CEE 690K ENVIRONMENTAL REACTION KINETICS Lecture #5 Rate - PDF document

9/24/2013 Updated: 24 September 2013 CEE690K Lecture #5 1 Print version CEE 690K ENVIRONMENTAL REACTION KINETICS Lecture #5 Rate Expressions: Chain Reactions Brezonik, pp.50-58 Introduction David A. Reckhow Secular Equilibrium 2  If k ii >> k i  The ratio of [B]/[A] approaches a constant  Divide equation for [B] by the equation for [A]   k [ A ]      i 0 k t k t  [ B ] e e k i t i ii [ A ] [ A ] e  0 k k ii i   k t [ B ] k e i     i k t k t e e i ii  [ ] A k k ii i   k       k k t i 1 e ii i  k k ii i  So when k ii >>k i , then the exponential approaches zero [ B ] k k   i i  [ A ] k k k ii i ii CEE690K Lecture #5 David A. Reckhow 1

9/24/2013 Example: Radium decay I 3  Natural 226 Ra decays as follows:     226 k 222 k 218 Ra Rn Po i ii t 1/2 =1620 yr t 1/2 =3.8 d k i =4.28x10 -4 yr -1 k i =6.6x10 +1 yr -1  Radon is used as tracer for vertical mixing from sediments to water column; Ra is mostly in sediments  Procedure:  Collect water column sample & measure purged Rn  Allow sample to reach secular equilibrium and again measure purged Rn  Difference is used to calculate amount of Rn diffused from sediments Ra Rn Ra CEE690K Lecture #5 David A. Reckhow Ra Rn Radium decay II 4  How long to wait for secular equilibrium?   [ B ] k       k k t i 1 e ii i  [ A ] k k ii i      4 [ Rn ] 4 . 28 x 10      4 66 4 . 28 x 10 t 1 e   4 % [ Ra ] 66 4 . 28 x 10      66 t 0 . 0000065 1 e  % of equilibrium value = 100%(1-e -66t )  92% at 14d  98% at 21d CEE690K Lecture #5 David A. Reckhow 2

9/24/2013 Chain Reactions I 5 Description   A multi-step reaction mechanism where the reactants form intermediates that react with more reactants that yield products plus more intermediates  Quite common for free radical reactions Three stages   Initiation (I) - initiators  Propagation (P) - promotors  Termination (T) - scavengers Evidence   Induction period  Unusual catalysis or repression  Strange rate equations (product in denominator, fractional order)  Unusual surface effects CEE690K Lecture #5 David A. Reckhow Chain Reactions II 6  Simple Generic Cycle “A” and “B” are reactive intermediates, or chain  carriers A 2 A 2    A B P B 2 ½ A 2    B A P A 2   A B 2 P A 2 2 B 2 P A 2 B CEE690K Lecture #5 David A. Reckhow 3

9/24/2013 Chain Reactions 7 CEE690K Lecture #5 David A. Reckhow Kinetic Modeling 8  In-class use of Scientist  Consecutive 2 nd order reactions // Example - A --> B --> C Kinetics // This model describes a system having a second order conversion from A to B. // B is subsequently converted to C by another second order reaction. IndVars: TIME DepVars: A, B, C, D Params: A0, D0, KAB, KBC, A' = -KAB*A*D D' = -KAB*A*D-KBC*B*D B' = KAB*A*D - KBC*B*D C' = KBC*B*D // Initial Conditions TIME = 0.0 A = A0 D = D0 B = 0.0 CEE690K Lecture #5 David A. Reckhow C = 0.0 4

9/24/2013 9  To next lecture CEE690K Lecture #5 David A. Reckhow 5