Ch3 Transformation Processes

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Ch3 Transformation Processes

• 3.A Governing Concepts?
• Stoichiometry
• Equilibrium
• Kinetics
• 3.B Phase Changes and Partitioning
• 3.C Acid-Base Reactions
• 3.D Oxidation-Reduction Reactions

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• Stoichiometry, is the application of material
  balance to transformation processes.
• Chemical equilibrium, describes how species
  partition between phases and how elements
  partition among chemical species if some specific
  restrictions are met.
• Kinetics, deals with the rate of reactions and
  provides information on how species
  concentrations evolve.

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Transformation Processes

• All phenomena that alter the chemical or physical
  state of environmental impurities
• Phase change, aicd-base reactions,
  oxidation-reduction reactions

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Stoichiometry

• Material balance
• Atoms and Charges conservation
• NOT molecules conservation
• A set of algebraic equations

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aCO2 bNO3- cHPO42- dH eH2O ?
C106H263O110N16P1 fO2
Ca 106
O2a 3b 4c e 110
2f Nb 16
Hc d 2e 263
Pc 1
/b2c d 0
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Chemical Equilibrium

• Base on theory of Thermodynamics
• A steady-state condition NOT a static condition
• A time dependence reaction
• Equilibrium equations
• Equilibrium constant, K

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• EXAMPLE 3.A.3 Water Vapor Concentration at
  Equilibrium
• Consider a sealed jar that is partially
  filled with pure liquid water and otherwise
  contains nitrogen gas. Assume that the
  temperature of the system is fixed at 293 K
  (20?). What is the steady-state molar
  concentration of H2O(g) in the gas phase above
  the liquid water?
• SOLUTION
• The water vapor pressure in the jar will
  reach the saturation vapor pressure (that is, the
  relative humidity will be 100 percent). The
  saturation vapor pressure of water at T 293 K
  is 2338 Pa (see 3.B.1).
• From the ideal gas law and the rule of
  partial pressures

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Kinetics

• Time for equilibrium in a system
• Rate-related problems
• Reaction rates
• Chemical descript to mathematical description
• Rate laws
• Link reaction rate to concentration of reactants
• Reaction order
• Zeroth, first, second order or enzyme reactions
• Determined empirically from experiments

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• Rate Laws
• For reaction ?, the expected form of the rate law
  is
• R?k?AaBß
• To be more explicit, rate laws for ? that are
  zeroth, first, or second order are shown below
• Zeroth-order reaction aß 0 R?
  k?
• First-order reaction a 1, ß 0
  R? k? A
• 
  or a 0, ß 1 R? k? B
• Second-order reaction aß 1 R?
  k? AB
• or a
  2, ß 0 R? k?A2
• 
  or a 0, ß 2 R? k?B2

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• Radon-222 is a naturally occurring radioactive
  gas formed by the decay of radium-226, a trace
  element in soil and rock. The radioactive decay
  of radon can be described by the elementary
  reaction.
• radon-222 gt polonium-218 alpha
  particle
• The rate constant for this reaction is k 2.1 X
  10-6 s-1, independent of temperature.At time t
  0, a batch reactor is filled with air containing
  radon at concentration C0.How does the radon
  concentration in the reactor change over time?

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• For t?0, only one reaction influences the radon
  concentration, CRn. The change in radon
  concentration is related to the reaction rate by
  the expression
• Since radon decay is an elementary reaction, we
  expect the rate law to be first-order
• R kCRn

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• The following expressions give the time rate of
  change in radon concentration and the initial
  condition
• 
  CRn (0)C0
• The differential equation can be solved by direct
  integration following rearrangement (see Appendix
  D, D.1 for details) to obtain
• CRn (t)C0exp-kt

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• The radon concentration decays exponentially
  toward zero with a characteristic time tk-1
  5.5 d (Figure 3.A.1)

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• Empirical Determination of Reaction Order and
  Rate Constant
• The differential equations and solutions
  describing the change in concentration over time
  for zeroth-, first-, and second-order reactions
  are summarized below. The functions, A(t), were
  obtained by direct integration in each case.
• Zeroth-order reaction
• First-order reaction
• Second-order reaction

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• (a) The data conform to a zeroth-order reaction
  with a rate constant K0 0.097 mM min-1.

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• (b) The compound decays by a first-order reaction
  with k1 0.03 min-1.

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• (c) The compound decays by a second-order
  reaction with k2 0.0095 mM-1 min-1.

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• Characteristic Time of Kinetic Processes and the
  Equilibrium Assumption
• Fast kinetics t r ltltt
• Kinetics may be ignored reaction proceeds
  rapidly to completion, or equilibrium conditions
  are effectively instantaneously achieved
  (e.g.,.acid-base.reactions in a water treatment
  process)
• Slow kinetics t r gtgtt
• Chemical transformations (and the associated
  kinetics) are slow enough to be neglected
  altogether (e.g., carbon monoxide oxidation in
  urban air)
• Intermediate kinetics t r t
• We cannot make any useful simplifying
  approximations we must consider in detail the
  effects of chemical kinetics on the system (e.g.,
  ozone in urban air)

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• The system we consider is a glass jar that can be
  sealed and maintained at a constant temperature
  (Figure3.A.3). Half of the jars volume is
  initially filled with pure liquid water the
  other half is filled with dry nitrogen (N,) gas
  at a pressure of 1 atm .
• Eventually, the rates of evaporation and
  condensation become balanced, and the state of
  chemical equilibrium is attained.
• An exploration of the rates of evaporation and
  condensation in this system will help us to
  better understand the relationship between
  kinetics an equilibrium.

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we can say that for a fixed temperature, the
rate of evaporation,?evaporation (with units of
molecules per time) is proportional to the
gas-water interface area
where k1 is a constant that depends on liquid
water temperature, Tw.A key factor is the rate at
which the gaseous water molecules strike the
surface. This rate will be proportional to the
inter- facial surface area, S
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water molecules, Cg (units mol/m3)?condensation
is proportional to both surface area and
gas-phase water molecule concentration
where Tg is the gas temperature. At equilibrium,
the liquid and gas temperatures are equal, Tw Tg
T, and the rates of evaporation and
condensation are equal. Therefore.
K' is a temperature-dependent constant
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fixed temperature
The rate of change in this number is given by the
difference between the rates of evaporation and
condensation
with initial condition
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The solution method is disctissed in detail in
Appendix D (D.1) The solution is given by
equation 3.A.33 and is plotted in Figure 3.A.5.
Note that the steady-state condition from
equation 3.A.31 is d(Cg)/dt 0, which leads to
the equilibrium result Cg k1/k2. This same
condition is obtained from equation 3.A.33 as t ?
8. The characteristic time required for the
water vapor concentration to approach equilibrium
can be determined by dividing the stock of water
vapor molecules in the system, VgCg, by the rate
of flow out due to condensation, k2SCg . The
result is t VgCg (k2SCg)-1 H/k2. This is also
seen to be the reciprocal of the argument of fin
the exponential term in equation 3.A.33.
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Figure 3.A.5 Time-dependent behavior of the
concentration of watervapor molecules in the gas
phase of the system depicted in Figure 3.A.3. The
steady-state concentration, k1/k2, is approached
with a characteristic time of H/k2,. The initial
rate of increase in vapor concentration is k1/H
and reflects the effects of evaporation alone,
since no condensation occurs when Cg 0.
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Phase Changes and Partitioning

• Vapor Pressure
• Liquid-gas
• Dissolution of species in water
• Gas-liquid, solid-liquid
• Sorption
• Gas-solid, liquid-solid

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• ???(??)???(?????)????(Henrys Law, KH
  )?NAPL(????, KWS)????(????, Ksp)
• ???(??)???????(??????, Kads, qmax, kf)

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Vapor Pressure

• Saturation, subsaturation, supersaturation
• Chemical structure is more strong factor than
  molecular weight
• Nonvolatile impurity reduces its vapor pressure

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Dissolution of species in water

• Partitioning between gas and water
• Henrys Law (CKP)
• Solubility of Nonaqueous-phase liquids
• CK
• Dissolution and precipitation of solid
• AaBb K

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Sorption

• Adsorption and Absorption
• Sorption isotherms - Equilibrium partitioning
• Linear, Langmuir, Freundlich
• Theory develop and Empirical data

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Acid-Base Reactions

• Hydrogen ion H H3O
• Chemical Equilibrium more important, Kinetics
  less important
• KwKw(T)HOH-, Ex3.c.1
• pH and pKA
• Carbonate systems

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• ???? pH ??????(????????)
• ????????????(?????)???(?????)???????(???)??????(?
  ??????????????????BOD??)

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Carbonate systems
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Carbonate systems
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Oxidation-Reduction reactions

• Electrons transfer
• Kinetics more important, Chemical equilibrium
  less important
• Oxidation state
• Corrosion (Metal is oxidized)

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Corrosion control methods

• Physical isolate (paint in air)
• Physical isolate (deposition a layer of CaCO3 on
  inner surface of pipes )
• Eliminate corrosive compound (O2)
• Cathodic protection (sacrificial anode)
• Corrosion and Scale

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• Combusion
• Atmospheric Oxidation Processes
• Microbial Reactions
• Microbial Redox processes
• Photosynthetic
• Aerobic respiration
• Nitrogen fixation
• Nitrification
• Nitrate reduction and Denitrification
• Methane Formation

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• Combustion Stoichiometry
• If exactly enough air is provided to fully
  oxidize the fuel without any excess oxygen, than
  the complete combustion of a pure hydrocarbon
  fuel using air as the as oxidizer can be
  represented by this overall reaction

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• Combustion Stoichiometry
• The relative amounts of fuel and air for
  nonstoichiometric combustion may be expressed in
  terms of the equivalence ratio, (?), defined by
  the expression

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• Combustion Stoichiometry
• The overall reaction for complete combustion of a
  pure hydrocarbon fuel under fuel-lean conditions
  can be expressed as follows

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• Photolytic Reactions
• In photolytic reactions, the energy to break the
  chemical bond of a reactant is supplied by
  absorption of a photon of light.
• In the troposphere, photolysis is caused by
  light of wavelengths 280 nm lt ? lt 730 nm (410 nm
  lt ? lt 650 nm defines the visible range).
  Shorter-wavelength light is absorbed by
  stratospheric ozone and oxygen molecules and does
  not penetrate to the troposphere.

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Microbial Reactions

• Photosynthetic Production of Biomass
• Photosynthetic microorganisms (algae and some
  bacteria) carry out photosynthesis reactions. In
  these reactions, energy-rich carbohydrate
  molecules are produced by combining carbon
  dioxide and water, using energy derived from
  sunlight. Overall, these reactions can be written
  in the form given below.

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Microbial Reactions

• Aerobic Respiration
• In the presence of oxygen, microorganisms degrade
  biomass to from carbon dioxide and water.
  Chemical energy that is released can be used by
  the organism. This process is the reverse of
  photosynthesis Carbon is oxidized and oxygen is
  reduced.

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Microbial Reactions

• Nitrogen Fixation
• We refer to compounds such as ammonia and nitrate
  that contain a single nitrogen atom as fixed
  nitrogen species. Certain groups of bacteria are
  capable of converting gaseous nitrogen to fixed
  nitrogen, in the form of the ammonium ion.

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Microbial Reactions

• Nitrate Reduction or Denitrification
• When oxygen is not available as the oxidizer to
  degrade biomass, microorganisms can use nitrate
  as the oxidizer (electron acceptor) instead.

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Microbial Reactions

• Sulfate Reduction
• Some environments that contain biodegradable
  materials lack both oxygen and nitrate to serve
  as the oxidizing agent. In such cases, sulfate
  may serve that role.

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Microbial Reactions

• Methane Formation (Methanogenesis)
• In the absence of oxygen, nitrate, and sulfate,
  biomass can still be converted to carbon dioxide
  as shown in the following reaction.

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Microbial Reactions

• Microbial Kinetics
• To predict the rate of contaminant degradation
  by microorganisms, we must also predict changes
  in the microbial population.
• the rates of microbial growth and contaminant
  degradation are described by kinetic rate
  equations of a general form.

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Microbial Reactions

• Microbial Kinetics
• The model equation for the rate of change of
  microbial cell concentration (X) in a batch
  reactor has this form

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Microbial Reactions

• Microbial Kinetics
• This equation contains three parameters µ is the
  net specific growth rate of cells, rg is the cell
  growth rate coefficient, and kd is the cell death
  rate coefficient.
• The most widely accepted form for describing the
  dependence of rg on S is

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Microbial Reactions

• Microbial Kinetics
• The net specific growth rate of cells can then be
  written in a form known as the Monod equation
  (sometimes called a saturation reaction)

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Microbial Kinetics
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Microbial Reactions

• Microbial Kinetics
• In fact, the cell yield coefficient represents
  the mass of cells produced per mass of substrate
  consumed.
• Therefore, the rate of change of substrate
  concentration due to microbial degradation is
  modeled as

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Microbial Reactions

• Biochemical Oxygen Demand
• Two factors are relevant in assessing the
  oxygen-depleting significance of BOD.
• The first factor is stoichiometric. We want to
  know the total amount of oxygen that is required
  for biodegradation of oxidizable compounds.
• The second factor is kinetic. We want to know how
  rapidly oxygen will be consumed in the oxidation
  process.

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Microbial Reactions

• Measuring BOD
• The basic procedure for measuring stoichiometric
  BOD is simple, consisting of the following steps.
• 1. Measure the initial dissolved oxygen content
  of water to be analyzed. Call this D0(0).
• 2. Fill a 300 mL glass bottle with a sample of
  the water. Seal the bottle with a stopper.
• 3. Incubate the water in the dark at 20ºC for 5
  days.
• 4. Measure the dissolved oxygen content of the
  incubated water. Call this DO5.
• 5. Compute the five-day BOD as BOD5 D0(0)
  DO5, where all have units of mg L-1.

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EXAMPLE 3.D.3

• A BOD test is run using 100 mL of treated
  wastewater mixed with 200 mL of pure water. The
  initial DO of the mix is 9.0 mg/L. After 5 days,
  the DO is 4.0 mg/L. After a long period of time,
  the DO is 2.0 mg/L and no longer seems to be
  decreasing. Assume that nitrification has been
  inhibited so that the only BOD being measured is
  carbonaceous.

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EXAMPLE 3.D.3

• (a) What is the 5-day BOD of the wastewater
  (mg/L)?
• (b) Estimate the ultimate carbonaceous BOD
  (mg/L).
• (c) What is the remaining BOD after 5 days
  (mg/L)?
• (d) Estimate the reaction rate constant, kBOD (d
  -1).

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EXAMPLE 3.D.3

• SOLUTION
• (a) The change in dissolved oxygen content in the
  test sample during the first five days is 9.0 -
  4.0 5.0 mg/L. Wastewater comprises only
  one-third of the test sample. To correct for
  dilution, we multiply by 3, so the BOD5 content
  of the wastewater is 15 mg/L.

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EXAMPLE 3.D.3

• SOLUTION
• (b) The ultimate carbonaceous BOD is the
  difference between the initial and final DO
  levels, corrected for dilution, so BODu (9.0 -
  2.0) 3 21 mg/L.
• (c) BODu BOD5 BOD(5), so the BOD remaining at
  5 days is BOD(5) 21 - 15 6 mg/L.

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EXAMPLE 3.D.3

• SOLUTION
• (d) The rate constant is estimated from the
  first-order model, given BODu and BOD(5)