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Equilibrium & KineticsEquilibrium & Kinetics
ENV 4101 Elements of Air Pollution
ENV 5105 Foundations of Air Pollution
Prepared by: Ying Li
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Equilibrium & Kinetics
Equilibrium Equilibrium constant
Free energy
Temperature effect
Kinetics
Order of Reactions (1st, 2nd, and pseudo 1st order)
Air Pollution Reactions
Lifetime, Half-life
Temperature effect (Arrenhius Equation)
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Equilibrium Constant
dDcCbBaA m
ba
f [B][A]krateforward !
dc
b [D][C]kratebackward !
dc
b
ba
f [D][C]k[B][A]k !
ba
dc
[B][A]
[D][C]!!
b
f
eq k
kK Equilibrium constant
Consider Reaction:
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Gibbs free energy and equilibrium
When not at equilibrium
QRTGGo
rr ln(!(
ba
dc
[B][A]
[ ][ ]!Q
At equilibrium 0!(rG
eq
o
r KRTG ln!(
(!
RT
GK
o
req exp
0( rG Reaction proceeds forward
Reaction proceeds backward0"( rG
dcbamConsider Reaction:
reactantsproducts
o
f
o
f
o
r GGG ((!(Gibbs free energy of reaction:
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Equilibrium
Example:Calculate the equilibrium constant, Keq, for the
conversion of nitric oxide (NO) to nitrogen dioxide
(NO2) in the presence of oxygen at 25 C.
222
1 NOONO m
Cmpd Gf (@298 K) Hf (@298 K)
NO 86.55 kJ/mol. 90.25 kJ/mol.
O2
0 0
NO2
51.29 kJ/mol. 33.18 kJ/mol.
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Effect of Temperature on Keq
Vant Hoff Equation
1. Can you find the equilibrium constant for the
conversion of NO to NO2 in presence of O2 at325 C?
2. Is the reaction favorable at higher or lower
temperature?
o
rH(Assuming does not change in the range of temperature interested
(!
211
211
lnTTR
H
K
K or
o
rH( - enthalpy of reaction
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Effect of Temperature on Keq
Concentrations of NO and NO2 at equilibrium in exhaust
What can you tell from this table about the
equilibrium concentrations of NO and NO2
?
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Kinetics
Order of Reaction
Productsp cCba
cba CBAk ][][][rateRxn ! .! cbaorderRxn
First-Order Reaction BA p ln [A]
t
k
Second-Order Reaction CBA pCAA p
1/[A]
t
k
Pseudo First-Order Reaction
][][ AkdtAd ! kteAA !
0][][
ktAA
!
0][
1
][
12
][
][
Akdt
Ad!
CBA p
][']][[][
AkABkdt
Ad!! When [B] >> [A]
How to determine the order of reaction
based on experimental data?
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Air Pollution Chemistry
Photodissociation (or Photolysis) Reactions
Lifetime, , is the time for the concentration of a compound to
reach a concentration that is 1/e times the initial concentration
Productsp RhA What is the order of the reaction?
How do you express the lifetime and half life of a
photolysis reaction as a function of the rate
constant?
Half life, t1/2, is the time for the concentration of a compoundto reach a concentration that is half of the initial concentration
ONOhNO p R2
tkthveAA
! 0][][
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Air Pollution Chemistry
Reactions of a compound with an atmospheric oxidant
What is the order of the reaction?
How do you express the lifetime of a compound with
respect to reaction with an atmospheric oxidant?
ProductsOxidant pA
Species Conc. (molecules cm-3)
OH 1106
NO3 5108
O3 71011
Concentration of oxidants in an unpolluted atmosphere
The rate constant for the reaction of propene with OH at 1 atm
pressure and 298 K is 2.610-11 cm3 molecule-1 s-1.What is the
lifetime of propene with respect to removal by OH in the
atmosphere?
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Activation Energy (Ea) and Catalysis
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Temperature Effect on Reaction Rate
The Arrenhius Equation
!RT
EAk aexp
k= Reaction rate constant (is it a real constant?)
A = Frequency factor
Ea = Activation energy (always +)
R= Ideal gas constant
T= Absolute temperature
Does the reaction rate increase or decrease as the
temperature increases?
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Determining the Activation Energy
!RT
EAk aexp
RT
EAk a! lnln
k T
Collect data for k as a
function of T
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Quick Reflections
Equilibrium Equilibrium constant
Free energy
Temperature effect
Kinetics
Order of Reactions (1st, 2nd, and pseudo 1st order)
Air Pollution Reactions
Lifetime, Halflife
Temperature effect (Arrenhius Equation)
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