Equilibrium & Kinetics

8/7/2019 Equilibrium & Kinetics

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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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Equilibrium & Kinetics