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CEE255A-L1-Intro&Kinetics - CEE 255A Physical&...

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Unformatted text preview: CEE 255A - Physical & Chemical Processes in Water and Wastewater Treatment Lecture 1 Introduction, Chemical Reactions, and Chemical Kinetics Dr. Minghua Li and Eric M.V. Hoek Civil & Environmental Engineering C&EE 255A Objectives Review basic chemistry, transport, and reactor engineering concepts underlying all physical-chemical processes: Chemical reactions and mass transfer principles Flow models, mass balances, and reactor engineering Study the principles underlying conventional and advanced physical-chemical processes: Oxidation, advanced oxidation and disinfection processes Precipitation, coagulation, and flocculation processes Porous media transport and filtration processes Adsorption, ion exchange, and aeration processes Membrane processes Apply the fundamental concepts towards analysis, design, and integration of physical-chemical processes: Conventional water treatment Municipal desalination and water reuse Industrial wastewater treatment and process water production Today's Lecture Introduction Basic description of physical-chemical processes Chemical reactions used to degrade contaminants Physical separations used to remove contaminants Reactors used in water & wastewater treatment (W/WWT) Traditional water sources and conventional water treatment Non-traditional water sources and advanced water treatment Principles of chemical kinetics Review of chemical kinetics - reactions and rate laws Integral method of analyzing kinetic data Differential method of analyzing kinetic data Why treat water & wastewater? To make it safe to drink Pathogens, carcinogens, toxics Particulates, organics, salts, colour and odor. Salts, minerals, dissolved gases Pathogens, nutrients, organics Salts, minerals, pathogens, toxics To make it pleasant to drink To protect valuable infrastructure To reduce environmental impact To make it a suitable for reuse What are we trying to "treat"? Pollutant Pathogenic microorganisms - virus, bacteria, & protozoa Dissolved solids - salts, minerals, hardness, alkalinity Natural organic matter - humic & fulvic acids, biopolymers Taste & odour compounds - MIB & geosmin Turbidity & suspended solids - soil particles, precipitates, microorganisms Synthetic organic compounds - industrial solvents, household cleaners Nutrients - nitrogen & phosphorous Toxic metals - Cu, Zn, Pb, Cd, Hg Reason for Removal protect humans from infectious disease acquired through drinking and bathing make water suitable for human consumption; control of scale and corrosion reduce colour & disinfection byproducts; facilitate disinfection; reduce biofilm growth make water palatable to drink facilitate disinfection; reduce BOD; improve aesthetics - clarity & color reduce BOD, toxicity, carcinogenicity reduce euthrophication of receiving waters & other environmental effects of discharge reduce toxicity to receiving environment All of the above pollutants can be categorized by particle size and chemical nature Physical Aggregate Contaminants Particles Particles are defined as finely divided solids larger than molecules but generally undistinguishable by the unaided eyes. Particles in water can be classified to their origin, size, chemical structure, charge characteristics and water-solid interface characteristics. Origin of particles in water - Soil-weathering (clay, silts, etc) - Biological activity (algae, bacteria, and other macro-organism) - Industrial and agriculture activities (asbestos, industrial dust, etc) Particles have a range of impacts on water quality. - Turbidity and color - A potential adsorption sink for toxic substances - Interfere with the disinfection process Can be removed by coagulation, sedimentation, filtration and membrane separation. Physical Aggregate Contaminants Color The color of a water is an indication of the organic content, including humic and fulvic acid, the presence of natural metallic ions, and turbidity. Typically, for portable water, color is aesthetic property. For industrial wastewater, color is indicator of contaminants concentration. Can be removed by coagulation, sedimentation, adsorption, oxidation and membrane separation. Inorganic Constituents Dissolved Solids Due to the dissolution, all the natural water contains certain amount of dissolved minerals. Commonly found inorganic chemical constituents in water in significant quantities (1-1000 mg/L) include calcium (Ca2+ ), iron (Fe3+), magnesium (Mg2+), sodium (Na+), potassium (K+), bicarbonate (HCO3-), chloride (Cl-), sulfate (SO42-), and nitrate (NO3-) Groundwater generally has higher dissolved mineral than surface water due to longer contact with soil and minerals. The initial mineral composition may be altered through natural chemical (oxidation, ion exchange, complexation, etc) and biological (biological metabolism) processes. http://www.emsl.pnl.gov/news/viewArticle.jsp?articleId=132 Inorganic Constituents Toxic Metals The main threats to human health from metals from water are associated with exposure to cupper (Cu), lead (Pb), cadmium (Cd), mercury (Hg), and arsenic(As). The major source of above toxic metals are from industrial and agriculture activities. Natural arsenic dissolution also poses services health threat to the area with arsenic rich minerals. EPA has set the arsenic standard for drinking water at 0.010 ppm (mg/L). In Bangladesh, 27 % of shallow tube-wells have been shown to have high levels of arsenic (above 0.05mg/L or ppm). Toxic metal can be treated via precipitation, adsorption, ion-exchange, oxidation, membrane separation etc. Organic Constituents Natural organic materials/matter (NOM). NOM is the term used to describe the complex matrix of organic chemicals originating from natural sources. - Secretions from metabolic activity of algae, protozoa, micro-organisms and higher life-forms. - Decay of organic matter, bodies, and cellular materials in aquatic environments - Excretions from aquatic organisms - Surface runoff from land. NOM is typically quantified using bulk parameters, such as TOC, DOC, UV-254, and SUVA. Historically, NOM affected the aesthetic quality of portable water (yellowish color). More recently, NOM was found to react with chlorine and form disinfection byproducts, which are often carcinogenic. Organic Constituents Organic Compounds Originated from Human Activities Industries that utilize large quantities of chemicals in manufacturing processes are major sources of organic pollutants. The properties of synthetic organic compounds could be extremely diverse. Many synthetic compounds cause health concern at very low concentration. Some of the compounds are specifically designed with high biological activity and work at low concentration, such as pesticides and pharmaceutical compounds. Pathogenic Microorganisms Aquatic pathogenic microorganisms Include bacteria, viruses, algae, protozoa, and helminths. Bacteria Single cell organisms. Size range from about 0.1 to 10 um. The membrane bounds the cell itself. Diverse physiological shapes. Negatively charge membrane over the range of pH of interest in water treatment Hard to remove by sedimentation. Pathogenic Microorganisms Virus True parasites totally depending on their host for the resources required for survival Can survival outside the host for certain amount of time. Typically range from 0.02-0.2 um, depending on hosts. Pathogenic Microorganisms Protozoans Unicellular, nonphotosynthetic organism Motile, moving via use of flagella. Size range from 1-50 micrometer. http://www.pirx.com/forum/viewtopic.php?f=3&t=3 http://www.sciencephotolibrary.com/images/download_lo_res.html?id=772600206 Pathogenic Microorganisms Algae Unicellular, photosynthetic organism Serving important role in food chain. Could be pathogenic to human by producing endotoxins. Most of them have limited ability to move. http://www.rechargenews.com/energy/biofuels/article182098.ece The Properties of Pollutants Chemical Nature Fraction Soluble Size (m) Inorganic <0.001 salts, hardness, alkalinity, P, N, metals clays, metal oxides, precipitates sediment of clays and minerals Organic Biological fulvic acids, phenols, nucleic acids, sugars, starches, SOCs polypeptides humic acids, proteins, lipids, polysaccharides wood & paper fibres, emulsified oil & grease coarse food particles viruses, bacteria, exopolymers protozoa, algae, fungi, oocysts, spores multi-celled microbes, worms, parasites dead plant and animal matter Colloidal 0.001 1.0 Filterable 1.0 100 Settleable 100 1,000 Grit, sand, silt Coarse >1,000 Stones, rocks, etc. plastic debris The Size of Water Pollutants What are Physical-Chemical Processes? There are two fundamental approaches to remove pollutants from water: Chemical Reactions destruction or conversion to an inert form Alters the chemical activity or structure of a pollutant by chemical oxidation, reduction, precipitation, or neutralization. Depends on the reactivity of the target compound (e.g., microbes, humics, TCE), the chemical reactant, and background solution chemistry. Creates two streams, one that is highly concentrated and one that is dilute with respect to the pollutant. Selectivity depends on the characteristics of the target compound, the basis for separation (e.g., size, charge, solubility), and the background solution chemistry. Physical Separations removal from the water Both reaction and separation processes are modeled using chemical reactor engineering concepts and methods. Removal by Chemical Reactions Acid-base reactions HA <=> H+ + A- Acid-base chemistry forms the foundation for understanding carbonate chemistry, corrosion, scaling, and stabilization of water, in addition to many water quality analyses (e.g., hardness/alkalinity titrations). pH control is common for process optimization (coagulant dosing, softening, etc.) as well as environment and infrastructure protection AaBb(s) <=> aAm+ + bBn- Ksp = {Am+ }a{Bn-}b Precipitation-dissolution reactions => {X} = activity = [X], where [X] = molarity; = activity coefficient Often used in combination with pH control for water softening, metal precipitation, or stabilization (providing buffer capacity to a corrosive water) Also, precipitation is used to generate `sweep flocs' in coagulation M(L)mx+ + nLy- <=> M(L)m+ nx-ny Selective binding of metal ions by inorganic anions (Cl -, OH-, etc.) and organic chelating agents is common in industrial wastewater treatment and recycling, as well as in many water quality analytical methods Complexation reactions Removal by Chemical Reactions Redox reactions (occur in pairs) Oxidation (half-reaction): Reduction (half-reaction): Redox couple/pair: OxA + ne- => RedA RedB => OxB + ne- OxA + RedB <=> OxB + RedA Chemical Oxidation: Uses strong oxidants such as ozone or hydrogen peroxide; if oxidation goes to completion, final products include CO2, water and metal oxides incomplete chemical oxidation generally results in compounds which can be readily oxidized biologically; oxidation also destroys pathogenic activity of microorganisms Chemical Reduction: Can be used to reduce toxic materials to their basic elements or to less toxic species, e.g. HgO to metallic mercury, or Cr6+ to the less toxic Cr3+ form However, reduction processes are generally used much less than other chemical reactions... Removal by Physical Separation Size fraction of pollutant (m) Soluble <0.001 adsorption ion exchange precipitation nanofiltration reverse osmosis electro-dialysis distillation evaporation air stripping Colloidal 0.001 1.0 coagulation/ flocculation ultrafiltration microfiltration Filterable 1.0 100 granular filtration flotation fine screens centrifugation Settleable 100 1,000 settling tanks medium screens hydrocyclones Coarse >1,000 settling tanks coarse screens Selection of Technologies 1. Characterize the raw water quality. (size distribution, density, chemical nature org./inorg./biol., physicochemical properties, toxicity, carcinogenicity) 2. Determine treated water quality. (BOD, COD, TOC, TSS, turbidity, colour, N, P, salinity, hardness, alkalinity, metals, SOCs, toxics, etc.) 3. What is the simplest and most cost effective way to go from 1 to 2? Learn from experience and testing. 4. Types of Physical-Chemical Reactors Reactor Types (a) Batch Reactor (b) MFR ("CSTR") (c) MFR's in Series (d) Rectangular PFR (e) Tubular PFR (f) Serpentine PFR (g) Downflow PBR (h) Upflow PBR (i) Fluidized PBR Examples of Phys-Chem Processes and Reactor Types Process Oxidation Disinfection Coagulation Lime Softening Air Stripping GAC Adsorption Ion Exchange Granular Filtration Membrane Filtration Reverse Osmosis Reactor Type CSTR or CSTRs in Series Serpentine PFR CSTRs in Series CSTR with Recycle Upflow Fluidized Beds Packed Tower; Diffused Gas Contactors Tubular PBR Tubular PBR Downflow PBR; Upflow PBR; Fluidized PBR Tubular PFR; Channel PBR Tubular PFR; Channel PBR Example Applications Oxidation of Iron & Manganese; dechlorination by SO2 Chlorination; Ozonation; ClO2, Chloramines Removal of Particulares and NOM using Ferric or Alum Removal of Hardness and other sparingly soluble mineral salts VOC removal; CO2 removal SOC removal; taste and odor control Removal of Hardness; Nitrate, Perchlorate, Arsenic, NOM, etc. Particulate, turbidity, and pathogen removal; AOC removal Removal of Colloidal Particles, Bacteria, Viruses Removal of Dissolved Solids, Salinity, DOC, and Metals Application of Physical-Chemical Processes Production of drinking water from unpolluted fresh water, brackish, and ocean water sources Advanced treatment of sewage for safe discharge to surface waters or recharge to aquifers Remediation of polluted surface and ground waters; environmental restoration Reuse of municipal, industrial, and agricultural wastewaters (potable vs. non-potable) Production of ultra-pure water for energy production (boiler feed) and high-tech industries Traditional Drinking Water Sources Fresh surface water Fresh ground water Dissolved Dissolved Low TDS (< 0.5 g/l) Low-to-med hardness Low-to-med nutrients (N,P,S,Fe) Low dissolved metals Low VOCs & SOCs Low gases (O2,N2,H2S,CO2) Low TDS (< 0.5 g/l) High hardness is typical Low nutrients (N,P,S,Fe) Medium to high metals Low VOCs & SOCs Med-to-high gases (O2,N2,H2S,CO2) Low organics Low metals/oxides Low bacteria & viruses Low silts and clays Low protozoa & algae Colloidal Colloidal Med-to-high organics & oxides Med-to-high bacteria & viruses Med-to-high silts and clays Med-to-high protozoa & algae Particulate Particulate Surface Water Treatment Preliminary treatment solids removal Rapid MFR coagulation Slow MFR flocculation Slow PFR sedimentation Rapid/Slow PBR filtration Slow PFR chemical disinfection Traditional Wastewater Sources Industrial wastewater Municipal wastewater Dissolved Dissolved Med-to-high TDS Med-to-high hardness Low nutrients (N,P,S,Fe) Med-high metals Med-high VOCs & SOCs Low-to-med gases (O2,N2,H2S,CO2) Low natural organics Low bacteria & viruses Low silts and clays Low protozoa & algae Colloidal Low TDS (~0.5-1 g/l) Med-to-high hardness Med-to-high nutrients (N,P,S,Fe) Med-to-high metals Low VOCs & SOCs Med-to-high gases (O2,N2,H2S,CO2) High organics, bacteria, protozoa, & viruses Low silts and clays Low algae & diatoms Colloidal Particulate Particulate Municipal Wastewater Treatment Preliminary treatment solids removal Slow PFR primary & secondary sedimentation MFR/PFR coagulation & activated sludge Slow PFR chemical disinfection Advanced Water Treatment (Classical) Rapid Mix Flocculation Softening Sedimentation Media Filtration GAC Adsorption Reverse Osmosis Chlorination Advanced Water Treatment (Modern) Pretreatment (MF/UF) Raw Water Product Water Reverse Osmosis (RO/NF) Adv. Oxidation (UV, O3, Cl- ) MF/UF Backwash Concentrate Removal, R = 1 - Cp Cf Recovery, Y = Qp Qf Non-Traditional (Alternative) Water Sources Ocean water Dissolved Brackish waters High TDS (~35 g/l) High hardness Low nutrients (N,P,S,Fe) Low metals Low gases (O2,N2,CO2) Low organics (except during algal blooms) Low metals/oxides Low bacteria (except during algal blooms) Low silts and clays Low protozoa, diatoms, & algae (except during algal blooms) (surface, ground, waste) Dissolved Colloidal Med-to-high TDS (1-20 g/l) Med-to-high hardness Variable nutrients (N,P,S,Fe) Variable metals (Fe,Cu,etc.) Low gases (O2,N2,CO2) Variable soil/WW organics Variable bacteria & viruses Variable silts and clays Variable protozoa & algae Colloidal Particulate Particulate Membranes vs. Conventional + Single Unit Process + Highly Automated + Less Land/Capacity + Stable Water Quality Expensive, Low Recovery Many Unit Processes Operator Controlled More Land/Capacity Variable Water Quality Inexpensive, High Recovery Basic Chemical Principles Irreversible Reaction Proceeds only in one direction and continues until the reactants are exhausted* Aggregation, Deposition, Oxidation, Adsorption A+BC+D Proceed in either direction, depending on the concentrations of reactants and products relative to the equilibrium concentrations Acid-base, Precipitation-Dissolution, Complexation A+BC+D Reversible Reaction * Strictly speaking, no chemical reaction is completely irreversible, but for many reactions the equilibrium point lies so far to the right that they are treated as irreversible reactions. The noted "irreversible reactions" can be reverse, but it requires significant energy input to achieve. Basic Chemical Principles Homogeneous Reactions Reaction occurs in bulk of the flowing water (aggregation, disinfection, precipitation, neutralization) Mixing increases the rate of molecular or particle collisions in the bulk, and thus, the overall rate of reaction Reaction occurs at the interface between two phases (absorption/stripping) or at a surface (adsorption, ion-exchange, or catalytic reactions) Diffusion of reactants to the reactive interface is often the rate limiting step, but the rate of mass transfer can be improved by increasing fluid flow velocity; and hence, these processes are typically "mass transfer limited" ... and appear 1st order. Heterogeneous Reactions Therefore, kA is also a function of mixing and fluid flow Reaction Mechanisms Many reactions proceed as a series of simple reactions between atoms, molecules and radical species. Elementary Reactions - Reaction mechanisms involving an individual reaction step are known as elementary reactions. - Elementary reactions can be used to describe what is happening on a molecular scale. Reaction Mechanisms Overall Reaction A Series of elementary reactions may be combined to yield an overall reaction. The overall reaction is determined by summing the elementary reactions and canceling out the compounds that occur on both sides of reaction. Overall Reaction: 2O3 3O2 ------------------- Elementary Reaction: + O3 + H 2O HO3 + OH - + HO3 + OH - 2HO2 O3 + HO2 HOi+2O2 HOi+HO H O + O Rate Law Rate of the reaction The rate of a chemical reaction (rA) is defined as the change in concentration of a constituent with time: change in concentration rate of reaction = change in time A negative or positive sign for the reaction rate indicates that species A is either disappearing or appearing respectively. aA + bB products rA = k[A]m[B]n Reaction Equilibrium Elementary Rate Laws and Molecularity A reaction has an elementary rate law if the reaction of each species is identical with the stoichiometric coefficient of that species for the reaction as written. An + Bn nC ; - rAn = k An C An C Bn The molecularity of a reaction refers to the number atoms, ions, or molecules involved (colliding) in the rate-limiting step of the reaction unimolecular, bimolecular, termolecular, etc. Reversible Reactions At equilibrium, rate laws reduce to the thermodynamic relationship governing species concentrations at equilibrium aA + bB cC + dD; K eq = k for k rev = a d CCeq C Deq a b C Aeq C Beq mol = L d + c -b - a Reaction Orders The Reaction Order and Rate Law The dependence of the reaction rate (r ) is almost A without exception determined experimentally. aA + bB cC + dD; - rA = k AC C B A The order of a reaction refers to the powers to which the concentrations are raised in the kinetic rate law. The reaction is order w.r.t. A and order w.r.t. B , but the overall order of the reaction is n (= + ). Thermodynamics vs Kinetics Thermodynamics tells the reaction direction and maximum possible extent. This can be used to determine whether the treatment process is feasible. Reaction kinetics describes how fast the reaction can occur, which can be used to design the size of the reactor to allow the reaction to proceed. Thermodynamics of Chemical Reaction For a reaction to proceed Entropy change of the system must be greater than 0 (generally can be satisfied) Free energy change must be less than 0. Slope of tangent line = G(rxn) Thermodynamics of Chemical Reaction For reaction aA + bB cC + dD The free energy change is GRxn, A {C}c / a {D}d / a o = -GRxn , A + RT ln { A}{B}b / a At equilibrium GRxn, A {C}c / a {D}d / a o = -GRxn , A + RT ln =0 b/a { A}{B} o GRxn , A {C}c / a {D}d / a = RT ln = RT ln K b/a { A}{B} Activity and Activity Constants Definition Activity is an "effective concentration" Activity constant is the conversion factor Expression {i} = [i] {i} = activity or effective concentration of ionic species, mole/L = activity coefficient for ionic species, [i] = concentration of ionic species in solution, mole/L In general, >1 for nonelectrolytes and < 1 for electrolytes. Activity and Activity Constants Values In dilute solutions, {i} = [i] For pure solids or liquids, [I] = 1; For gases, activity {i} = Pi (partial pressure); For solvents or miscible liquids: {i} = i xi (mole fraction) Activity Constants For I<0.005M A=constant (0.51 @25oC), log10 i = - AZ i I 2 1 2 I 12 2 log10 i = - AZ i 1 - 0.3I For 0.005M<I<0.1M, + I 2 1 Z is the value of valence Basic Chemical Kinetics Activation Energy Even though a reaction is thermodynamically favorable, the actual reaction rate is still unknown. The reaction rate is controlled by activation energy, that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction. Perchlorate Basic Chemical Kinetics The Reaction Rate "Constant" The rate of disappearance of A, rA, depends on temperature and composition; thus, the rate can be written as the product of a reaction rate constant, k, and a function of the concentrations (activities) of the various species involved in the reaction. rA = {kA(T)} {fn(CA, CB, ...)} The algebraic equation that relates to the species concentrations is called the kinetic expression, or rate law The rate constant, k, is a strong function of temperature kA(T) = Aexp( EA/RT)..."Arrhenius equation" A = pre-exponential factor E = activation energy, J/mol or cal/mol R = gas constant = 8.314 J/molK = 1.987 cal/molK T = absolute temperature, K Basic Chemical Kinetics The Reaction Rate "Constant" The activation energy is equated with the minimum energy that must be possessed by reacting molecules before the reaction will occur. It is determined experimentally by carrying out the reaction at several different temperatures. ln kA = ln A EA/(RT) log kA = log A EA/(2.3RT) Taking the log of the Arrhenius eq'n linearizes kinetic data. -2.0 -2.2 -2.4 log k (s -1 ) -2.6 -2.8 -3.0 -3.2 -3.4 -3.6 0.0030 0.0031 0.0031 1/T (K-1) 0.0032 0.0032 T (K) 313 318 323 328 333 1/T (K ) 0.0032 0.0031 0.0031 0.0031 0.0030 -1 k (s ) 0.00043 0.00103 0.00180 0.00355 0.00717 -1 log k (s ) -3.37 -2.99 -2.74 -2.45 -2.14 -1 y = -6087.6x + 16.121 R2 = 0.9998 Basic Chemical Kinetics Reaction Order and Rate Law Order Oth 1st 2nd Empirical Models nth pseudo 1st declining 1st Rate Law rA = kA rA = kACA rA = kACA2 Rate Constant molL-1s-1 s-1 Lmol-1s-1 rA = kACAn Ln-1mol-(n-1)s-1 rA = kBODCBOD molL-1s-1 k1st , 0 rA = kACA molL-1s-1 n (1 + Fi t ) i kA = kA = declining 1st order rate constant k1st , 0 Fi, ni = fitting parameters (1 + Fi x) ni k1st,0 = initial first order rate constant st,0 Collection and Analysis of Rate Data Integral Method of Rate Analysis The integral method is a trial and error method, in which we (1) guess the reaction order, (2) integrate the batch reactor differential equation, and (3) fit the model to the data. * requires that the overall reaction order is an integer... A products ... -(dCA/dt) = rA = kCA Zero Order Reaction dCA/dt = k (integrate) CA = CA0 kt k A plot of CA versus t is linear... First Order Reaction dCA/dt = kCA (integrate) ln(CA0/CA) = kt k A plot of ln(CA0/CA) versus t is linear... Second Order Reaction dCA/dt = kCA2 (integrate) 1/CA 1/CA0 = kt k Collection and Analysis of Rate Data Integral Method Zero Order 30 Zero Order Fit 25 y = -1.034x + 21.484 R2 = 0.930 20 C , mol/L 15 10 5 0 0 5 10 t , min 15 20 Collection and Analysis of Rate Data Integral Method First Order 2.5 First Order Fit 2.0 y = 0.100x R2 = 1.000 ln(C/C0), mol/L 1.5 1.0 0.5 0.0 0 5 10 t , min 15 20 Collection and Analysis of Rate Data Integral Method Second Order 0.4 0.3 0.3 1/C, L/mol 0.2 0.2 0.1 0.1 0.0 0 5 10 t, min 15 20 25 Second Order Fit y = 0.012x + 0.010 R2 = 0.930 Collection and Analysis of Rate Data Batch reactors are primarily used to determine rate law parameters Differential Method of Rate Analysis For irreversible reactions, it is often possible to determine the reaction order, , and the rate constant, k, by numerically differentiating concentration vs. time experimental data. A products ... -(dCA/dt) = rA = kCA A + B products ... rA = kCACB (how do we find and ?) Perform reaction 1-time with CB >> CA... "pseudo 1st order" in A rA = kCACB k'CA ; k'= kCB kCB0 Perform reaction 1-time with CA >> CB... "pseudo 1st order" in B rA = kCACB k"CB ; k"= kCA kCA0 Perform reaction 1-time with known CA0 & CB0 (once and are known) k = ( rA)/CACB (L/mol)+-1s-1 Collection and Analysis of Rate Data Differential Method of Rate Analysis Taking the log of -(dCA/dt) = kCA gives: ln (-dCA/dt) = ln k + ln CA Hence, the slope of a plot of ln (-dCA/dt) vs. ln CA gives 1.5 Example: ln (-dCA/dt) 1.0 0.5 0.0 -0.5 -1.0 -1.5 1.0 ln(-dCA/dt)= lnCA - lnk y = 1.00x - 2.30 =1.0 k=exp(-2.30)=0.10 1.5 2.0 2.5 3.0 3.5 ln(CA) How can we generate such a plot? Collection and Analysis of Rate Data Differential Method of Rate Analysis -dCA/dt can be determined from experimental rate data Numerical Method (requires constant time steps, 0 n) "Three Point Differentiation" (see Fogler or any numerical methods text) Initial Point: dCA/dt = (-3CA0 + 4CA1 CA2)/2 t Central Points: dCA/dt = (CA,i+1 CA,i-1)/2 t Final Point: dCA/dt = (CA,n-2 4CA,n-1 + 3CA,n)/2 t A,n-1 Collection and Analysis of Rate Data Differential Method of Rate Analysis Example: Numerical Method t 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 CA 25.0 20.5 16.8 13.7 11.2 9.2 7.5 6.2 5.0 4.1 3.4 dC A /dt -2.471 -2.060 -1.687 -1.381 -1.131 -0.926 -0.758 -0.621 -0.508 -0.416 -0.333 ln (C A ) 3.22 3.02 2.82 2.62 2.42 2.22 2.02 1.82 1.62 1.42 1.22 ln (-dC A /dt ) 0.905 0.723 0.523 0.323 0.123 -0.077 -0.277 -0.477 -0.677 -0.877 -1.099 Collection and Analysis of Rate Data Differential Method of Rate Analysis 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 1.0 ln(-dCA/dt)= lnCA - lnk y = 1.00x - 2.30 ln (-dCA/dt) =1.0 k=exp(-2.30)=0.10 1.5 2.0 2.5 3.0 3.5 ln(CA) Homework Purchase course textbook, Water Treatment: Principles and Design, MWH, 2005. Review Chapters 1 to 4 as needed. Highly recommended for students that do not have a strong Environmental Science/Engineering background Read Chapters 5 and 6.1-3 in Water Treatment by end of this week... ...
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