Chapter 6:

Air-Organic Solvent and Air-Water Partitioning

in other words

Henry’s Law

equilibrium partitioning between air and water

Air

Water

Octanol

A gas is a gas is a gasT, P

Fresh, salt, ground, poreT, salinity, cosolvents

NOM, biological lipids, other solvents T, chemical composition

Pure Phase(l) or (s)

Ideal behavior

PoL

Csatw

Csato

KH = PoL/Csat

w

KoaKH

Kow = Csato/Csat

w

Kow

Koa = Csato/Po

L

Ranges of KH

Partitioning between air and any solvent

iLililiil pxpf *

(recall that in an ideal solution, = 1)

If is constant, even close to solubility, then:

iliHiLililiil xlKpxpf )(* '

iLilil

iiH p

x

plK *)('

units of pressure over mole fraction (no one uses)

il

iiH C

plK )(

units of pressure over molar conc Pa-m3/mol or Pa-L/mol

RT

lK

C

ClK iH

il

iaial

)()( “dimensionless” units or Lwater/Lair

VP/solubilityif activity coefficients do not change, even as the chemical approaches saturation, then Henry’s law may be estimated as the compounds vapor pressure divided by its aqueous solubility

ilsat

Li

iH C

plK

*

)(

this is, I think, a useful concept that has been lost in the new edition of the text.

If a compound has both a low VP and a low solubility, it can be difficult to judge what its HLC will be.

VP ranges over 1012

solubility ranges over 1012

HLC ranges over 107

Factors influencing HLC

• Temperature

• Salinity

• Cosolvents

Temperature dependance of HLC

cstRT

HlK ial

iH

)(ln '

Eilivapial HHH

H “Henry” = H vaporization minus the excess enthalpy of solubilization

When solvent is similar to solute, HE may be negligible

water

Pure liquid

air

HE

vapHH “Henry”

21)1(

)2( 11ln

TTR

H

K

Kaw

TH

THNote: you can use any units for Kaw in this equation except dim’less

units for Kaw in this equation must be pressure-L/mol (and must match R)

211

2 11ln

TTR

RTH

K

K avaw

awT

awT

If you want to use dim’less units, use this form of the equation

If you can’t find HE, then just use Hvap

Effect of salinity and cosolvents on HLCSalinity will increase HLC by decreasing the solubility (increasing the activity coefficient) of the solute in water.

Account for salinity effects via Setschenow constant:

totsi saltK

iawsaltiaw KK ][, 10

Cosolvents will decrease HLC by increasing the solubility (decreasing the activity coefficient) of the solute in water.

Account for cosolvent effects via:

vsi f

iawviaw KfK 10)(i

c is the cosolvent term, which depends on the identity of both the cosolvent and solute

fv is the volume fraction of cosolvent

LFERs relating partition constant in different air-solvent systems

• Once again, partitioning depends on size, polarity/polarizability, and H-bonding

• IF these interactions are similar in both solvents, then a simple LFER is sufficient:

bKaK iaia 21 loglog

A familiar estimation technique

cstba

pn

nVsK

ii

iDi

Diixial

)()(

)(2

1ln

2

23/2

Note that this is a generic equation for estimating the partition of a compound between air and any solvent.

It is similar to the equation we used to estimate vapor pressure and solubility, but is slightly less complicated

molar volume describes vdW forces

refractive index describes polarity

additional polarizability term

H-bonding

Table 6.2

For water:

25.20459.0)(2.11)(74.8

)(71.52

1540.0ln

2

23/2

ixii

iDi

Diixiaw

V

n

nVK

That darn cavity term is back!

Measurement of Henry’s Law

• Relatively few measured values available.

• Hard to measure when solubility is low.

• Two approaches: static and dynamic

Static determination

• Static equilibration between air and water in a vessel such as a gas-tight syringe

• See problem 6.5

Dynamic determination• batch air or gas stripping

• first must generate an aqueous solution containing a relatively high concentration of analyte

• first order process:t

V

GK

iwiww

iaw

eCtC

)0()(

csttV

GKtC

w

iawiw

)(ln

where G = volume of gas

Vw = volume of water

Estimation technique

• Vapor Pressure/Solubility

• how good is either?

Estimation Technique: Bond contribution methods

• In the absence of any other info, QSAR methods give good approximation.

• Hine and Mookerjee 1975– bond contribution method

– 292 compounds

• Nirmalakhadan and Speece, 1988– connectivity indexes

– same data set as H&M but excludes amines, ethers, aldehydes & ketones

– good to within a factor of 1.8 for most compounds

• Meylan and Howard 1991– bigger data set (345 compounds)

– also good to within 1.8

• Pitfalls– How good are the calibration data? Measured or estimated from VP/soly?

– Human error?

– How big is the data set?

KH from fragment constants: structure-property relationships

structure-property relationships used to predict many things

specific structural units increase or decrease and compound's KH by about the same amount.

KH estimation method: j

ji

iH FfKlog

where f are factors for structural units, and F are correction factors for affects such as polyhalogenation, etc.

Note: factors for fragments attached to aliphatic carbons (C-H) are not the same as those attached to aromatic carbons (Car-H)Example: C-Cl = -0.30 Car-Cl = +0.14

table 6.4 j

ji

iH FfKlog

Benzene

biphenyl

aliphatic alcohols

Examples:hexane:

log Kiaw (n-hexane) = 14(C-H) + 5(C-C) + 0.75

0.75 is the correction factor for a linear or branched alkane

log Kiaw (n-hexane) = 14*0.1197 + 5*-0.1163 + 0.75 = 1.84

experimental value is 1.81

benzene:

logKiaw (benzene) = 6(Car-H) + 6(Car-Car)

logKiaw (benzene) = 6(0.1543) + 6(-0.2638) = -0.66

experimental value is –0.68

Example: PCBs by M&H method• Calibration set includes 12 halogenated benzenes: mean

error = 21% and 3 PCBs error = 47% (is this good enough?)

• Validation set includes some PCBs and chlorobenzenes, they are predicted OK.

• Best to start with a known compound:– 4-CBP logKh = -0.63 2-CBP log Kh = -0.09

– subtract Car-H = -0.1543

– add one Car-Cl = +0.0241

– result = -0.76 (err = 7%) -0.22 (err = 78%)

– measured: 4,4’ CBP = -0.79; 2,5 CBP = -0.47

• Cl in the 2 position has a large effect on Kh. These estimation methods cannot account for that.

Other properties can be used to predict HLC

• works best when compounds are closely structurally related.

PAHs

PCBs- chlorine number

Problem 6.3

1,1,1-TCA

Cair = 0.9 mg/m3

Cwater = 2.5 mg/m3

Is this compound volatilizing from, or absorbing into, the arctic ocean at 0C and at 10C?

Salinity = 0.35%o

homeworkProblems 6.5 and 6.1