Updated: 5 September 05 Print versin CEE 370 Envirnmental Engineering Principles Lecture #5 Envirnmental Chemistry III: Kinetics & ctivity Reading: Mihelcic & Zimmerman, Chapter 3 Davis & Masten, Chapter Mihelcic, Chapt 3. David Rechw CEE 370 L#5 Kinetics ase Hydrlysis dichlrmethane (DCM) Frms chlrmethanl (CM) and chlride Classic secnd rder reactin (mlecularity ) Rate [ DCM ][ OH d[ DCM ] d[ OH ] ] d[ CM ] d[ Cl First rder in each reactant, secnd rder verall ] David Rechw CEE 370 L#5 Lecture #5 Dave Rechw
Kinetic principles Law Mass ctin Fr elementary reactins a b rate C a C b prducts where, C = cncentratin reactant species, [mles/liter] C = cncentratin reactant species, [mles/liter] a = stichimetric ceicient species b = stichimetric ceicient species = rate cnstant, [units are dependent n a and b] David Rechw CEE 370 L#5 3 Kinetics: zer rder Reactins rder n in reactant c When n=0, we have a simple zer-rder reactin Example: bidegradatin,4-d Cncentratin 90 80 70 60 50 40 30 0 0 0 c n Slpe 0 mg/ l/ min c c t 0 0 40 60 80 Time (min) David Rechw CEE 370 L#5 4 Lecture #5 Dave Rechw
Kinetics: First Order When n=, we have a simple irstrder reactin This results in an expnential decay Example: decay 37 Cs rm Chernbyl accident Cncentratin 90 80 70 60 50 40 30 0 0 0 c 0 0 40 60 80 Time (min) David Rechw CEE 370 L#5 5 c 0. 03 min => prducts c e t Kinetics: First Order (cnt.) This equatin can be linearized gd r assessment rm data Cncentratin (lg scale) 00 0 c Slpe 0. 03 min ln c ln c t 0 0 40 60 80 Time (min) David Rechw CEE 370 L#5 6 Lecture #5 Dave Rechw 3
Kinetics: Secnd Order When n=, we have a simple secnd-rder reactin + => prducts This is a reactin between tw identical mlecules Mre cmmn t have dierent mlecules reacting (see next slide) Cncentratin 90 80 70 60 50 40 30 0 0 0 c c c t c 0 0 40 60 80 Time (min) David Rechw CEE 370 L#5 7 0. 005L/ mg/min Kinetics; Pseud- st Order When yu have tw dierent species reacting via nd rder inetics verall + => prducts I ne reactant (c ) is present in great excess versus the ther, the cncentratin that ne can be treated as cnstant and lded int the rate cnstant t get a pseud-irst rder reactin bs c David Rechw CEE 370 L#5 8 where c bs c c Frm here yu can use the irst rder equatins Lecture #5 Dave Rechw 4
Cmparisn Reactin Orders Curvature: nd>st>zer Cncentratin 90 80 70 60 50 40 30 0 0 0 Zer Order First Order Secnd Order 0 0 40 60 80 Time (min) David Rechw CEE 370 L#5 9 Hal-lives Time required r initial cncentratin t drp t hal, ie., c=0.5c Fr a zer rder reactin: 0.5c cc t 0.5c c t c Fr a irst rder reactin: c e t 0.5c t c Try example 3.5 & 3.6 in Mihelcic David Rechw CEE 370 L#5 0 e t t ln() 0.693 Lecture #5 Dave Rechw 5
Temperature Eects Temperature Dependence Chemist's pprach: rrhenius Equatin ctivatin energy d(ln ) E Pre-expnential Factr a E a / RTa dt RT T e a e T a T 93 0 K a E ( T 93)/ RT 93 a a a Engineer's pprach: C T0 C Or mre generally where T is any baseline temperature T T David Rechw a R = universal gas cnstant =.987 cal/ K/mle T a = abslute temp ( K) Typical values: =.0 t.5 T T ctivity ctivity is the eective r apparent cncentratin, which may be slightly dierent rm the true analytical cncentratin These tw dier substantially in waters with high TDS, such as sea water. We identiy these tw as llws: Curved bracets ({X}) indicate activity Square bracets ([X]) indicate cncentratin Usually this is mlar cncentratin This may als be used when we re nt very cncerned abut the dierences between activity and cncentratin David Rechw CEE 370 L#6 Lecture #5 Dave Rechw 6
Why the dierence? Mstly lng-range interactins between uninterested bystanders (chemical species that are nt invlved in the reactin) and the tw dancers interest (thse species that are reacting) David Rechw CEE 370 L#6 3 ctivity & Inic Strength Equilibrium qutients are really written r activities, nt cncentratins in mst natural waters activities are nearly equal t the mlar cncentratins In saline waters, we must accunt r dierences between the tw activity ceicients ( r ) are used r this Inic Strength (I r µ) is used t determine the extent crrectin I r K David Rechw CEE 370 L#6 4 c d C D a b C i z i Lecture #5 Dave Rechw 7
David Rechw CEE 370 L#6 5 Crrelatins r inic strength µ vs. speciic cnductance: Russell pprximatin µ =.6 x 0-5 x K (in µmh/cm) µ vs. TDS: Langlier apprximatin µ ~.5 x 0-5 x TDS (in mg/l) David Rechw CEE 370 L#6 6 Lecture #5 Dave Rechw 8
Crrectins t In ctivity pprximatin Equatin pplicable Range r I Debye-Hücel lg 0.5z I <0 -.3 Extended Debye-Hücel Güntelberg Davies I lg 0.5z <0-0.33a I I <0 -, slutins lg 0.5z I multiple electrlytes I <0.5 lg 0.5z 0. I I Frm Stumm & Mrgan, Table 3.3 (pg.03) 0.3, based n Mihelcic David Rechw CEE 370 L#6 7 Kinetic mdel r equilibrium Cnsider a reactin as llws: The rates are: r { }{ } r b { C}{ D} b + = C + D Since all reactins are reversible, we have tw pssibilities C D C D b nd at equilibrium the tw are equal, r =r b { }{ } { C}{ D} We then deine an equilibrium cnstant (K eq ) K eq b b { C}{ D} { }{ } David Rechw CEE 370 L#6 8 Lecture #5 Dave Rechw 9
Kinetic mdel with mles In terms mlar cncentratins, the rates are: r r b b C C D D nd at equilibrium the tw are equal, r =r b b C C D D nd slving r the equilibrium cnstant (K eq ) K eq b C C D D C D C D David Rechw CEE 370 L#6 9 T next lecture David Rechw CEE 370 L#5 0 Lecture #5 Dave Rechw 0