Environmental Models Fugacity approach

Transcription

1 Environmental Models Fugacity approach Equilibrium artition coefficients Definition, experimental assessment The fugacity approach to partition coefficients Fugacity definitions for a gas, a liquid, a solid Fugacity coefficients in the gas in the liquid phase Relationships between fugacity coefficients and solubility alculation of partition coefficients from fugacity coefficients Henry s Law constant Temperature dependence of the Henry s Law constant Non equilibrium: Fluxes across the air-water interface

2 Environmental fate of organic pollutants Atmospheric Transport Dry Deposition ontinental Inputs A ater-article artitioning ertical Fluxes Gas-article artitioning G Air-ater Exchange Bioaccumulation Advection Degradation et Deposition

3 hemical Fate in the Environment Air A oils Rivers Oceans BF, O Biota: plankton, fish, mammals Air-water partitioning A Air-oil partitioning A i Biota-water partitioning (or bioconcentration factor) BF B ibiota

4 artition of chemicals in ideal laboratory systems artition coefficient: ratio of concentrations at equilibrium. A, eq iw, eq air OA io, eq, eq All are T-dependent water ow io, eq iw, eq octanol NB: Octanol is a surrogate for natural organic matter benzene HB A O If A,eq mol m -3, then,eq mol l mol l - O,,eq mol l mol l -

5 Equilibrium partition constants and thermodynamics hase A hase B Equilibrium partitioning between A and B AB ib Δ AB constant e AB G i / RT Δ G ln AB AB i + ln( cte) RT here Δ AB G i is the free energy of transfer from A to B. It has an entropic and enthalpic controbution

6 artitioning. Types of interactions

7 artition of chemicals in the environment Experimental determination of ( O ) at a given T,eq O,eq x O, eq O2,eq x O,eq O3,eq x O,eq O4,eq x O 0 0 time io,eq O 0 0,eq

8 artition of chemicals in the environment The experimental determination of should cover all environmental properties (T and ranges) ater/air: volatility ater/octanol: hydrophobicity

9 artition of chemicals in the environment

10 artition of chemicals in the environment hemical potentials μ i : not measurable, logarithmically-related to concentration μ i μ 0 + i i RT ln : vapor pressure of i hase transfer occurs from the higher to the lower μ i, and stops when μ i are equals in all phases. Fugacity f (Lewis 90): calculable, linearly-related to concentration mol m -3 Z f mol m -3 a - a μ i (real gas) μ 0 i + RT ln f fi i 0

11 The fugacity approach to partition Fugacity is a sort of partial pressure, that applies as well to compartments when no gas phase exists (organisms). hemicals diffuse from compartments where their fugacity is high to the compartment where their fugacity is the lowest. At equilibrium, the fugacity of a chemical is equal in all phases fi (l) fi(s) f i (g) The environmental partitionning of a substance is driven by its fugacity capacity Z in all compartments: Z, Z, Z ifish. Z i is constant for each chemical and compartment.

12 alculation of using fugacity coefficients ariation of Z, Z,f, f,, towards equilibrium ase : at benza constant, benzene equilibrates to a water phase benza.2 mol m Z benza mol m -3 a - f benza in a benz mol m Z benz mol m -3 a - f benz 500 in a Time Time 0 At equilibrium, f Z Z f Z Z ,eq,eq, eq,eq,eq

13 alculation of using fugacity coefficients ase 2: benz constant, benzene equilibrates to the air phase benza benz 0.25 mol m mol m mol m -3 a Z benza Time f benza Z benz mol m -3 a - Time f benz At equilibrium, f f Z Z,eq,eq, eq,eq,eq Z Z

14 Fugacity in the gas phase f i (g) φ i i φ i x i tot x i is the molar fraction in the gas phase The fugacity coefficient φ i except at low temperatures, and except if intermolecular interactions occur alculation of Z Fugacity and Z in the gas phase F i (g) i for all non ionic substances Z f n A x x n x n n Tot φι Tot A φι Tot Z Z A φi n R T Tot φι Tot φι Tot Tot n A RT Tot A n Tot R T Z 0-4 mol m -3 a - for non ionic substances

15 Fugacity of gases and liquids

16 Fugacity in a liquid phase Fugacity in the liquid phase f i (l) ( x γ f R ) x γ x is the molar fraction in the liquid (water) phase γ is the activity coefficient. It can be viewed as the ratio of the activity (or fugacity) of i to the activity (or fugacity) that i would have in a pure solution of its own kind. L n γi lnγ i0 ( x i2 ) γ i0 when x i 0 alculation of Z Z f n ol x x γ n ol x n Tot ntot n γι ol γ ι Z mol m -3 a - / γ! ymbol: corresponds to molar volume in m 3 mol - a m -3 mol - ater m 3 mol -

17 Fugacity and Z in the gas phase Table 3.2 schwar. ag 8

18 Fugacity in condensed phases (liquid and solid) apor pressure of a liquid i, L and of a solid i, i L i, i, L supercooled

19 Fugacity in the liquid phase Relationships between Z and solubility i For a liquid at its solubility limit, thus at equilibrium fi, eq (l) i L i, eq (w) γ xsat i L f At equilibrium: f i, eq(l) f xsat γ mol m -3 x sat γ i,eq (w) Z x sat For a solid that melts into a liquid phase, at its solubility limit, thus at equilibrium fi, eq (s) f i i, eq (w) γ xsat i L supercoole d At equilibrium: f i, eq(s) f i,eq (w) x sat γ i i L supercooled F γ x sat γ F

20 Fugacity in the liquid phase saturation of a gas that condensates into the liquid phase, at equilibrium: f f (g) i, eq i L i, eq (w) γ xsat i L At equilibrium: f i, eq(s) x sat sat γ f i,eq (w) x sat γ

21 alculation of using thermodynamic parameters Exercise. Determine relevant thermodynamic properties and air-water partitioning properties of benzene, liquid at 298 from: i L 2700 a water 22.8 mol m -3, R8.34 J mol mol m -3 Z A benzene φi R T R T Z benzene x sat γ L L A benzene Z Z γ benzene 2437 x sat X

22 Air-water exchange: Henry Law s constant Air-water equilibrium can be characterized by two constants, the A and the Henry Law s constant, H (or H). A, also named the dimensionless constant,eq,eq,eq (m 3 of water) (m 3 of air) - Z Z γ φi R T Definition of the Henry Law s constant i, eq H (atm l mol- ),eq a (m 3 of water) mol - For a gas or a liquid, at equilibrium i, eq and, eq sat H sat apor pressure at T olubility at T

23 Air-water exchange The Henry Law s constant is related to A,eq,eq i A n i R T,eq i H,eq R T R T,eq 'H Dimensionless» f i H H i, eq,eq (g) f ( ) x i i γ,eq and γ x x, eq, eq γ 0, eq x, eq γ φi R T, eq H φi R T H R T

24 The fugacity approach to partition: do not forget Alike all, A and H are relatedtot T dependence is a critical factor of air-water partition T is a preminent criteria driving contaminant repartion through volatilization and condensation. To understand T dependence of air-water partition, thermodynamic allows to predict relationships, and they should be validated by measurements afterwards.

25 T dependence of artitioning G i Δ ln AB AB + ln( cte) RT d ln dt d( Δ R G / T ) + AB AB i d ln( cte) dt R Δ ABH 2 T i ln AB ( T ( T ) ) Δ H R T2 T AB 2 AB i Temperature dependence of Henry Law s constant H γ H sat

26 Temperature dependence of T dependence of air-water exchange d dt ΔH 2 R T vap d ΔH R vap dt 2 T H ln Δ vap - + R T A

27 T dependence of air-water exchange apor pressures of classes of contaminants, at 25 o

28 T dependence of air-water exchange Temperature dependence of γ iw x sat γ d ln x dt sat ΔH R T exc sol 2 ln x ΔHsol R T exc sat + B

29 T dependence of air-water exchange ater solubilities of classes of contaminants at 25 o sat x sat γ

30 T dependence of air-water exchange T dependence of H H γ ln ΔH R T vap - + A ln γ ΔHsol R T exc - B ln ( H M ) ΔH R vap + ΔH T exc sol + A B ln H ΔH R vap + ΔH T exc sol + A B ln M

31 T dependence of air-water exchange H values of classes of contaminants at 25 o

32 Multimedia Environmental Models The fugacity approach hase A hase B chemical i Estimation of the fraction of chemical i in A (F i,a ) AB ib F i,a mass of i in A total mass of i A A + ib B + ib B A + BA B A

33 Multimedia Environmental Models The fugacity approach hase A hase B hase k chemical i Estimation of the fraction of chemical i in A (F i,a ) when there are k phases (air, water, aerosols, biota, sediments ) AB ib F i,a mass of i in A total mass of i A + ib B A + + i + k n B na n A

34 Multimedia Environmental Models The fugacity approach (we change Zf) hase A hase B hase k chemical i At equilibrium the fugacity (f i ) in all media is the same (f A f B..f f ) Estimation of the fraction of chemical i in A (F i,a ) when there are k phases (air, water, aerosols, biota, sediments ) F AB i,a ib Z Z ib mass of i in A total mass of i Z A + Z Z ib B A + + Z i + k n B na n A