can be 1st order
2nd order
Saturation Type
Partially Autocatalytic (function of
reactant & product)
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Autocatalytic reaction rates are functions of the product concentration.
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1st order Autocatalytic Rxn. aA bB r = k [B] = rA = a k [B] rB = b k [B] 2nd order Autocatalytic Rxn. aA Bb r = k [B] [A] = rA = a k [A][B] rB = b k [A] [B]
bBr
aAr
bBr
aAr
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Effect of Temperature On
Reaction Rate Coefficients
The temperature dependence of the rate constant is given by
Van’t Hoff- Arhenius relationship
)1T_
2T(
1
2
k
k
31
For BOD
θ = 1.047 for temperatures between 20o - 30 oC
Theta remains constant for only a small range of temperatures.
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11 lnln
RT
EAk a
22 lnln
RT
EAk a
Subtracting ln k2 from ln k1 gives
)11
(lnln12
21TTR
Ekk a
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)11
(ln122
1
TTR
E
k
k a
)(ln21
21
2
1
TT
TT
R
E
k
k a
)11
(lnln12
21TTR
Ekk a
)1T_
2T(
1
2
k
k
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EXAMPLE:
A first order reaction rate constant, k1 at 20°C = 0.23/d.
If river temperature is 25°C, what will k2 be in that environment?
k2 = k1(1.047)(T-20) = 0.23(1.047)(T-20) = 0.30/d
)1T_
2T(
1
2
k
k
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Analysis of Experimental Data
Methods to determine the order of a reaction from experimental data
1-) Method of Integration
2-) Differential Method 3-) Time Reaction Method 4-) Isolation Method
Most commonly used
35
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If straight line plot is obtained It is assumed that the order of the rxn corresponds to the rxn. plotted
I.Method of Integration
→ Integrated forms of the various rate expressions (Oth order, 1st order, etc..)
→ Plotting the experimental data functionally based on the integrated form of the rate expression
→ Determine the reaction rate constant from the plot.
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a) Irreversible Zero-Order Reaction A P
ktCaCa )0()t(
Plot Ca(t) versus t
To determine reaction rate constant (k)
Ca(
t)
37
t
0
t
0
c
c
dt.k]A[da
a
kdt
]A[drA
k0]A[kdt
]A[drA
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b) Irreversible First Order Reaction A P
k[A]dt
d[A]rA
t
0
dtk
C
C[A]
d[A](t)a
(0)a
ktLnCaLnCa )0()t(
ktCa
CaLn)0(
)t(
kt
)0(a(t)aeCC
)0(
)t(
Ca
CaLn
To determine reaction rate constant (k)
Plot versus t
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ktCaCa )0()t(
Ca(
t)
kt
)0(a(t)aeCC
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Half Life
Time required for the amount of substance to decrease to half its initial value
2
aa
CC
)0(
)t( 2/1
For 1st order rxn :
eCCkt
)0()t(.aa
eCC 2/1
2/1
t.k
)0()t(.aa
eCC 2/1t.k
)0(
)0(.a2
a
e 2/1t.k21
e.Ln2
1Ln 2/1t.k 2/1t.k
2
1Ln
k
693.0
k
2Lnt 2/1
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c) Irreversible Second Order Reaction A+A P
2
Ak[A]
dt
d[A]r
t
0
dtk
C(t)
a
(0)Ca2[A]
d[A]
kt|[A]
1(t)
(0)
Ca
Ca
To determine reaction rate constant (k)
Plot versus t
1/C
a(t)
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)(
1
)(
1
tCkt
tC aa
)(
1
tCa
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d) Irreversible Parallel Reaction (1st order)
b
r
a
r[A]kr ba
11
c
r
a
r[A]kr ca
22
cC
bB k1
aA
k2
a, b, c = 1
[A][A][A]
21 kkdt
dra
.[A]kdt
d[B]r 1b
[A]kdt
d[C]r 2c
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[A]k[A]kdt
d[A]r 21a
).[A]k(kdt
d[A]21
t
0
dt).2
k1
(k
Ca(t)
Ca(0)[A]
d[A]
t).kk()LnCLnC(21
)0(a)t(
a
t).kk(LnCLnC21
)0(a)t(
a
T).kk(
)0(Ca
)t(Ca
Ln 21
eCCt.)kk(
)0()t(
.21.aa
cC
bB k1
aA k2
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d) Irreversible Parallel Reaction (1st order-continue)
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eCCt.)kk(
)0()t(
.21.aa
cC
bB k1
aA k2
44
d) Irreversible Parallel Reaction (1st order-continue)
kt
)0(a(t)aeCC 1st order reaction
1st order irreversible parallel reaction
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.[A]k
.[A]k
dtd[C]
dtd[B]
r
r
2
1
c
b
2
1
c
b
k
k
d[C]
d[B]
r
r
c
c
b
b
C
C
C
C
tt
kdk)(
)0(
)(
)0(
[C][B]12
].[].[ )0()(1)0()(2 CcCcCC tt kk bb
][
][
)0()(
)0()(2
1
CcCcCC
t
t bbkk
45
cC
bB k1
aA k2
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II.Differential Method
Assumption: The rate of rxn is proportional to the nth power of concentration.
n
A k[A]dt
d[A]r
For 2 different concentrations at 2 different times;
,tt 1 1AA nAkdt
Ad][
][1
1
,tt 2 2AA nAkdt
Ad][
][2
2
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If logarithm of each of the above equation is taken and the k values are equated:
]nlog[Alogkdt
]d[Alog 1
1
]nlog[Alogkdt
]d[Alog 2
2
]log[A]log[A
)dt]d[Alog()dt]d[Alog(n
21
21
n
11 ]k[A
dt
]d[A
n
22 ]k[A
dt
]d[A
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Example: Determine the order of the reaction and the reaction rate constant for the following data derived from on experiment carried out in a batch reactor. Solve the problem a)Using Integration Method b)Using Differential Method
Time (min)
[A] mol/L
0 100 1 50 2 37 3 286 4 23.3 5 19.6 6 16.9 7 15.2 8 13.3 9 12.2
10 11.1 48