CEE 670 TRANSPORT PROCESSES IN ENVIRONMENTAL AND WATER RESOURCES ENGINEERING. Kinetics Lecture #1

Transcription

1 Updated: 8 Deember 0 Print version CEE 670 TRNSPORT PROCESSES IN ENVIRONMENTL ND WTER RESOURCES ENGINEERING Kinetis Leture # Introdution: Simple Rate Laws Clark, Brezonik, pp.-39 Introdution Kinetis Examples Fe + oxidation by O almost instantaneous at high ph quite slow at low ph high D.O. may help Oxidation of organi material Formation of solid phases luminum hydroxide Quartz sand

2 3 Utility of Kinetis Empirial nalysis Moderate Rate Estimate reation time (harateristi time) for; Engineered systems (size of tanks) Natural quati Systems (WQ modeling) tmospheri systems (air pollution modeling) Fast Rates Evaluate simple ompetitive kinetis Determine omplex reation stoihiometries Define omplex or yli reation webs Postulate major pathways Slow Rates Reation time for global proesses Human impats Theoretial nalysis ll Rates: understand mehanisms Predit other reation kinetis Chemistry and Environmental Engineering 4 Math Biology Environmental Engineering Physis Chemistry

3 Engineered & Natural Systems 5 Kinetis is the soure of reations and rates quati Chemistry Reations Physiohemial Proesses Surfae Chemistry Kinetis Proess Design Environmental Modeling Transport Env. Miro Biologial Proesses Relation with other Chemistry Disiplines 6 Physial Chemistry nalytial Chemistry Inorgani Chemistry Thermodynamis Chemistry K Organi Chemistry Kinetis With water hemistry, ornerstone of the good grad programs in our field 3

4 7 Time Sales & Kinetis Engineered Systems Time and Length sales 8 4

5 Sulfur in lakes I 9 Forms Methionine Gas: H S, SO Liquid SO - 4, HS -, mino aids with S Solids: MeS x, pyrites (FeS ), elemental S Cysteine Mass Transfer ir:water Sediment:water Reations Chemial: oxidation, redution, preipitation, omplexation, hydrolysis Biologial: biosynthesis, use as TE, release Sulfur in Lakes II 0 Brezonik; example - Sulfur yling depends on bioti & abioti redox kinetis, preip, dissolution, omplexation, et. Observed in-lake loss of sulfate by mirobial sulfate redution Monod kinetis from lab ultures 5

6 Sulfur in lakes (ont.) Typial sulfate depth profile around sediment water interfae Kinetis of abioti oxidation of sulfide speies HS - S - Sulfur in lakes (ont.) Makinawite (FeS) Forms in redued sediments Dissolves by first order rate, also atalyzed by low ph d[ S] tot k [ H ] k V Where /V is the FeS surfae area to total volume ratio rrhenius temperature plot Pankow & Morgan, 979 [ES&T, 3(0)48] 6

7 Thermo vs Kinetis 3 Reation of oxygen and nitrogen N O H O H NO3 Thermodynamis tells us: In the oeans, {H + } aq ~0-8, and {NO 3- }~0.6M Then, onsidering p N =0.70, we alulate: But the real p O is 0. atm K p O.8x0 atm { H } aq{ NO } p p 3 aq.5 O Why does thermo fail us here? the reation is very slow. N Reation Kinetis 4 Irreversible reation is one in whih the reatant(s) proeed to produt(s), but there is no signifiant bakward reation, In generalized for, irreversible reations an be represented as: a + bb Produts i.e., the produts do not reombine or hange to form reatants in any appreiable amount. n example of an irreversible reation is hydrogen and oxygen ombining to form water in a ombustion reation. We do not observe water spontaneously separating into hydrogen and oxygen. 7

8 5 Reation Kinetis: Reversibility reversible reation is one in whih the reatant(s) proeed to produt(s), but the produt(s) reat at an appreiable rate to reform reatant(s). a + bb pp + qq Most reations must be onsidered reversible n example of a reversible biologial reation is the formation of adenosine triphosphate (TP) and adenosine diphosphate (DP). ll living organisms use TP (or a similar ompound) to store energy. s the TP is used it is onverted to DP, the organism then uses food to reonvert the DP to TP. 6 Extent of Reation I Has the reation ourred if an so how lose to ompletion is it? Consider a generi reation a bb... pp qq... Bringing the reatants to the produts side, we get a bb... pp qq... 0 nd using the Greek,, to equal the various stoihiometri oeffiients, B... P Q... 0 B nd the law of onservation of mass requires: i i MW i 0 P Q MW M moleular weight 8

9 Extent of Reation II 7 Mathematially defined as: The hange in #moles of a reatant or produt as ompared to the starting amount divided by the stoihiometri oeffiient, ( n i n io ) i d dn nd therefore: i i nd what we all the reation rate is: n d i d V di rate Where [ i ] is the V i molar onentration i of substane i Gibbs Energy and reation extent 8 G Changes as reation progresses due to hanging onentrations G reahes a minimum at the point of equilibrium Stumm & Morgan Fig..5; Pg. 45 dg G d Extent of reation 9

10 9 Elementary Reations When reatant moleules ollide with the right orientation and energy level to form new bonds Elementary reations proeed in one step and diretly produe produt with no intermediates Many observable reations are really just ombinations of elementary reations (multi-step reations) Starting out with some and B, we observe that E and F are the end produts B C D fast C E D C F B E F slow fast Cont. S&M: Fig.. Pg. 7 0 Elementary reations single step in a reation sequene Involves or reatants and or produts Can be desribed by lassial hemial kinetis Law of mass ation # of reatant speies in an elementary reation is all the moleularity 0

11 Law of mass ation For elementary reations, we an write the rate expression diretly from the stoihiometry a bb produts d[ ] a b rate [ ] [ ] d[ ] a Reation order Overall order: n=a+b Order with respet to =a, B=b, C=0. k B The rate onstant, k, is in units of -n t - Elementary vs non-elementary I Base Hydrolysis of dihloromethane (DCM) Forms hloromethanol (CM) and hloride Elementary reation, therefore seond order overall (moleularity of ) Rate k[ DCM ][ OH d[ DCM ] d[ OH ] First order in eah reatant, seond order overall ] d[ CM ] d[ Cl ]

12 Elementary vs non-elementary II 3 The reation of hydrogen and bromine H Br HBr ( g ) ( g ) ( g ) Sometimes used as an example of an elementary reation in old hemistry textbooks Careful study has show the following kinetis d[ HBr] k[ H ][ Br 0.5 ( g ) ( g) [ HBr( g ) ] k [ Br( g ) ] Thus it is not an elementary reation! ] Elementary Reations 4 Reall: Law of Mass tion For elementary reations a bb k rate kc C produts a b where, B C = onentration of reatant speies, [moles/liter] C B = onentration of reatant speies B, [moles/liter] a = stoihiometri oeffiient of speies b = stoihiometri oeffiient of speies B k = rate onstant, [units are dependent on a and b]

13 Simple Zero Order 5 Reations of order n in reatant d k n When n=0, we have a simple zero-order reation d k Conentration k Slope 0 mg/ l/ min kt Time (min) o Simple first order k B 6 B B When n=, we have a simple firstorder reation This results in an exponential deay When there is not a subsequent or bak reation Bo Conentration ( ) o e Bo o kt d k Time (min) k min o e kt 3

14 First order (ont.) k B 7 This equation an be linearized good for assessment of k from data Conentration (log sale) d 00 k Slope ln k min ln o kt Time (min) 8 Simple Seond Order reation This results in an espeially wide range in rates More typial to have nd order in eah of two different reatants Conentration Time (min) k produts o d When n=, we have a simple seond-order k k k 0.005L / mg o t / min 4

15 Simple Seond Order (ont.) 9 gain, the equation an be linearized to estimate k from data o k t /Conentration Time (min) d k Slope k 0.005L / mg / min Comparison of Reation Orders 30 Curvature as order hanges: nd > st >zero Conentration Zero Order First Order Seond Order Time (min) 5

16 Variable Kineti Order 3 ny reation order, exept n= d k n n n n k t n o n o n n n k t n o CEE690K Leture # Half-lives 3 Time required for initial onentration to drop to half, i.e.., =0.5 o For a zero order reation: o kt 0.5o o kt For a first order reation: e o kt 0.5 o o e CEE690K Leture # kt t t 0.5 k o ln() k k 6

17 Example: Benzyl Chloride 33 Use: Manufature of benzyl ompounds, perfumes, pharmaeutials, dyes, resins, floor tiles Toxiity Intensely irritating to skin, eyes, large doses an ause CNS depression Emission 45,000 lb/yr Fate Benzyl hloride undergoes slow degradation in water to benzyl alohol CEE690K Leture # Benzyl hloride II Soures: Shwarzenbah et al., 993, Env. Organi Chemistry 97, J. Chem.So. Chem. Comm , ta Chem. Sand. : , J. Chem. So Benzyl hloride to benzyl alohol H CH Cl O CH OH 5ºC Nuleophili substitution S N or S N? HCl How to distinguish? Salt effets d[ ] k[ ] Temperature 0.ºC 5ºC K 0.04x0-5 s -.38x0-5 s - T / 9. d 0.58 d CEE690K Leture # 7

18 35 To next leture 8