chapter 6: air-organic solvent and air-water partitioning in other words henry’s law equilibrium...
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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
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.
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
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
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: 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
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.
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
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