CEE 697K ENVIRONMENTAL REACTION KINETICS Lecture #2 Rate - - PowerPoint PPT Presentation

CEE 697K

ENVIRONMENTAL REACTION KINETICS

Introduction

David A. Reckhow

CEE 697K Lecture #2 1

Updated: 4 September 2013

Print version

Lecture #2

Rate Expressions: Bromide + Chlorine case study & lab project

Kumar & Margerum paper

Reactions with Chlorine

HOCl + natural organics (NOM)

Oxidized NOM and inorganic chloride

• Aldehydes

Chlorinated Organics

• TOX
• THMs
• HAAs

Cl Cl Cl C H Br Cl Cl C H Br Cl Br C H Br Br Br C H Chloroform Bromodichloromethane Chlorodibromomethane Bromoform

The THMs

The Precursors!

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The Haloacetic Acids

Cl Cl Cl C COOH Br Cl Cl C COOH Br Cl Br C COOH Br Br Br C COOH Trichloroacetic Bromodichloroacetic Chlorodibromoacetic Tribromoacetic Acid Acid Acid Acid

(TCAA)

Cl Cl H C COOH Br Cl C COOH Br Br H C COOH Dichloroacetic Bromochloroacetic Dibromoacetic Acid Acid Acid

(DCAA)

H

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Distribution: Variability within a single system

 Example: New

Haven Service Area

 DS model

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 Sept 11, 1997

 22:00  chlorine

New Haven Distribution System

Lake Saltonstall WTP West River WTP Lake Gaillard WTP Millrock Basins Maltby Tank

3,400 pipes 2,500 junctions

3 MG 8.7 MG

2.0 mg/L DOC (Treated) pH 7 1.8 mg/L chlorine dose

CEE 697K Lecture #2

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 Sept 11, 1997

 22:00  TTHM

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 Sept 11, 1997

 22:00  HAA6

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Single Cell Gel Electrophoresis Genotoxicity Potency Log Molar Concentration (4 h Exposure)

10-6 10-5 10-4 10-3 10-2

IAA BAA CAA DIAA TBAA DBAA 3,3-Dibromo-4-oxopentanoic Acid 2-Bromobutenedioic Acid 2-Iodo-3-bromopropenoic Acid 2,3-Dibromopropenoic Acid DBNM BDCNM TBNM TCNM BNM BCNM DBCNM DCNM CNM Bromoacetamide Dibromoacetamide Tribromopyrrole MX Bromate EMS +Control Haloacetic Acids Halo Acids Haloacetamides Halonitromethanes Other DBPs

DBP Chemical Class

Not Genotoxic: DCAA, TCAA, BDCAA, Dichloroacetamide, 3,3-Dibromopropenoic Acid, 3-Iodo-3-bromopropenoic Acid, 2,3,3,Tribromopropenoic Acid July 2006 Chloroacetamide Trihloroacetamide Iodoacetamide Haloacetonitriles Bromoacetonitrile Dibromoacetonitrile Bromochloroacetonitrile Chloroacetonitrile 3,3-Bromochloro-4-oxopentanoic Acid Iodoacetonitrile Trichloroacetonitrile Dichloroacetonitrile BIAA CDBAA BCAA

 Work of Michael Plewa

 Univ. of Illinois

8

Genotoxicity

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Bromide: THM Formation

Bromide Concentration (mg/L)

0.0 0.4 0.8 1.2 1.6 2.0

Percent of TTHM

20 40 60 80 100 CHCl3 CHBrCl2 CHBr2Cl CHBr3

Data from: Minear & Bird, 1980

96 hours, pH 7.0 5 mg/L Chlorine Dose 1 mg/L Humic Acid

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Impact of Bromide on DHAA Formation

Bromide Concentration (mg/L)

1 2 3 4 5

Concentration (µg/L as Cl-)

20 40 60 80 100

CHCl2COOH CHClBrCOOH CHBr2COOH pH 7, 25oC, 7 days 25 mg/L chlorine dose 2.9 mg/L TOC

From Pourmoghaddas, 1990

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Formation of Brominated THMs

A C

C H Cl Cl Cl C H Br Cl Cl C H Br Br Cl C H Br Br Br

B D E F

HOCl HOCl HOCl HOCl HOCl HOCl

HOCl Br HOBr Cl

k

+  →  +

− −

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THM Br/(Cl+Br)

0.0 0.2 0.4 0.6 0.8 1.0

THM Mole Fraction (THM4 only)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 CHCl3 CHBrCl2 CHBr2Cl CHBr3 CHCl3 Lab tests CHBrCl2 Lab tests CHBr2Cl Lab tests CHBr3 Lab tests

Full-scale data (small symbols) from Weinberg et al., 2002

(All 12 plants)

Lab data (large symbols) from Hua & Reckhow, 2004 Lines are geometric model

Bromo speciation

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Case study: chlorine + bromide

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 Observed reaction

 Nucleophilic attack of bromide on oxygen in

hypochlorous acid

 k2 = 2.95 x103 M-1s-1 at 25ºC

 Note that HOCl deprotonates at elevated pHs  From Farkas et al., 1949

 Transfer of Cl+ to form intermediate (BrCl)

 From: Kumar & Margerum, 1987

− −

+ →  + Cl HOBr Br HOCl

k2

BrCl O H A Br HOCl HA

k

+ + →  + +

− − 2

3

− −

+   → ← + Cl Br Br BrCl

fast 2

− −

  → ← +

3 2

Br Br Br

fast

Background

 Absorbance for

monitoring reaction

 Known equilibria

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CEE 697K Lecture #2

Alkaline Experiments

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 Pseudo-1st order

 Bromide in great excess

 Slow reactions

 Could be monitored directly by

conventional UV spectrophotometer

 292 nm peak for hypochlorite

(OCl-)

 Followed for 4 half-lives

 Complete from: 1.1 sec – 4 hr

 Plot ln(At-A∞) vs time

 Slope is kobs

Kobs is a linear function of Bromide

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pH dependency

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Overall pH dependence

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 How to explain pH effect on 2nd order rate constant?

 See also, Brezonik, pg 230; figure 4-20

Buffer Tests

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 Low pH  High pH

Buffer Effect

 Proposed dependence on

HA

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CEE 697K Lecture #2

( )

] [ ] [ ] [

− + +

+ = Br HA k H k k k

HA H

• bs

] [ ] [ 1 1 ] [

] [ + +

+ = + = =

+

H K C H C C HA

a T T H K T

a

α

        + + = −      

+ + −

] [ ] [ ] [ ] [ H K buffer k k H k Br k

a T HA H

• bs

1 2 2

10 ) 15 . 25 . 1 (

− −

± = s M x kHA

1 2

3 . 1 9 . 8

− −

± = s M kHA

HPO4

• 2

HCO3

 High pH only  More generally

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CEE 697K Lecture #2

( )

] [ ] [ ] [

− + +

+ = Br HA k H k k k

HA H

• bs

( )

] [ ] ][ [ ] [ ] [ )] ( [

− − −

+ + = + − Br OCl HA k HOCl k OCl k dt I Cl d

HA HOCl

( )

] ][ [ ] [ ] [ ] [

− − + −

+ + = − Br OCl HA k H k k dt OCl d

HA H

Acidic Experiments

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 Pseudo-1st order

 Bromide in great excess

 Fast reactions

 Required high-speed setup

 Stopped-flow spectrophotometer

 Could monitor 2º product

 266 nm peak for tribromide (Br3

• )

 Followed for 4 half-lives

 Complete from 0.40-0.01 sec

 Plot ln(At-A∞) vs time

 Slope is kobs

Stopped-flow

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 Principle  Commercial instruments  Limitations

 Correct for slow mixing speed (km)

 For Durrum instrument: km = 1700 s-1

( ) [ ]

m

• bs k

k

• bs
• bs

k k

′

− ′ = 1

Kobs is still linear with Br-

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 No difference in mechanism?

Acidic data: impact of acids

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 General and specific acid

Overall pH dependence

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 Three effective zones

 See also, Brezonik, pg 230; figure 4-20 HOCl OCl- H+ + HOCl

Catalysis: comparison with pKa

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 Bronsted catalysis  Indicates that HA engages in greater

donation of proton to OCl- than to HOCl

H3O+ HCO3

• HPO4
• 2

CH3COOH CH2ClCOOH H2O

( )

α a A HA

K G k =

27 . = α 75 . = α

Mechanisms

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 Proposed mechanism  Alternative

 Less likely

Temperature: Arrhenius Equation

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 Arrhenius Equation

 Where R is the universal gas constant

 Transforms to:

/

a

E RT

k Ae− =

8.3145

• J

R M K =

1 ( ) ( )

a T

E Ln k Ln A R T   = −   

Ln(k) 1/T

1 1

a b a

E R T T Tb Ta

k k e

  − −    

=

Or:

Pizza Kinetics

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 Leenson, 1999

 What are the kinetics of

pizza spoilage?

 Do they conform to

Arrhenius?

• J. Chem Ed., 76:4:504-505

Pizza II

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 Arrhenius plot

 t~k

Time (min)

20 40 60 80 100

Absorbance at 292 nm (cm-1)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Lab Project Example Data #I

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 0.1 M NaOH

What is the Absinf ?

Time (min)

20 40 60 80

Ln (A292-A292inf)

• 6
• 5
• 4
• 3
• 2
• 1

b[0]฀-1.5509712892 b[1]฀-0.0400283854

Lab Project Example Data #II

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 0.1 M NaOH

Set Absinf = 0.085

time vs ln(A-Ainf) Plot 1 Regr

Time (min)

20 40 60 80

Absorbance at 292 nm (cm-1)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Lab Project Example Data #III

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 0.05 M NaOH

Set Absinf = ?

Time (min)

20 40 60 80

Ln (A292-A292inf)

• 9
• 8
• 7
• 6
• 5
• 4
• 3
• 2
• 1

b[0]฀-1.4076822953 b[1]฀-0.0862394216

Lab Project Example Data #IV

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 0.05 M NaOH

Set Absinf = 0.094 Maybe too high ? Downward curvature

time vs ln(A-Ainf) Plot 1 Regr

Time (min)

20 40 60 80

Ln (A292-A292inf)

• 7
• 6
• 5
• 4
• 3
• 2
• 1

b[0]฀-1.6667372496 b[1]฀-0.0679233226

Lab Project Example Data #V

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 0.05 M NaOH

Set Absinf = 0.092 Looks better, except for final data where relative error is high, Use only earlier data?

Time (min)

10 20 30

Ln (A292-A292inf)

• 4.5
• 4.0
• 3.5
• 3.0
• 2.5
• 2.0
• 1.5
• 1.0

b[0]฀-1.5462593144 b[1]฀-0.0744460114

Lab Project Example Data #VI

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 0.05 M NaOH

Set Absinf = 0.092 Using only earlier data where relative error is low, Better linearity and estimate of kobs?

Related systems

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CEE 697K

ENVIRONMENTAL REACTION KINETICS

Introduction

David A. Reckhow

CEE 697K Lecture #2 39

Updated: 4 September 2013

Print version

Lecture #2b

Introduction: Simple Rate Laws

Brezonik, pp.31-39

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Variable Kinetic Order

 Any reaction order, except n=1 n nc

k dt dc − =

( )

[ ] (

)

1 1 1

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

= =

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

Mixed Second Order

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 Two different reactants  Initial Concentrations are different; [A]0≠[B]0

 The integrated form is:  Which can be expressed as:

products B A

k

→  +

2

= ≡ ≡ dt A d dt d V rate

A

] [ 1 1 ν ξ

( )( )

x B x A k B A k dt dx − − = =

2 2

] [ ] [ ] ][ [

t k B A A B B A

2

] [ ] [ ] [ ] [ ln ] [ ] [ 1 = − ( )

2

] [ ] [ log ] [ ] [ 43 . ] [ ] [ log A B t B A k B A − − =

] [ ] [ log B A

t

] [ ] [ log B A

Mixed Second Order

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 Initial Concentrations are the same; [A]0=[B]0

 The integrated form is:  Which can be integrated:

products B A

k

→  +

2

( )( )

x A x A k A A k dt dx − − = =

2 2

] [ ] [ ] ][ [

2

] [ 1 2 ] [ 1 A t k A + =

] [ 1 A

t

] [ 1 A

x B x A B A − = − = = ] [ ] [ ] [ ] [

∫ ∫

= dt k A A d

A 2 2

] [ ] [ ν

t k A A

2

2 ] [ 1 ] [ 1 = −

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Pseudo first order

 For most reactions, n=1 for each of two different

reactants, thus a second-order overall reaction

1 1 2 B Ac

c k dt dc − =

1 1 5

min 10 9 . 3

− − −

= Lmg x k

 Many of these will have one reactant in great excess (e.g., B)

 These become “pseudo-1st

• rder in the limiting reactant,

as the reactant in excess really doesn’t change in concentration

B

c

A

c

products B A

k

→  +

2

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

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Pseudo-1st order (cont.)

 Since C2 changes little

from its initial 820 mg/L, it is more interesting to focus

• n CA

 CA exhibits simple 1st

• rder decay, called

pseudo-1st order

 The pseudo-1st order rate

constant is just the “observed rate” or kobs

1 1 2 B Ac

c k dt dc − =

t k Ao A

• bs

e c c

−

=

1 5 2

min 032 . ) 820 ( 10 9 . 3

− −

≈ = ≈ x c k k

B

• bs

Example: O3 & Naphthalene

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 How long will it take for ozone (4.8

mg/L dose) to reduce the concentration of naphthalene by 99%?

 Used in moth balls and as a chemical

intermediate

 2nd order reaction; k2 = 3000 M-1s-1

 Table 1 in Hoigne & Bader, 1983 [Wat.

• Res. 17:2:173]

 Industrial WW with 0.1mM naphthalene

 Both reactants are at same (0.1mM)

concentration

 Therefore, this reduces to a simple 2nd

• rder reaction

t k A A

2

] [ 1 ] [ 1 + = t 3000 10 1 10 1

4 6

+ =

− −

min 5 . 5 sec 330 000 , 990 3000 = = = t t

O3 & Naphthalene (cont.)

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 Contaminated river water (0.001 mM)  Now ozone is in great molar excess, so this is a pseudo-1st

• rder reaction

t B k

e A A

2

] [

] [ ] [

−

=

( )

( )

sec 4 . 15 3 . 605 . 4 10 3000 10 10 ln ] [ ] [ ] [ ln

4 6 8 2

= − = − − = − =      

− − −

t t t t B k A A

Molecularity of three: 3rd order kinetics

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 Quite improbably, but sometimes happens

 Three different reactants

 Complicated integrated form exists

 Two different reactants

 Integrated form:

products C B A

k

→  + +

3

( )( )( )

x C x B x A k C B A k dt dx − − − = =

3 3

] [ ] [ ] [ ] ][ ][ [

products B A

k

→  +

3

2

( ) ( )

x B x A k B A k dt dx − − = =

2 3 2 3

] [ 2 ] [ ] [ ] [

( )( ) ( )

t k A B B A A B A A A B A A

3 2

] [ ] [ 2 ] [ ] [ ] [ ] [ ln ] [ ] [ ] [ ] [ 2 ] [ ] [ − = + − −

3rd Order (cont.)

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 Only one reactant or Initial Concentrations are the same

 The integrated form is:  Which can be integrated:

products A

k

→  3 3

( )( )( )

x A x A x A k A A A k dt dx − − − = =

3 3

] [ ] [ ] [ ] ][ ][ [

2 3 2

] [ 1 6 ] [ 1 A t k A + =

2

] [ 1 A

t

2

] [ 1 A

∫ ∫

= dt k A A d

A 3 3

] [ ] [ ν

t k t k A A

A 3 3 2 2

6 2 ] [ 1 ] [ 1 = − = − ν

3rd Order (cont.)

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 Pseudo-2nd order reactions  When one of the reactants has a fixed concentration

 E.g., present in excess or buffered, or acts catalytically

 Like a regular 2nd order reaction with two reactants but

• bserved constant is fundamental rate constant times

concentration of the 3rd reactant.

 The integrated form:

t C k B A A B B A ] [ ] [ ] [ ] [ ] [ ln ] [ ] [ 1

3

= −

• bs

k

Example: chlorate formation

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 Formation of chlorate in concentrated hypochlorite

solutions

 Concern: chlorate is toxic

 MCLG=0.2 mg/L

 Stoichiometry

 Is this 3rd order? Be skeptical!

 Observed kinetics

 So, why is it 2nd order?

− − −

+ → Cl ClO OCl 2 3

3

[ ]

2 3 ]

[

− −

= OCl k dt ClO d

• bs

Chlorate example (cont.)

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 Answer: this is a reaction pathway composed of two

elementary reactions

 Step #1  Step #2

 In multi-step reactions such as these, we say that

 the overall rate is determined by the slowest step

 Called the “rate-limiting step” or RLS

 Rate law is written based on the RLS

 Subsequent steps are ignored  Prior steps are incorporated as they determine the

concentrations of the RLS reactants

− − −

+  →  Cl ClO OCl

slow 2

2

− − − −

+  →  + Cl ClO ClO OCl

fast 3 2

Homework #2 is based on this reaction

H

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Reversible reaction kinetics

For a general reversible reaction:

k qQ + pP bB + aA k

r f

↔

And the rate law must consider both forward and reverse reactions:

where, kf = forward rate constant, [units depend on a and b] kb or kr = 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 P q = stoichiometric coefficient of species Q

q Q p P r b B a A f

C C k C C k rate − =

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Stumm & Morgan

• Fig. 2.10
• Pg. 69

] [ ] [

2 1

B k A k dt dB − =

eq

K k k A B B k A k dt dB ≡ = − = =

2 1 2 1

] [ ] [ ] [ ] [

 Kinetic law  Eventually the reaction

slows and,

 Reactant concentrations

approach the equilibrium values

Reversible 1st order (cont.)

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 Solution to non-equilibrium reaction period

 See Brezonik, pg 37-38 for details

 Where k* = kf + kr

 And:  Where:

{ }

t k f r

e k k A k A

*

*

] [ 1 ] [

−

+ =

k P A k

r f

↔

t k equ equ

e A A A A

*

] [ ] [ ] [ ] [

−

= − −

( )

equ equ equ r f

A P K k k ] [ ] [ = =

Linearized version

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 To next lecture