Document Text Contents
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226 Elements of Environmental Engineering: Thermodynamics and Kinetics
log k0 IAN INB
IAB
Slope = –1 Slope = +1
Actual curve
lo
g
k
pH
FIGURE 5.11 Variation in acid–base hydrolysis rate with pH for organic compounds in the
environment.
a base. Hence, there exist several permutations that should be considered in deriving
rate equations for acid–base catalysis. Moore and Pearson (1981) enumerate nine
such mechanisms. Table 5.4 lists these reaction mechanisms, the rate expressions,
and some examples from environmental engineering.
As noticed in Section 5.4.2, the specific hydrolysis rate constants can be estimated
using an LFER relationship. For example,Wolfe, Zepp, and Paris (1978) showed that
log kB for base-catalyzed hydrolysis of N-phenyl carbamates is related to the pKa of
the alcohol group.
An aspect of homogeneous catalysis that we have not considered thus far is the
action of enzymes (X = enzyme). This is an important aspect of environmental
bioengineering and is relegated to Chapter 6 where rates of enzyme reactions are
considered.
EXAMPLE 5.12 OBTAINING ko, kA, AND kB FROM RATE DATA
The reaction α glucose 6β glucose is called mutarotation. Acids and bases catalyze it.
At 291K, the following first-order rate constants were obtained for the process using
acetic acid in an aqueous solution containing 0.02M sodium acetate.
Acetic acid (mol/L) 0.02 0.105 0.199
k (min−1) 1.36 × 10−4 1.40 × 10−4 1.46 × 10−4
In the general expression for k, both kH and kOH are negligible under these conditions.
kB is also negligible under these conditions. Hence, k = k0 + kacid[acid]. A plot of k
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Concepts from Chemical Reaction Kinetics 227
TABLE 5.4
Different Types of Acid–Base Hydrolysis Mechanisms in Environmental
Chemistry
Type Reaction Rate Expression Examples
I S + H+ � SH+ kKeq[S][H+][R] Ester, amide, and ether
hydrolysisSH+ +W slow−−−→ P
II SH + H+ � HSH+ kKeqKa[BH+][HA] Hydrolysis of
alkyl-benzoimides,
keto–enol changes
HSH+ + B slow−−−→ BH+ + SH
III HS + HA � HS · HA kKeq[HS][HA][B] Mutarotation of glucose
HS · HA + B slow−−−→ P
IV S + HA � S · HA kKeq[S][HA][R] General acid catalysis,
hydration of aldehydesS · HA + R → P
V S− + HA slow−−−→ SH +A− k[S−][HA] Decomposition of
diazoacetateSH
fast−−→ P
VI HS + B � S− + BH+ kKeq[SH][R][OH−]/Kb Caisen condensation
S− + R slow−−−→ P
VII HS + B slow−−−→ S− + BH+ k[HS][B] General base catalysis
S− fast−−→ products
VIII R + S � T [T]
[∑
i kι[Bι] +
∑
j kj[HAj]
]
Aromatic substitutions
IX HS + B � B · HS kKeq[B][HS][R] General base catalysis,
ester hydrolysisB · HS slow−−−→ P
Source: From Moore, J.W. and Pearson, R.G. 1981. Kinetics and Mechanism, 3rd ed. New York:
Wiley-Interscience.
Note: S represents reactant, B is the general base, HA is the general acid, and R is a reactant whether
acid or base.
versus [acid] gives as intercept, k0 = 1.35 × 10−4 min−1, and slope, kacid = 5.6 ×
10−5 L/molmin. The correlation coefficient is 0.992. This is a general method of
obtaining k. For catalysis by different species, each k value can be isolated as given
above.
EXAMPLE 5.13 EFFECTOFSUSPENDEDSEDIMENT (SOIL) ONTHEHOMOGENEOUSLY
CATALYZED HYDROLYSIS OF ORGANIC COMPOUNDS
Since atmospheric moisture (e.g., fogwater and rain) and lake and river water contain
suspended solids, the rate of hydrolysis of organics is likely to be influenced by them.
This example will illustrate the effect for some organic compounds.
Many organic compounds that are common pollutants (e.g., pesticides—malathion
and dichloro-diphenyl-trichloroethane (DDT)) have low reactivity and are known
to associate with colloidal matter that has high organic carbon content (see Chapter 4).
continued
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468 Index
Vapor species wet deposition, 137
Vegetation. see alsoAir-vegetation partition
constant
atmosphere partition coefficient, 171–174
atmospheric pollutants uptake, 172
Vermiculite surface properties, 158
Vertical and horizontal dispersion coefficients, 323
Vicinal water, 154
Vinyl chloride, 329
Viscosity, 11
Volatile organic compounds (VOC), 98, 144
desorption, 299
reaction rate constant, 198
transport and surface impoundment, 151
Volatilization
compound from water, 122
rate constant and expression, 292
W
Washout ratio, 138
calculation, 141
Wasted work, 28
Waste treatment
separation processes, 120
systems air/water equilibrium, 150–151
Wastewater lagoon
benzene concentration, 136
submerged bubble aeration, 300
Wastewater oxidation
ozone in continuous reactor, 308
ozone reactor, 309
Wastewater stream, 174–175
Wastewater tank, 152
Wastewater treatment, 173
Water, 70
air relative humidity, 368
and atmosphere chemicals exchange, 120
confined in capillary, 65
dissolution, 132
droplets in air, 64
ester hydrolysis, 231–232
fugacity capacities definition, 52
heterogeneous catalysis, 231–232
and organic solvents concentration units, 44
partition constants and mass transfer
coefficients, 145
photochemical reactions, 311–312
photochemical transient species, 312
pollutant concentration, 436
tetrahedral cage molecule, 74
Water environment, 290–298
aeration basins air stripping, 299–302
fate and transport, 290–294
lakes and oceans chemicals, 290–292
natural streams biochemical oxygen demand,
295–298
natural waters photochemical reactions,
311–312
oxidation reactor, 303–308
photolytic rate constants, 247
surface waters chemicals, 293–294
wastewater treatment photochemical reactions,
309–310
water pollution control, 299–312
Water pollutants
control, 299–312
food chain bioaccumulation, 394
Well-mixed box model, 316
Well-mixed troposphere and stratosphere, 318
Well-stirred surface evaporation, 293
Wet deposition, 137
Wilson equation, 87
Work, 14, 16, 28
Y
Young–Laplace equation, 34, 63
chemical thermodynamics, 33–34
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“78194_C005.tex” — page 226[#38] 15/4/2009 16:50
226 Elements of Environmental Engineering: Thermodynamics and Kinetics
log k0 IAN INB
IAB
Slope = –1 Slope = +1
Actual curve
lo
g
k
pH
FIGURE 5.11 Variation in acid–base hydrolysis rate with pH for organic compounds in the
environment.
a base. Hence, there exist several permutations that should be considered in deriving
rate equations for acid–base catalysis. Moore and Pearson (1981) enumerate nine
such mechanisms. Table 5.4 lists these reaction mechanisms, the rate expressions,
and some examples from environmental engineering.
As noticed in Section 5.4.2, the specific hydrolysis rate constants can be estimated
using an LFER relationship. For example,Wolfe, Zepp, and Paris (1978) showed that
log kB for base-catalyzed hydrolysis of N-phenyl carbamates is related to the pKa of
the alcohol group.
An aspect of homogeneous catalysis that we have not considered thus far is the
action of enzymes (X = enzyme). This is an important aspect of environmental
bioengineering and is relegated to Chapter 6 where rates of enzyme reactions are
considered.
EXAMPLE 5.12 OBTAINING ko, kA, AND kB FROM RATE DATA
The reaction α glucose 6β glucose is called mutarotation. Acids and bases catalyze it.
At 291K, the following first-order rate constants were obtained for the process using
acetic acid in an aqueous solution containing 0.02M sodium acetate.
Acetic acid (mol/L) 0.02 0.105 0.199
k (min−1) 1.36 × 10−4 1.40 × 10−4 1.46 × 10−4
In the general expression for k, both kH and kOH are negligible under these conditions.
kB is also negligible under these conditions. Hence, k = k0 + kacid[acid]. A plot of k
Page 244
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Concepts from Chemical Reaction Kinetics 227
TABLE 5.4
Different Types of Acid–Base Hydrolysis Mechanisms in Environmental
Chemistry
Type Reaction Rate Expression Examples
I S + H+ � SH+ kKeq[S][H+][R] Ester, amide, and ether
hydrolysisSH+ +W slow−−−→ P
II SH + H+ � HSH+ kKeqKa[BH+][HA] Hydrolysis of
alkyl-benzoimides,
keto–enol changes
HSH+ + B slow−−−→ BH+ + SH
III HS + HA � HS · HA kKeq[HS][HA][B] Mutarotation of glucose
HS · HA + B slow−−−→ P
IV S + HA � S · HA kKeq[S][HA][R] General acid catalysis,
hydration of aldehydesS · HA + R → P
V S− + HA slow−−−→ SH +A− k[S−][HA] Decomposition of
diazoacetateSH
fast−−→ P
VI HS + B � S− + BH+ kKeq[SH][R][OH−]/Kb Caisen condensation
S− + R slow−−−→ P
VII HS + B slow−−−→ S− + BH+ k[HS][B] General base catalysis
S− fast−−→ products
VIII R + S � T [T]
[∑
i kι[Bι] +
∑
j kj[HAj]
]
Aromatic substitutions
IX HS + B � B · HS kKeq[B][HS][R] General base catalysis,
ester hydrolysisB · HS slow−−−→ P
Source: From Moore, J.W. and Pearson, R.G. 1981. Kinetics and Mechanism, 3rd ed. New York:
Wiley-Interscience.
Note: S represents reactant, B is the general base, HA is the general acid, and R is a reactant whether
acid or base.
versus [acid] gives as intercept, k0 = 1.35 × 10−4 min−1, and slope, kacid = 5.6 ×
10−5 L/molmin. The correlation coefficient is 0.992. This is a general method of
obtaining k. For catalysis by different species, each k value can be isolated as given
above.
EXAMPLE 5.13 EFFECTOFSUSPENDEDSEDIMENT (SOIL) ONTHEHOMOGENEOUSLY
CATALYZED HYDROLYSIS OF ORGANIC COMPOUNDS
Since atmospheric moisture (e.g., fogwater and rain) and lake and river water contain
suspended solids, the rate of hydrolysis of organics is likely to be influenced by them.
This example will illustrate the effect for some organic compounds.
Many organic compounds that are common pollutants (e.g., pesticides—malathion
and dichloro-diphenyl-trichloroethane (DDT)) have low reactivity and are known
to associate with colloidal matter that has high organic carbon content (see Chapter 4).
continued
Page 485
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468 Index
Vapor species wet deposition, 137
Vegetation. see alsoAir-vegetation partition
constant
atmosphere partition coefficient, 171–174
atmospheric pollutants uptake, 172
Vermiculite surface properties, 158
Vertical and horizontal dispersion coefficients, 323
Vicinal water, 154
Vinyl chloride, 329
Viscosity, 11
Volatile organic compounds (VOC), 98, 144
desorption, 299
reaction rate constant, 198
transport and surface impoundment, 151
Volatilization
compound from water, 122
rate constant and expression, 292
W
Washout ratio, 138
calculation, 141
Wasted work, 28
Waste treatment
separation processes, 120
systems air/water equilibrium, 150–151
Wastewater lagoon
benzene concentration, 136
submerged bubble aeration, 300
Wastewater oxidation
ozone in continuous reactor, 308
ozone reactor, 309
Wastewater stream, 174–175
Wastewater tank, 152
Wastewater treatment, 173
Water, 70
air relative humidity, 368
and atmosphere chemicals exchange, 120
confined in capillary, 65
dissolution, 132
droplets in air, 64
ester hydrolysis, 231–232
fugacity capacities definition, 52
heterogeneous catalysis, 231–232
and organic solvents concentration units, 44
partition constants and mass transfer
coefficients, 145
photochemical reactions, 311–312
photochemical transient species, 312
pollutant concentration, 436
tetrahedral cage molecule, 74
Water environment, 290–298
aeration basins air stripping, 299–302
fate and transport, 290–294
lakes and oceans chemicals, 290–292
natural streams biochemical oxygen demand,
295–298
natural waters photochemical reactions,
311–312
oxidation reactor, 303–308
photolytic rate constants, 247
surface waters chemicals, 293–294
wastewater treatment photochemical reactions,
309–310
water pollution control, 299–312
Water pollutants
control, 299–312
food chain bioaccumulation, 394
Well-mixed box model, 316
Well-mixed troposphere and stratosphere, 318
Well-stirred surface evaporation, 293
Wet deposition, 137
Wilson equation, 87
Work, 14, 16, 28
Y
Young–Laplace equation, 34, 63
chemical thermodynamics, 33–34
