CVEN 5424 Environmental Organic Chemistry Lecture 8 – Henry’s Law Constant and Air-Water Exchange Kinetics

Announcements Reading  Chapter 6, Air-Water Partition  Chapters 18, 19, and 20 (for next lecture) Problem sets PS 3 due today PS 4 out today; due next Tuesday Office hours – semester Wednesday 9-10 am Thursday 4-5:30 pm Monday 9-10:30 am Exam 1 Tues Feb 16, noon, to Thurs Feb 18, 10 am

Air-Water Exchange Equilibrium

Air-Water Exchange  Phase transfers  pure liquid or solid to gas pure liquid vapor p*

Air-Water Exchange  Phase transfers  pure liquid or solid to gas  pure liquid, solid, or gas to water pure liquid vapor pure liquid aqueous solution p*C w sat

Air-Water Exchange  Another phase exchange  air-water exchange = pure liquid aqueous solution vapor aqueous solution vapor

Air-Water Exchange  Phase exchange A water  A air  Henry’s Law constants (bar L mol -1 ) dimensionless (mol L a -1 mol -1 L w )

Air-Water Exchange compound Henry’s Law constant K aw (dimensionless) benzene phenol trichloroethene phenanthrene ,2’,5,5’-tetrachlorobiphenyl

Air-Water Exchange  Estimates by vapor pressure / solubility

Air-Water Exchange  Estimates by vapor pressure / solubility

Air-Water Exchange  Example: chloroethene (a gas)  estimated K aw =  experimental K aw =

Air-Water Exchange  Example: chlorobenzene (a liquid)  estimated K aw =  experimental K aw =

Air-Water Exchange  Example: pyrene (a solid)  estimated K aw =  experimental K aw =

Air-Water Exchange

 Temperature dependence  enthalpy of liquid-air phase change,  al H  Two components of  al H:  vap H -  w H E  enthalpy to vaporize  vap H, related to p L *  (excess) enthalpy to solubilize  w H E, related to C w sat  for solids and gases, melting and condensation enthalpies cancel out

Air-Water Exchange  Liquid: (getting to gas phase) (getting out of water phase)

Air-Water Exchange  Liquid:  Solid: (getting to gas phase) (getting out of water phase)

Air-Water Exchange  Liquid:  Solid:  Gas: gas already in gas phase (getting to gas phase) (getting out of water phase)

Air-Water Exchange dichlorodifluoromethane (gas) toluene (liquid) naphthalene (solid) pyrene (solid)

Air-Water Exchange  Temperature dependence  liquids (e.g., benzene, tetrachloroethylene) ln p* 1/T ln C w sat 1/T ln K H 1/T =+

Air-Water Exchange  Temperature dependence  solids (e.g., naphthalene, 1,4-dichlorobenzene) ln p* 1/T ln C w sat 1/T ln K H 1/T =+

Air-Water Exchange  Temperature dependence  gases (e.g., vinyl chloride, chloromethane) ln p* 1/T ln C w sat 1/T ln K H 1/T =+

Air-Water Exchange  Effect of salt  Salting out decreases solubility; increases K aw

Air-Water Exchange  Effect of salt  Salting out decreases solubility; increases K aw

Air-Water Exchange  Effect of salt  pyrene, K aw =  seawater  [salt] tot = 0.5 M  K S = 0.30

Air-Water Exchange  Effect of co-solvents  Co-solvents increase solubility; decrease K H

Air-Water Exchange  Effect of co-solvents  Co-solvents increase solubility; decrease K H

Air-Water Exchange  Effect of co-solvents  naphthalene, K aw =  20% acetone solution  f v = 0.2   c = 6.5

Air-Water Exchange  Partition between air and water  importance of keeping bubbles out of water samples for VOCs  40 mL vial  39 mL water, 1 mL bubble  VOC is chloromethane  K aw =  what fraction of the chloromethane is in the bubble?

Air-Water Exchange  Partition between air and water

Air-Water Exchange  Partition between air and water

Air-Water Exchange  Partition between air and water

Air-Water Exchange Kinetics  Chapter 18 Transport by Random Motion  read Sections 1, 3  Example 18.3 errata  Answer a, b, and c are actually b, c, and d  Answer d is actually a  skim Sections 2, 4  Chapter 19 Transport Through Boundaries  read Sections 1, 2 (skip advanced topics)  skim Sections 3, 4  skip Section 5

Air-Water Exchange Kinetics  Equilibrium versus kinetics water air

Air-Water Exchange Kinetics  A barge carrying chloroform down the Mississippi River runs aground and ruptures. The spill contaminates a large volume of water at C w sat of CHCl 3. The wind speed at 2 m height is 3 m s -1. The mean depth of the river is 10 m. The water and air temperature are 20  C.  What is the initial flux of chloroform from the river?  What is the half-life of chloroform volatilization?

Air-Water Exchange Kinetics  Equilibrium versus kinetics water air

Quiz  Which compound will volatilize faster? compound K H (bar L mol -1 ) M w (Da) carbon tetrachloride vinyl chloride2262.5

Quiz  Which compound will volatilize faster? diffusion coefficient inversely proportional to molecular weight compound K H (bar L mol -1 ) M w (Da) carbon tetrachloride vinyl chloride2262.5

Air-Water Exchange Kinetics  Fick’s Laws – molecular diffusion  F flux (mass per area per time; e.g., mol m -2 s -1 )  D diffusion (area per time; m 2 s -1 )  C concentration (mass per volume; mol L -1 )  x spatial coordinate (length; m)

Air-Water Exchange Kinetics  Diffusion coefficient

Air-Water Exchange Kinetics  Diffusion coefficient Einstein, A. (1905) Ann. d. Physik 17, 549. Stokes, G. G. (1851) Cambridge Philos. Trans. 9,

Air-Water Exchange Kinetics  Diffusion in air  inversely proportional to molar volume compound mw (g mol -1 ) V (cm 3 mol -1 ) D a (cm 2 s -1 ) H2OH2O methane benzene tetrachloroethene ,2’,4,4’,5,5’- hexachlorobiphenyl

Air-Water Exchange Kinetics  Molar volume element contribution (cm 3 mol -1 ) C16.5 H2.0 O5.5 N5.7 S17.0 Cl19.5 rings-20.2 Fuller et al. (1966)

Air-Water Exchange Kinetics  Molar volume element contribution (cm 3 mol -1 ) C16.5 H2.0 O5.5 N5.7 S17.0 Cl19.5 rings-20.2 Fuller et al. (1966)

Air-Water Exchange Kinetics  Molar volume element contribution (cm 3 mol -1 ) C16.5 H2.0 O5.5 N5.7 S17.0 Cl19.5 rings-20.2 Fuller et al. (1966)

Air-Water Exchange Kinetics  Estimating D a (Fuller et al., 1966)  T absolute temperature (K)  mw air average molecular mass of air (28.97 g mol -1 )  mw c molecular mass of compound (g mol -1 )  P air total pressure of the air (atm)  V air average molar volume of air (20.1 cm 3 mol -1 )  V c molar volume of compound (cm 3 mol -1 )

Air-Water Exchange Kinetics  Estimating D a  relative to known compound  water, benzene, etc.

Air-Water Exchange Kinetics  Diffusion of tetrachloroethene in air at 25  C

Air-Water Exchange Kinetics  Diffusion of tetrachloroethene in air at 25  C

Air-Water Exchange Kinetics  Diffusion in water  inversely proportional to molar volume compound mw (g mol -1 ) V (cm 3 mol -1 ) D w (cm 2 s -1 ) O2O  methane  benzene  tetrachloroethene  ,2’,4,4’,5,5’- hexachlorobiphenyl  10 -5

Air-Water Exchange Kinetics  Estimating D w   viscosity of the water (cp, g cm -1 s -1 )  V molar volume of the compound

Air-Water Exchange Kinetics  Estimating D w  diffusion volume  molecular weight

Air-Water Exchange Kinetics  Diffusion of PCE in water at 25  C

Air-Water Exchange Kinetics  Diffusion of PCE in water at 25  C

Air-Water Exchange Kinetics  Diffusion of PCE in water at 25  C

Air-Water Exchange Kinetics  Flux of molecules across air-water interface  driven by concentration gradient  controlled by molecular diffusion  Water across air-water interface  evaporation  Gases across air-water interface  oxygen  carbon dioxide

Air-Water Exchange Kinetics

Evaporation, that random breach of surface tension by molecules "which happen to acquire exceptionally high velocities.“ Brave "happening"! – they fly the minute distance across and join another state of matter, sacrificing, as they depart, heat to the attraction of the molecules still water, like a wedlocked beauty leaving behind her filmy nightgowns as she flees to a better lover. John Updike, Ode to Evaporation

Air-Water Exchange Kinetics  Three models:  stagnant film  surface renewal  boundary layer

Air-Water Exchange Kinetics  Stagnant film model  stagnant air layer below well-mixed air  stagnant water layer above well- mixed water  equilibrium applies only in boundary layers  most applicable to ocean, lakes, slow rivers well-mixed water well-mixed air C zwzw zaza 0 CwCw C a/w C w/a CaCa stagnant water ~0.01 cm stagnant air ~0.1 cm

Air-Water Exchange Kinetics  Surface renewal model  parcels of air spend some time at interface  parcels of water spend some time at interface  equilibrium between parcels at interface  most applicable to smaller, faster-flowing streams in which stagnant films unlikely water air C 0 CwCw C a/w C w/a CaCa

Air-Water Exchange Kinetics  Boundary layer model  similar to stagnant film model  continuous, not step-like, drop in diffusivity  accounts for turbulence  most versatile, recommended by SGI

Air-Water Exchange Kinetics  A barge carrying chloroform down the Mississippi River runs aground and ruptures. The spill contaminates a large volume of water at C w sat of CHCl 3. The wind speed at 2 m height is 3 m s -1. The mean depth of the river is 10 m. The water and air temperature are 20  C.  What is the initial flux of chloroform from the river?  What is the half-life of chloroform volatilization?

Air-Water Exchange Kinetics  Spills in the Mississippi River  oil (crude, diesel)  at least 44 major spills post-Katrina  27,000,000 L  xylene  tanker collided with barge  160,000 L  “pyrolysis gasoline”  tanker collided with barge  product of ethylene manufacture; benzene  17,000 L  cumene  barge accident at lock  31,000 L

Air-Water Exchange Kinetics  Spills in the Mississippi River  ethylene glycol  leaking railroad tank car  77,000 L  pentachlorophenol  ship accident; required dredging  16 tons  fluorosilicic acid (H 2 SiF 6 )  highly corrosive acid; used for fluoridation  leaking tank; causing damage to other tanks at chemical transfer facility; pumped into river  1,700,000 L  chloroform  barge sank near Baton Rouge  500,000 L

“ I entered upon the small enterprise of ‘learning’ twelve or thirteen hundred miles of the great Mississippi with the easy confidence of my time of life. If I had really known what I was about to require of my faculties, I should not have had the courage to begin. I supposed that all a pilot had to do was to keep his boat in the river, and I did not consider that that could be much of a trick, since it was so wide.” - Mark Twain, Life on the Mississippi

Air-Water Exchange Kinetics  Stagnant film model (Whitman, 1923)  flux  v w water piston velocity  resistance of the water side  CO 2 moving through water  v a air piston velocity  resistance of the air side  H 2 O moving through air piston velocity (cm s -1 ) “resistance” conc. gradient (mol cm -3 ) “driving force” flux (mol cm -2 s -1 )

Air-Water Exchange Kinetics  C w  chloroform solubility, C w sat  C w = M = mol cm -3  this is the initial concentration, so the flux is only initial  C a  wind continuously brings air free of chloroform  C a  0  K aw  chloroform K H = bar L mol -1 (at 25  C)  K aw = 0.16

Air-Water Exchange Kinetics  Piston velocity of chloroform through water v w  estimate for CO 2, relate to CHCl 3  depends solely on wind speed (Eqn )  u 10 wind speed at 10 m height (m s -1 )

Air-Water Exchange Kinetics  Piston velocity of chloroform through water v w  correct wind speed for height (Eqn )  u z wind speed at height z (m s -1 )  z height of wind measurement (m)  3 m s -1 at 2 m height

Air-Water Exchange Kinetics  Piston velocity of chloroform through water v w  relating CHCl 3 to CO 2 (Eqn 20-25)

Air-Water Exchange Kinetics  Temperature correction for v w  two “corrections” at the same time  D w (T 2 )  for unknown compound  for temperatures other than 20  C

Air-Water Exchange Kinetics  Piston velocity of chloroform through water v w

Air-Water Exchange Kinetics  Piston velocity of chloroform through air v a  estimate for H 2 O, relate to CHCl 3  depends solely on wind speed (Eqn )

Air-Water Exchange Kinetics  Piston velocity of chloroform through air v a  relating CHCl 3 to H 2 O (Eqn )

Air-Water Exchange Kinetics  Temperature correction for v a  two “corrections” at the same time  D a (T 2 )  for unknown compound  for temperatures other than 20  C

Air-Water Exchange Kinetics  Piston velocity of chloroform through air v a

Air-Water Exchange Kinetics  Flux of chloroform through air-water interface “water-side controlled” or “water-side limited”

Air-Water Exchange Kinetics  Half-life of chloroform volatilization  rate expression  simplification of flux (mol cm -2 s -1 ) (mol cm -3 s -1 ) (cm s -1  mol cm -3 )

Air-Water Exchange Kinetics  Half-life of chloroform volatilization  total mass volatilized per time (mol s -1 )

Air-Water Exchange Kinetics  Half-life of chloroform volatilization  total mass volatilized per time

Air-Water Exchange Kinetics  Half-life of chloroform volatilization  volatilization rate coefficient (s -1 ) (cm s -1 ) (cm)

Air-Water Exchange Kinetics  Half-life of chloroform volatilization  change in C w with time:

Air-Water Exchange Kinetics  Half-life of chloroform volatilization

Next Lecture  Air-water exchange kinetics using the boundary layer model