[PDF] - CEE 697K ENVIRONMENTAL REACTION KINETICS Lecture #1 Introduction: PDF Document

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CEE 697K

ENVIRONMENTAL REACTION KINETICS

Introduction

David A. Reckhow

CEE697K Lecture #1 1

Updated: 3 September 2013

Print version

Lecture #1

Introduction: Basics

Brezonik, pp.1-31

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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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Utility of Kinetics

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CEE697K Lecture #1

3  Empirical Analysis  Moderate Rate  Estimate reaction time (characteristic time) for;

 Engineered systems (size of tanks)  Natural Aquatic Systems (WQ modeling)  Atmospheric systems (air pollution modeling)

 Fast Rates  Evaluate simple competitive kinetics

 Determine complex reaction stoichiometries

 Define complex or cyclic reaction webs

 Postulate major pathways

 Slow Rates  Reaction time for global processes

 Human impacts

 Theoretical Analysis  All Rates: understand mechanisms  Predict other reaction kinetics

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Chemistry and Environmental Engineering

Environmental Engineering Math Biology Physics Chemistry

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Engineered & Natural Systems

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 Kinetics is the source of reactions and rates Process Design

Environmental Modeling

Aquatic Chemistry

Env. Micro

Surface Chemistry

Kinetics Biological Processes

Physico- chemical Processes

Transport Reactions

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Relation with other Chemistry Disciplines

Chemistry

Physical Chemistry Kinetics Thermodynamics Analytical Chemistry

680

Inorganic Chemistry Organic Chemistry

697K

 With water chemistry, A cornerstone of the good grad

programs in our field

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Time Scales & Kinetics

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Engineered Systems

Time and Length scales

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Sulfur in lakes I

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 Forms  Gas: H2S, SO2  Liquid SO4

2, HS-, Amino acids with S

 Solids: MeSx, pyrites (FeS2), elemental S  Mass Transfer  Air:water  Sediment:water  Reactions  Chemical: oxidation, reduction, precipitation, complexation,

hydrolysis

 Biological: biosynthesis, use as TEA, release

Methionine Cysteine

Sulfur in Lakes II

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 Brezonik; example 1-2  Sulfur cycling depends on biotic

& abiotic redox kinetics, precip, dissolution, complexation, etc.

Observed in-lake loss of sulfate by microbial sulfate reduction Monod kinetics from lab cultures

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Sulfur in lakes (cont.)

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 Typical sulfate depth profile

around sediment water interface

 Kinetics of abiotic oxidation of

sulfide species

HS- S-2

Sulfur in lakes (cont.)

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 Mackinawite (FeS)  Forms in reduced sediments  Dissolves by first order rate,

also catalyzed by low pH

 Where A/V is the FeS surface

area to total volume ratio

 Arrhenius temperature plot

 

2 1

] [ ] [ k H k V A dt S d

tot

 

 Pankow & Morgan, 1979 [ES&T, 13(10)1248]

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Thermo vs Kinetics

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 Reaction of oxygen and nitrogen  Thermodynamics tells us:  In the oceans, {H+}aq~10-8, and {NO3

}~0.26M

 Then, considering pN2=0.70, we calculate:  But the real pO2 is 0.21 atm  Why does thermo fail us here? the reaction is very slow.

  

  

3 2 2 2 1 2

2 2 2 NO H O H O N

5 . 2 2 3 2 6 . 2

2 2

} { } { 10

O N aq aq

p p NO H K

  

  atm x pO

7

10 8 . 2

2



  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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Reaction Kinetics

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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15 Reaction Kinetics: Reversibility

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.  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

Extent of Reaction I

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 Has the reaction occurred if an so how close to completion is it?  Consider a generic reaction  Bringing the reactants to the products side, we get  And using the Greek, , to equal the various stoichiometric

coefficients,

 And the law of conservation of mass requires:

.... ....      qQ pP bB aA .... ....        qQ pP bB aA .... ....       Q P B A

Q P B A

   





i i iMW



MW  M  molecular weight

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Extent of Reaction II

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 Mathematically defined as:  The change in #moles of a reactant or product as compared

to the starting amount divided by the stoichiometric coefficient, 

 And therefore:  And what we call the reaction rate is:

i io i

n n   ) (  

dt dn dt d

i i 

          1

 

dt c d dt V n d dt d V rate

i i i i

                            1 1 1

Where [ci] is the molar concentration

f substance “i”

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Gibbs Energy and reaction extent

 G Changes as reaction

progresses due to changing concentrations

 G reaches a minimum at the

point of equilibrium

Stumm & Morgan

Fig. 2.5; Pg. 45

 d dG G 



Extent of reaction

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19 Elementary Reactions

 When reactant molecules

collide with the right

rientation and energy level

to form new bonds

 Elementary reactions proceed

in one step and directly produce product with no intermediates

 Many “observable” reactions

are really just combinations

f elementary reactions

(multi-step reactions)

F E B A F C D A E C D C B A           2 2

fast slow fast Starting out with some A and B, we

bserve that E and F are the end

products

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Cont.

 Elementary

reactions

 A single step in a

reaction sequence

 Involves 1 or 2 reactants and 1 or 2 products  Can be described by classical chemical kinetics

 Law of mass action

 # of reactant species in an elementary reaction is

call the molecularity

S&M: Fig. 2.11

Pg. 72

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Law of mass action

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 For elementary reactions, we can write the rate

expression directly from the stoichiometry

 Reaction order  Overall order: n=a+b  Order with respect to A=a, B=b, C=0.

products bB aA  

b a A

B A k dt A d a dt A d rate ] [ ] [ ] [ 1 ] [ 1     

The rate constant, k, is in units of c1-nt-1

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Elementary vs non-elementary I

 Base Hydrolysis of dichloromethane (DCM)  Forms chloromethanol (CM) and chloride  Elementary reaction, therefore second order overall

(molecularity of 2)

 First order in each reactant, second order overall

dt Cl d dt CM d dt OH d dt DCM d OH DCM k Rate ] [ ] [ ] [ ] [ ] ][ [

  

      

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Elementary vs non-elementary II

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 The reaction of hydrogen and bromine  Sometimes used as an example of an elementary

reaction in old chemistry textbooks

 Careful study has show the following kinetics  Thus it is not an elementary reaction!

) ( ) ( 2 ) ( 2

2

g g g

HBr Br H  

] [ ] [ 5 . ) ( 2 ) ( 2

) ( 2 ) (

1 ] ][ [ ] [

g g

Br HBr g g

k Br H k dt HBr d   

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Elementary Reactions

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 B k = rate constant, [units are dependent on a and b]

 Recall: Law of Mass Action  For elementary reactions

products bB aA

k

  

b B a AC

kC rate 

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10 20 30 40 50 60 70 80 90 20 40 60 80 Time (min) Concentration

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Simple Zero Order

 Reactions of order

“n” in reactant “c”

 When n=0, we have

a simple zero-order reaction

dc dt kcn  

dc dt k  

c c kt





k mg l  10 / / min

Slope

10 20 30 40 50 60 70 80 90 20 40 60 80 Time (min) Concentration

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Simple first order

 When n=1, we

have a simple first-order reaction

 This results in an

“exponential decay”

A

kc dt dc  

kt Ao A

e c c





k 



0 032

1

. min

products A

k

 

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First order (cont.)

 This equation can

be linearized

 good for

assessment of “k” from data

A A

kc dt dc  

10 100 20 40 60 80 Time (min) Concentration (log scale)

kt c c

Ao A

  ln ln

k 



0 032

1

. min

Slope

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10 20 30 40 50 60 70 80 90 20 40 60 80 Time (min) Concentration

Simple Second Order

 This results in an

especially wide range in rates

 More typical to

have 2nd order in each of two different reactants

2 2

1

A A A

c k dt dc   

t c k c c

Ao Ao A 2

2 1 1   min / / 0015 .

2

mg L k   When n=2, we have a simple second-order reaction

products A

k

  2 2

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Simple Second Order (cont.)

 Again, the equation can be linearized to

estimate “k” from data

2 2

1

A A A

c k dt dc   

0.02 0.04 0.06 0.08 0.1 0.12 20 40 60 80 Time (min) 1/Concentration

t k c c

Ao A 2

2 1 1  

min / / 0015 . 2

2

mg L k 

Slope

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Comparison of Reaction Orders

 Curvature as order changes: 2nd>1st>zero 10 20 30 40 50 60 70 80 90 20 40 60 80 Time (min) Concentration Zero Order First Order Second Order

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Variable Kinetic Order

 Any reaction order, except n=1 n nc

k dt dc  

 

  



1 1 1

 

  

n n

n
t

c k n c c

  t

k n c c

n n

n

1 1 1

1 1

  

 

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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:

c c kt





2 1

5 . kt c c



 k c t

5

.

2 1 

c c e

kt





2 1

5 .

kt

e

c c





k k t 693 . ) 2 ln(

2 1

 

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Example: Benzyl Chloride

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 Use:  Manufacture of benzyl compounds, perfumes,

pharmaceuticals, dyes, resins, floor tiles

 Toxicity  Intensely irritating to skin, eyes, large doses can cause

CNS depression

 Emission  45,000 lb/yr  Fate  Benzyl chloride undergoes slow degradation in water to

benzyl alcohol

Benzyl chloride II

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25ºC

Sources:

Schwarzenbach et al., 1993, Env. Organic Chemistry
1972, J. Chem.Soc. Chem. Comm. 425-6
1967, Acta Chem. Scand. 21:397-407
1961, J. Chem. Soc. 1596-1604

] [ ] [ A k dt A d  

 Benzyl chloride to benzyl alcohol  Nucleophilic substitution  SN1 or SN2?

 How to distinguish?

 Salt effects

CH2Cl CH2OH

H2O HCl

Temperature 0.1ºC 25ºC K 0.042x10-5 s-1 1.38x10-5s-1 T1/2 19.1 d 0.58 d

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 To next lecture