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Ch3 Transformation Processes

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. 化學反應程序 觀念： 化學計量 ( 反應質量平衡、物質不滅 ) 化學平衡 ( 動態平衡、平衡方程式 ) 化學動力 ( 反應階次、酵素反應 ) 反應類型： 相轉換 ( 分配 ) 、 酸鹼反應、

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Ch3 Transformation Processes

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  1. 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 Environmental Engineering Science

  2. 化學反應程序 • 觀念： • 化學計量(反應質量平衡、物質不滅) • 化學平衡(動態平衡、平衡方程式) • 化學動力(反應階次、酵素反應) • 反應類型： • 相轉換(分配)、 • 酸鹼反應、 • 氧化還原反應 Environmental Engineering Science

  3. 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. Environmental Engineering Science

  4. Transformation Processes • All phenomena that alter the chemical or physical state of environmental impurities • Phase change, aicd-base reactions, oxidation-reduction reactions Environmental Engineering Science

  5. Stoichiometry • Material balance • Atoms and Charges conservation • NOT molecules conservation • A set of algebraic equations Environmental Engineering Science

  6. aCO2 + bNO3- + cHPO42- +dH+ + eH2O → C106H263O110N16P1 + fO2 C：a = 106 O：2a + 3b + 4c + e = 110 + 2f N：b = 16 H：c + d + 2e = 263 P：c = 1 +/–：–b–2c + d = 0 Environmental Engineering Science

  7. Chemical Equilibrium • Base on theory of Thermodynamics • A steady-state condition NOT a static condition • A time dependence reaction • Equilibrium equations • Equilibrium constant, K Environmental Engineering Science

  8. 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: Environmental Engineering Science

  9. 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 Environmental Engineering Science

  10. Rate Laws • For reaction γ, the expected form of the rate law is Rγ=kγ[A]α[B]β • To be more explicit, rate laws for γ that are zeroth, first, or second order are shown below: • Zeroth-order reaction : α=β= 0 Rγ = kγ • First-order reaction : α= 1, β= 0 Rγ= kγ [A] or α= 0, β= 1 Rγ= kγ [B] • Second-order reaction : α=β= 1 Rγ= kγ [A][B] or α= 2, β= 0 Rγ= kγ[A]2 or α= 0, β= 2 Rγ= kγ[B]2 Environmental Engineering Science

  11. 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 —> 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? Environmental Engineering Science

  12. 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 Environmental Engineering Science

  13. 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] Environmental Engineering Science

  14. The radon concentration decays exponentially toward zero with a characteristic timeτ~k-1 = 5.5 d (Figure 3.A.1) Environmental Engineering Science

  15. 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: Environmental Engineering Science

  16. (a) The data conform to a zeroth-order reaction with a rate constant K0 = 0.097 mM min-1. Environmental Engineering Science

  17. (b) The compound decays by a first-order reaction with k1= 0.03 min-1. Environmental Engineering Science

  18. (c) The compound decays by a second-order reaction with k2= 0.0095 mM-1 min-1. Environmental Engineering Science

  19. Characteristic Time of Kinetic Processes and the Equilibrium Assumption • Fast kinetics τ r <<τ 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 τ r >>τ Chemical transformations (and the associated kinetics) are slow enough to be neglected altogether (e.g., carbon monoxide oxidation in urban air) • Intermediate kinetics τ r～τ 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) Environmental Engineering Science

  20. The system we consider is a glass jar that can be sealed and maintained at a constant temperature (Figure3.A.3). Half of the jar’s 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. Environmental Engineering Science

  21. we can say that for a fixed temperature, the rate of evaporation,γevaporation (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 Environmental Engineering Science

  22. water molecules, Cg (units: mol/m3)γcondensation 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 Environmental Engineering Science

  23. fixed temperature The rate of change in this number is given by the difference between the rates of evaporation and condensation: with initial condition Environmental Engineering Science

  24. 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 → ∞. 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 τ~ 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. Environmental Engineering Science

  25. 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. Environmental Engineering Science

  26. Phase Changes and Partitioning • Vapor Pressure • Liquid-gas • Dissolution of species in water • Gas-liquid, solid-liquid • Sorption • Gas-solid, liquid-solid Environmental Engineering Science

  27. 化學反應程序 • 反應類型： • 相轉換(溶解)：蒸汽壓(揮發性溶劑)、氣液相(Henry’s Law, KH )、NAPL(水溶解度, KWS)、固液相(溶解度積, Ksp) • 相轉換(吸附):固液相、氣固相(吸附數學模式, Kads, qmax, kf) Environmental Engineering Science

  28. Vapor Pressure • Saturation, subsaturation, supersaturation • Chemical structure is more strong factor than molecular weight • Nonvolatile impurity reduces its vapor pressure Environmental Engineering Science

  29. Dissolution of species in water • Partitioning between gas and water • Henry’s Law (C=KP) • Solubility of Nonaqueous-phase liquids • C=K • Dissolution and precipitation of solid • [A]a[B]b = K Environmental Engineering Science

  30. Environmental Engineering Science

  31. Sorption • Adsorption and Absorption • Sorption isotherms - Equilibrium partitioning • Linear, Langmuir, Freundlich • Theory develop and Empirical data Environmental Engineering Science

  32. Acid-Base Reactions • Hydrogen ion [H+] [H3O+] • Chemical Equilibrium more important, Kinetics less important • Kw=Kw(T)=[H+][OH-], Ex3.c.1 • pH and pKA • Carbonate systems Environmental Engineering Science

  33. 化學反應程序 • 反應類型： • 酸鹼反應: pH 值、強酸弱酸(碳酸鹽系統、酸雨) • 氧化還原反應：氧化態、腐蝕(陰極防蝕法)、燃燒(過剩空氣量)、大氣氧化反應(自由基)、微生物反應(有機物氧化、硝化、脫硝、微生物動力學、BOD特性) Environmental Engineering Science

  34. Carbonate systems Environmental Engineering Science

  35. Carbonate systems Environmental Engineering Science

  36. Oxidation-Reduction reactions • Electrons transfer • Kinetics more important, Chemical equilibrium less important • Oxidation state • Corrosion (Metal is oxidized) Environmental Engineering Science

  37. 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 Environmental Engineering Science

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

  39. 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: Environmental Engineering Science

  40. Combustion Stoichiometry • The relative amounts of fuel and air for nonstoichiometric combustion may be expressed in terms of the equivalence ratio, (ψ), defined by the expression Environmental Engineering Science

  41. Combustion Stoichiometry • The overall reaction for complete combustion of a pure hydrocarbon fuel under fuel-lean conditions can be expressed as follows: Environmental Engineering Science

  42. 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 < λ < 730 nm (410 nm < λ < 650 nm defines the visible range). Shorter-wavelength light is absorbed by stratospheric ozone and oxygen molecules and does not penetrate to the troposphere. Environmental Engineering Science

  43. 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. Environmental Engineering Science

  44. 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. Environmental Engineering Science

  45. 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. Environmental Engineering Science

  46. 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. Environmental Engineering Science

  47. 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. Environmental Engineering Science

  48. 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. Environmental Engineering Science

  49. 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. Environmental Engineering Science

  50. Microbial Reactions • Microbial Kinetics • The model equation for the rate of change of microbial cell concentration (X) in a batch reactor has this form: Environmental Engineering Science

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