Updated: 3 September 2013 Print version Lecture #5 Kinetics and Thermodynamics: Fundamentals of Kinetics and Analysis of Kinetic Data (Benjamin, 1.6) (Stumm & Morgan, Chapt.2 ) (pp.16-20; 69-81) David Rechow CEE 680 #5 1
Elementary Reactions When reactant molecules collide with the right orientation and energy level to form new bonds Many observable reactions are really just combinations of elementary reactions Starting out with some A and B, we observe that E and F are the end products A + A + 2A + B 2C D B C E C E + + + D F F slow fast fast David Rechow CEE 680 #5 2
Cont. S&M: Fig. 2.11 Pg. 72 Elementary reactions A single step in a reaction sequence Involves 1 or 2 reactants and 1 or 2 products Can be described by classical chemical inetics David Rechow CEE 680 #5 3
Kinetics Examples Fe +2 oxidation by O 2 almost instantaneous at high ph quite slow at low ph high D.O. may help Oxidation of organic material Formation of solid phases Aluminum hydroxide Quartz sand David Rechow CEE 680 #5 4
Kinetics Base Hydrolysis of dichloromethane (DCM) Forms chloromethanol (CM) and chloride Classic second order reaction (molecularity of 2) Rate [ DCM ][ OH d[ DCM ] ] d[ OH ] First order in each reactant, second order overall d[ CM ] d[ Cl ] David Rechow CEE 680 #5 5
Reaction Kinetics Irreversible reaction is one in which the reactant(s) proceed to product(s), but there is no significant bacward reaction, In generalized for, irreversible reactions can be represented as: aa + bb Products i.e., the products do not recombine or change to form reactants in any appreciable amount. An example of an irreversible reaction is hydrogen and oxygen combining to form water in a combustion reaction. We do not observe water spontaneously separating into hydrogen and oxygen. David Rechow CEE 680 #5 6
Reaction Kinetics: Reversibility A reversible reaction is one in which the reactant(s) proceed to product(s), but the product(s) react at an appreciable rate to reform reactant(s). aa + bb pp + qq Most reactions must be considered reversible An example of a reversible biological reaction is the formation of adenosine triphosphate (ATP) and adenosine diphosphate (ADP). All living organisms use ATP (or a similar compound) to store energy. As the ATP is used it is converted to ADP, the organism then uses food to reconvert the ADP to ATP. David Rechow CEE 680 #5 7
Kinetic principles Law of Mass Action For elementary reactions aa + bb rate C a C b A B products where, C A concentration of reactant species A, [moles/liter] C B concentration of reactant species B, [moles/liter] a stoichiometric coefficient of species A b stoichiometric coefficient of species B rate constant, [units are dependent on a and b] David Rechow CEE 680 #5 8
Reaction Kinetics (cont.) Reactions of order n in reactant c dc When n0, we have a simple zero-order reaction dc Concentration 90 80 70 60 50 40 30 20 10 0 c n Slope David Rechow CEE 680 #5 9 c c 10 mg / l / min o t 0 20 Time 40 (min) 60 80
Reaction Kinetics (cont.) When n1, we have a simple first-order reaction This results in an exponential decay Concentration 90 80 70 60 50 40 30 20 10 0 dc c 1 David Rechow CEE 680 #5 10 c 0. 032 min 1 c e o t 0 20 40 60 80 Time (min)
Reaction Kinetics (cont.) This equation can be linearized good for assessment of from data Concentration (log scale) 100 10 dc c 1 Slope ln c 0. 032 min 1 ln 0 20 40 60 80 Time (min) c o t David Rechow CEE 680 #5 11
Reaction Kinetics (cont.) dc c 2 When n2, we have a simple second-order reaction This results in an especially wide range in rates More typical to have 2 nd order in each of two different reactants Concentration 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 Time (min) David Rechow CEE 680 #5 12 c c o 1+ 1 c t o 0. 0015L / mg / min
Reaction Kinetics (cont.) Again, the equation can be linearized to estimate from data dc c 2 Time (min) 0 20 40 60 80 1 c 1 c o + t 1/Concentration 0.12 0.1 0.08 0.06 0.04 0.02 Slope 0. 0015L / mg / min 0 David Rechow CEE 680 #5 13
Comparison of Reaction Orders Curvature as order changes: 2 nd >1 st >zero Concentration 90 80 70 60 50 40 30 20 10 0 Zero Order 0 20 40 60 80 Time (min) First Order Second Order David Rechow CEE 680 #5 14
Reaction Kinetics (cont.) dc For most reactions, n1 for each of two different reactants, thus a second-order overall reaction c 1 c 1 1 2 c 2 5 3.9x10 Lmg 1 min c 1 1 Many of these will have one reactant in great excess These become pseudo- 1 st order in the limiting reactant, as the reactant in excess really doesn t change in concentration David Rechow CEE 680 #5 15
Reaction Kinetics (cont.) dc 1 1 c 1 c2 Concentration 90 80 70 60 50 40 30 20 10 0 c 1 c 1 o obs c e 2 obs 0.032 min 0 20 40 60 80 Time (min) t 3.9x10 1 5 Since C 2 changes little from its initial 820 mg/l, it is more interesting to (820) focus on C 1 C 1 exhibits simple 1 st order decay, called pseudo-1 st order The pseudo-1 st order rate constant is just the observed rate or obs David Rechow CEE 680 #5 16
Variable Kinetic Order Any reaction order, except n1 dc c n c 1 1 + 1 n 1 c n 1 o ( n )t 1 c c o [ ( ) ] 1 1+ n 1 c n 1 t ( n 1) o David Rechow CEE 680 #5 17
Half-lives Time required for initial concentration to drop to half, i.e.., c0.5c o For a zero order reaction: c c t 0.5c c t 1 2 c o o o For a first order reaction: c e o t 1 t 0.5c c e 2 o o 0.5c David Rechow CEE 680 #5 18 t t 1 2 1 2 o ln(2) 0.693
Reactions in Series A 3 1 2 B C D 1 2 3 0.1 day -1 Fig. 2.9 Pg. 68 David Rechow CEE 680 #5 19
Reversible reaction inetics For a general reversible reaction: aa + bb f pp + qq b And the rate law must consider both forward and reverse reactions: r A f C a A C b B - b C p P CQ q where, f forward rate constant, [units depend on a and b] b bacward rate constant, [units depend on a and b] C P concentration of product species P, [moles/liter] C Q concentration of product species Q, [moles/liter] p stoichiometric coefficient of species P q stoichiometric coefficient of species Q David Rechow CEE 680 #5 20
Reversible 1 st order reactions Kinetic law db 1[ A] 2[ B] Eventually the reaction slows and, Reactant concentrations approach the equilibrium values db 0 1[ A] 2[ B] [ B] 1 K eq [ A] Fig. 2.10 Pg. 69 2 David Rechow CEE 680 #5 21
Temperature Effects Temperature Dependence Chemist's Approach: Arrhenius Equation d(ln ) E a 2 dt RT a e T a T 293 o K a E ( T 293)/ RT 293 a a a Engineer's Approach: 20 o C θ T 20 o C Activation energy T Ae Or more generally where T o is any baseline temperature T θ T David Rechow 22 a E Pre-exponential Factor a / RT a R universal gas constant 1.987 cal/ o K/mole T a absolute temp ( o K) o Typical values: θ1.02 to 1.15 T T o
Determination of E a and A Use Arrhenius equation Tae natural log of both sides Evaluate slope and intercept T Ae a E a / RT E a 1 ln T a ln A R T a a David Rechow CEE 680 #5 23
G Π Catalysis A Catalyst enhances rates by providing alternative pathways with lower activation energies It is not consumed in the reaction Homogeneous Acid/base catalysis Trace metal catalysis Heterogeneous Reactions on particle surfaces G Reactions mediated by microorganisms (enzymes) Engineered surface catalysis Catalytic converters, activated carbon reactants products Reaction coordinate David Rechow CEE 680 #5 24
Analysis of Rate Data Integral Method Least squares regression of linearized form Differential Method estimate instantaneous rate at nown time and reactant concentration Initial rate Method more rigorous, but slow Method of Excess only when 2 or more reactants are involved David Rechow CEE 680 #5 25
Kinetic model for equilibrium Consider a reaction as follows: A + B C + D Since all reactions are reversible, we have two possibilities A + A + f B C + B b C + D D r f The rates are: f { A}{ B} { C}{ D} And at equilibrium the two are equal, r f r b { A}{ B} { C}{ D} f We then define an equilibrium constant (K eq ) K b f eq b r b { C}{ D} { A}{ B} b David Rechow CEE 680 #5 26
Kinetic model with moles [ ] [ ] B A f f B A r David Rechow CEE 680 #5 27 In terms of molar concentrations, the rates are: And at equilibrium the two are equal, r f r b And solving for the equilibrium constant (K eq ) [ ] [ ] D C b b D C r [ ] [ ] [ ] [ ] [ ][ ] [ ][ ] B A D C B A D C b f eq B A D C B A D C K [ ] [ ] [ ] [ ] D C b B A f D C B A
To next lecture David Rechow CEE 680 #5 28