elementary reactions - umass amherst
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CEE 680 Lecture #5 1/29/2020
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Lecture #5
Kinetics and Thermodynamics: Fundamentals of Kinetics and Analysis of Kinetic Data
(Stumm & Morgan, Chapt.2 )
(pp.16‐20; 69‐81)
David Reckhow CEE 680 #5 1
(Benjamin, 1.6)
Updated: 29 January 2020 Print version
Elementary Reactions When reactant molecules collide with the right orientation and energy level to form new bonds
Many “observable” reactions are really just combinations of elementary reactions
FEBA
FCDA
EC
DCBA
2
2
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fast
slow
fast
Starting out with some A and B, we observe that E and F are the end products
CEE 680 Lecture #5 1/29/2020
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Cont.
Elementaryreactions
A single step in areaction sequence
Involves 1 or 2 reactants and 1 or 2 products
Can be described by classical chemical kinetics
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S&M: Fig. 2.11Pg. 72
Kinetics Examples
Fe+2 oxidation by O2
almost instantaneous at high pH
quite slow at low pH
high D.O. may help
Oxidation of organic material
Formation of solid phases Aluminum hydroxide
Quartz sand
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CEE 680 Lecture #5 1/29/2020
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Kinetics
Base Hydrolysis of dichloromethane (DCM)
Forms chloromethanol (CM) and chloride
Classic second order reaction (molecularity of 2)
First order in each reactant, second order overall
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dt
Cld
dt
CMd
dt
OHd
dt
DCMdOHDCMkRate
][][][][]][[
Reaction Kinetics Irreversible reaction
is one in which the reactant(s) proceed to product(s), but there is no significant backward reaction,
In generalized for, irreversible reactions can be represented as:
aA + bB Products
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i.e., the products do not recombine or change to form reactants in any appreciable amount. An example of an irreversible reaction is hydrogen and oxygen combining to form water in a combustion reaction. We do not observe water spontaneously separating into hydrogen and oxygen.
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Reaction Kinetics: Reversibility A reversible reaction
is one in which the reactant(s) proceed to product(s), but the product(s) react at an appreciable rate to reform reactant(s).
aA + bB pP + qQ
Most reactions must be considered reversible
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An example of a reversible biological reaction is the formation of adenosine triphosphate (ATP) and adenosine diphosphate (ADP). All living organisms use ATP (or a similar compound) to store energy. As the ATP is used it is converted to ADP, the organism then uses food to reconvert the ADP to ATP.
Kinetic principles Law of Mass Action
For elementary reactions
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where,CA = concentration of reactant species A, [moles/liter]CB = concentration of reactant species B, [moles/liter]a = stoichiometric coefficient of species A
b = stoichiometric coefficient of species Bk = rate constant, [units are dependent on a and b]
productsbBaA kbB
aACkCrate
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Reaction Kinetics (cont.) Reactions of order “n” in reactant “c”
When n=0, we have a simple zero‐order reaction
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dc
dtkcn
dc
dtk
ktcc o
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80
Co
nce
ntr
atio
n
Time (min)
k mg l 10 / / min
Slope
Reaction Kinetics (cont.) When n=1, we have a simple first‐order reaction
This results in an “exponential decay”
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dc
dtkc 1
c c eokt
0102030405060708090
0 20 40 60 80
Time (min)
Co
nc
en
tra
tio
n
k 0 032 1. min
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Reaction Kinetics (cont.)
This equation can be linearized
good for assessment of “k” from data
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dc
dtkc 1
10
100
0 20 40 60 80
Time (min)
Co
nc
en
tra
tio
n (
log
sc
ale
)
ktcc o lnln
k 0 032 1. min
Slope
0102030405060708090
0 20 40 60 80
Time (min)
Co
nc
en
tra
tio
n
Reaction Kinetics (cont.)
This results in an especially wide range in rates
More typical to have 2nd order in each of two different reactants
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dc
dtkc 2
c ckc to
o
1
1k L mg 0 0015. / / min
When n=2, we have a simple second-order reaction
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Reaction Kinetics (cont.) Again, the equation can be linearized to estimate “k” from data
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dc
dtkc 2
0
0.02
0.04
0.06
0.08
0.1
0.12
0 20 40 60 80
Time (min)
1/C
on
ce
ntr
ati
onkt
cc o
11
k L mg 0 0015. / / min
Slope
Comparison of Reaction Orders
Curvature as order changes: 2nd>1st>zero
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0102030405060708090
0 20 40 60 80
Time (min)
Co
nc
en
tra
tio
n
Zero Order
First Order
Second Order
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Reaction Kinetics (cont.) For most reactions, n=1 for each of two different reactants, thus a second‐order overall reaction
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12
11ckc
dt
dc
115 min109.3 Lmgxk
Many of these will have one reactant in great excessThese become “pseudo‐1st order in the limiting reactant, as the reactant in excess really doesn’t change in concentration
2c
1c
0102030405060708090
0 20 40 60 80
Time (min)
Co
nc
en
tra
tio
n
Reaction Kinetics (cont.)
Since C2 changes little from its initial 820 mg/L, it is more interesting to focus on C1
C1 exhibits simple 1st
order decay, called pseudo‐1st order The pseudo‐1st order rate constant is just the “observed rate” or kobs
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12
11ckc
dt
dc
tko
obsecc 11
1
52
min032.0
)820(109.3
xkckobs
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Variable Kinetic Order Any reaction order, except n=1
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nkcdt
dc
11
111
1
nno
o
tkcncc
ktncc n
on
111
11
Half‐lives Time required for initial concentration to drop to half, i.e.., c=0.5co For a zero order reaction:
For a first order reaction:
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c c kto 2
15.0 ktcc oo k
ct o5.0
21
c c eokt 2
1
5.0kt
oo ecc
k
kt
693.0
)2ln(2
1
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Kinetic problem If the half‐life of bromide in the presence of excess chlorine is 13 seconds (pseudo‐1st order reaction,
What is the pseudo‐1st order rate constant
how long does it take for 99% of the bromide to be oxidized?
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HOCl Br HOBr Clk
Reactions in Series
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DCBA kkk 321
Fig. 2.9Pg. 68
k1=k2=k3=0.1 day-1
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Reversible reaction kinetics
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For a general reversible reaction: f
b
k
aA + bB pP + qQ
k
And the rate law must consider both forward and reverse reactions:
A f Aa
Bb
b Pp
Qqr = k C C - k C C
where,kf = forward rate constant, [units depend on a and b]kb = backward rate constant, [units depend on a and b]CP = concentration of product species P, [moles/liter]CQ = concentration of product species Q, [moles/liter]p = stoichiometric coefficient of species Pq = stoichiometric coefficient of species Q
Reversible 1st order reactions Kinetic law
Eventually the reaction slows and,
Reactant concentrations approach the equilibrium values
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Fig. 2.10Pg. 69
][][ 21 BkAkdt
dB
eqKk
k
A
B
BkAkdt
dB
2
1
21
][
][
][][0
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Analysis of Rate Data
Integral Method Least squares regression of linearized form
Differential Method estimate instantaneous rate at known time and reactant concentration
Initial rate Method more rigorous, but slow
Method of Excess only when 2 or more reactants are involved
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Kinetic model for equilibrium
DCBA
DCBA
b
f
k
k
}}{{ BAkr ff
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Consider a reaction as follows:
Since all reactions are reversible, we have two possibilities
The rates are:
And at equilibrium the two are equal, rf=rb
We then define an equilibrium constant (Keq)
}}{{ DCkr bb
A + B = C + D
}}{{
}}{{
BA
DC
k
kK
b
feq
}}{{}}{{ DCkBAk bf
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Kinetic model with moles
BAff BAkr
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In terms of molar concentrations, the rates are:
And at equilibrium the two are equal, rf=rb
And solving for the equilibrium constant (Keq)
DCbb DCkr
BA
DC
BA
DC
b
feq BA
DC
BA
DC
k
kK
DCbBAf DCkBAk
To next lecture
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