Transcript Vapor Pressure - Department of Environmental Sciences

Chapter 6:
Air-Organic Solvent and Air-Water
Partitioning
in other words
Henry’s Law
equilibrium partitioning between air and water
KH = PoL/Csatw
Kow = Csato/Csatw
Koa = Csato/PoL
Air
A gas is a gas is a gas
T, P
Koa
KH
Octanol
Po L
Water
Fresh, salt, ground, pore
T, salinity, cosolvents
Csat
w
Kow
Pure Phase
(l) or (s)
Ideal behavior
NOM, biological lipids,
other solvents
T, chemical composition
Csato
Ranges of KH
Partitioning between air and any solvent
fil  pi   il xil p *iL
(recall that in an ideal solution,  = 1)
If  is constant, even close to solubility, then:
'
fil  pi   il xil p *iL  KiH
(l )  xil
pi
K (l ) 
  il  p *iL
xil
'
iH
pi
K iH (l ) 
Cil
Cia KiH (l )
Kial (l ) 

Cil
RT
units of pressure over mole
fraction (no one uses)
units of pressure over molar conc
Pa-m3/mol or Pa-L/mol
“dimensionless” units or Lwater/Lair
VP/solubility
if 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
p* Li
K iH (l )  sat
C il
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
'
ln K iH
(l )  
ln
ln
K H (T 2 )
K H (T 1)
 al H i
 cst
RT
 H
 aw
R
K awT 2  aw H  RTav

K awT 1
R
1 1
  
 T1 T2 
1 1
  
 T1 T2 
units for Kaw in this equation must be
pressure-L/mol (and must match R)
Note: you can use any units for Kaw
in this equation except dim’less
If you want to use dim’less units, use
this form of the equation
air
al Hi  vap Hi  HilE
H “Henry” = H vaporization
minus the excess enthalpy of
solubilization
When solvent is similar to
solute, HE may be negligible
H “Henry”
vapH
water
HE
Pure
liquid
If you can’t find HE, then just use Hvap
Effect of salinity and cosolvents on HLC
Salinity will increase HLC by decreasing the solubility
(increasing the activity coefficient) of the solute in water.
Account for salinity effects via Setschenow constant:
K iaw, salt  K iaw 10
 K is [ salt ]tot
Cosolvents will decrease HLC by increasing the solubility
(decreasing the activity coefficient) of the solute in water.
Account for cosolvent effects via:
 is  f v
Kiaw ( f v )  Kiaw 10
ic 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:
log Kia1  a  log Kia2  b
A familiar estimation technique
molar volume
describes vdW
forces
refractive
index
describes
polarity
2



n
2/3
Di  1
  p( i )
ln K ial  s Vix   2
 nDi  2 

additional
 a( i )  b(  i )  cst
polarizability
term
H-bonding
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
Table 6.2
For water:
2



n
2/3
Di  1
  5.71( i )
ln K iaw  0.540Vix   2
 nDi  2 

 8.74( i )  11.2(  i )  0.0459Vix  2.25
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:
Ciw (t )  Ciw (0)  e

Kiaw G
t
Vw
K iaw  G
ln Ciw (t ) 
 t  cst
Vw
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:
log KH   fi   Fj
i
j
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
log KH   fi   Fj
i
aliphatic alcohols
Benzene
biphenyl
j
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
4
2
lnKH
0
Molecular weight
b = 12.19
m = -0.05747
r ² = 0.8999
Surface area
b = 14.89
m = -0.1392
r ² = 0.7901
-2
Boiling point
b = 10.96
m = -0.02722
r ² = 0.8657
-4
-6
0
100
200
SA (A2)
300
MW (g/mol)
400
BP (C)
500
600
PCBschlorine
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
homework
Problems 6.5 and 6.1