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Chapter 5:Aqueous Solubility
equilibrium partitioning of a compound between its pure phase and water
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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
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water• covers 70% of the earth’s surface• is in constant motion• is an important vehicle for transporting
chemicals through the environment
Solubility• is important in its own right• will lead us to Kow and Kaw
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Relationship between solubility and activity coefficient
Consider an organic liquid dissolving in water:
iLiLiLiL xRT ln* for the organic liquid phase
iwiwiLiw xRT ln* for the organic chemical in the aqueous phaseat equilibrium (maximum solubility):
iLiLiwiwLiiw xRTxRT lnln0
RT
RTRT
x
x satiwiL
iL
satiw lnln
ln
At saturation!
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The relationship between solubility and activity coefficient is:
RT
RTRT
x
x satiwiL
iL
satiw lnln
ln
Assume: xiL = 1 and iL = 1
RT
G
RT
RTx
satEiw
satiwsat
iw
,lnln
Solubility = excess free energy of solubilization (comprised of enthalpy and entropy terms) over RT
satiw
satiwx
1
satiww
satiw
VC
1
or for liquids
The activity coefficient is the inverse of the mole fraction solubility
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Solids
must account for the effect of “melting” of solid
i.e. additional energy is needed to melt the solid before it can be solubilized:
RTGsatiw
satiw
ifusesCLC /)()(
is
iLifus p
pRTG
*
ln
is
iLsatiw
satiw p
psCLC
*
)()(
1
)(ln
0
0
T
T
R
TS
p
p mmfus
L
s
Recall Prausnitz:
At any given temperature
RTG
satiw
satiw
ifusesCV
/
)(
1
Substitute activity coefficient for liquid solubility and rearrange:
Use this for HW 5.5
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Phase change costs
or
Why bother with the
hypothetical liquid?
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Melting point vs. boiling point
Tm and Tb vs. MW
y = 2.768x - 152.94R2 = 0.9524
y = 0.6573x + 13.002R2 = 0.3016
0
100
200
300
400
500
600
700
100 120 140 160 180 200 220 240 260
MW (g/m ol)
Tm
or
Tb
(C
)
MW Tm TbNaphthalene 128.2 80.6 217.9
Fluorene 166.2 113 295Phenanthrene 178.2 99.5 340.2Anthracene 178.2 217.5 342Fluoranthene 202.3 110.8Pyrene 202.3 156Benz[a]anthracene 228.3 159.8 435Benzo[a]pyrene 252.3 176.5 584
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Gases
• solubility commonly reported at 1 bar or 1 atm (1 atm = 1.013 bar)
• O2 is an exception
• the phase change “advantage” of condensing the gas to a liquid are already incorporated.
• the solubility of the hypothetical superheated liquid (which you might get from an estimation technique) may be calculated as:
i
iLpiw
satiw p
pCLC i
*
)( Actual partial pressure of the gas in your system
theoretical “partial” pressure of the gas at that T (i.e. > 1 atm)
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concentration dependance of
In reality,at saturation at
infinite dilution
However, for compounds with > 100 assume:
at saturation = at infinite dilution
i.e. solute molecules do not interact, even at saturation
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Molecular picture of the dissolution process
The two most important driving forces in determining the extent of dissolution of a substance in any liquid solvent are
• an increase in disorder (entropy) of the system
• compatability of intermolecular forces of attraction.
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Ideal liquidsThe solubility of ideal liquids is determined by energy lowering from mixing
the two substances. For ideal liquids in dilute solution in water, the intermolecular attractive forces are identical, and Hmix = 0. The molar free energy of solution is:
Gs = Gmix= -TSmix = RT ln (Xf/Xi) Gs ,Gmix = Gibbs molar free energy of solution, mixing (kJ/mol)
-TSmix = Temperature Entropy of mixing (kJ/mol)R = gas law constant (8.414 J/mol-K)T = temperature (K)
Xf, Xi = solute mole fraction concentration final, initial
Note: mole fraction of solvent 1 for dilute solutions (dilute solution has solute conc <10-3 M)
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solventsolute
two-phase form - low disorder
solution form - high disorder
dissolution
The greater the dilution, the smaller (i.e., more negative) the value of Gs and the more
spontaneous in the dissolution process
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Nonideal liquids The intermolecular attractive forces are not normally equal in magnitude between organics and
water. Gs Gmix (no longer equal)
Instead:
Gs = Gmix + Ge
Ge = Excess Gibbs free energy (kJ/mol)
Gs = Hs - TSs = He - T(Smix + Se)
He, Se = Excess enthalpy and excess entropy (kJ/mol)
He = intermolecular attractive forces; cavity formation (solvation)
Se = cavity formation (size); solvent restructuring; mixing
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Enthalpy:
For small molecules, enthalpy term is small (± 10 kJ/mol)
Only for large molecules is enthalpy significant (positive)
Entropy:
Entropy term is generally favorable
Except for large compounds, for which water forms a “flickering crystal”, which fixes both the orientation of the water and of the organic molecule
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Solubility ProcessA mechanistic perspective of solubilization
process for organic solute in water involves the following steps:
a. break up of solute-solute intermolecular bonds
b. break up of solvent-solvent intermolecular bonds
c. formation of cavity in solvent phase large enough to accommodate solute molecule
d. vaporization of solute into cavity of solvent phase
e. formation of solute-solvent intermolecular bonds
f. reformation of solvent-solvent bonds with solvent restructuring
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Estimation techniqueActivity coefficients and water solubilities can be estimated a
priori using molecular size, through molar volume (V, cm3/mol).
Molar volumes in cm3/mol can be approximated:
Ni = number of atoms of type i in jth molecule
ai = atomic volume of ith atom in jth molecule (cm3/mol)
nj = number of bonds in jth molecule (all types)
a values: see p. 149
Solubility can approximated using a LFER of the type:
dsizecLC satiw )()(lnbsizeaLiw )()(ln
)56.6)(())(( ijijiji naNV
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Molar volume here must be estimated by the atom fragment technique (see p. 149)
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This type of LFER is only applicable within a group of similar compounds:
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Another estimation technique
49.90472.0)(1.11)(77.8
)(78.52
1572.0lnln
2
23/2*
ixii
iDi
DiixiLiw
V
n
nVp
Note that this is similar to the equation we used to estimate vapor pressure, but is much more complicated! Also, introduced , the polarizability term.
This approach is universal – valid for all compounds/classes/types
This approach can also be used (with different coefficients) to predict other physical properties (for example, solubility in solvents other than water).
VP describes self:self interactions
molar volume describes vdW forces
refractive index describes polarity
additional polarizability term
H-bonding cavity term
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Factors Influencing Solubility in Water
• Temperature
• Salinity
• pH
• Dissolved organic matter (DOM)
• Co-solvents
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Temperature effects on solubilityGenerally:• as T , solubility for solids.• as T , solubility can or for liquids and gases. • BUT For some organic compounds, the sign of Hs changes; therefore,
opposite temperature effects exist for the same compound!
The influence of temperature on water solubility can be quantitatively described by the van't Hoff equation as:
ln Csat = -H/(RT) + Const.
211
2 11ln
TTR
H
C
C
Tsat
Tsat recall from thermodynamic lecture
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What H is this?
EiwwL HH Liquids:
Solids: ifusEiwws HHH
ivapEiwwa HHH OR
Pure liquid
water
gas
Pure solid ifus H
iwLH
iws H
iwa H
isubHivapH
solid
liquid
aqueous
gas
EiwH the energy (enthalpy) needed to get the liquid (real or
hypothetical) compound into aqueous solution
Note: sometimes energy states are higher/lower, so some of these enthalpy terms could be negative!
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1/T
lnC
sat
Solids, liquids, gases…cst
RT
HHsC
Eiwifussat
iw
)(ln
cstRT
HLC
Eiwsat
iw )(ln
cstRT
HHgC
Eiwivapsat
iw
)(ln
Solids
Liquids
Gases
Parameters for this plot:
kJ/mol 20
kJ/mol 10
kJ/mol 20
ivap
Eiw
ifus
H
H
H
solid
liquidgas
Tb Tm
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Salinity effects on solubilityAs salinity increases, the solubility of neutral organic
compounds decreases (activity coefficient increases)
Ks = Setschenow salt constant (depends on the compound and the salt)
[salt] = molar concentration of total salt.
The addition of salt makes it more difficult for the organic compound to find a cavity to fit into, because water molecules are busy solvating the ions.
totsi saltK
iwsaltiw][
, 10
k
kssalti
sseawateri xKK k,,
typical seawater[salt] = 0.5M
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pH can increase apparent solubity
pH effect depends on the structure of the solute. If the solute is subject to acid/base reactions then pH is vital in
determining water solubility. The ionized form has much higher solubility than the neutral
form. The apparent solubility is higher because it comprises both the
ionized and neutral forms. The intrinsic solubility of the neutral form is not
affected.We will talk about this more when we look at
acid/base reactions
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Dissolved organic matter (DOM) can increase apparent solubility
DOM increases the apparent water solubility for sparingly soluble (hydrophobic) compounds. DOM serves as a site where organic compounds can partition, thereby enhancing water solubility. Solubility in water in the presence of DOM is given by the relation:
Csat,DOM = Csat (1 + [DOM]KDOM) [DOM] = concentration of DOM in water, kg/L
KDOM = DOM/water partition coefficientAgain, the intrinsic solubility of the compound is not
affected.
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Co-solvent effect on solubility
• the presence of a co-solvent can increase the solubility of hydrophobic organic chemicals
• co-solvents can completely change the solvation properties of “water”
• examples:– industrial wastewaters
– “gasohol”
– engineered systems for soil or groundwater remediation
– HPLC
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focus on
• sparingly soluble solutes
• completely water-miscible organic solvents– methanol, ethanol, propanol, acetone, dioxane,
acetonitrile, dimethylsulfoxide, dimethylformamide, glycerol, and moreWhat do these solvents have in common?
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In general• solubility increases exponentially as
cosolvent fraction increases.
• need 5-10 volume % of cosolvent to see an effect.
• extent of solubility enhancement depends on type of cosolvent and solute– effect is greatest for large, nonpolar solutes– more “organic” cosolvents have greater effect
propanol>ethanol>methanol
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Bigger, more non-polar compounds are more affected by co-solvents
Different co-solvents behave differently, behavior is not always linear
We can develop linear relationships to describe the affect of co-solvents on solubility. These relationships depend on the type and size of the solute
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Quantifying cosolvent effect can be complex, so assume log-linear relationship between solubility and volume fraction of cosolvent (fv)
)()(log)(log 11vv
civ
satilv
satil fffxfx
if fv1 = 0, then we are describing the solubility
enhancement relative to the standard aqueous solubility:
vci
satilv
satil fxfx log)(log
ic is the slope term, which depends on the both the
cosolvent and solute
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Problem 5.4• estimate the solubilities of 1-heptene and
isooctane (2,2,4 trimethylpentane)compound MW Tb Csat @ 25C
g/mol C mg/L1-pentene 70.1 30 1482-me-1-pentene 84.2 60.7 781-hexene 84.2 63.4 504-me-1-pentene 84.2 53.9 482,2-dimethylbutane 86.2 49.7 12.82,2-dimepentane 100.2 79.2 4.42,2,3-trime butane 100.2 80.9 4.43-me hexane 100.2 92 3.31-octene 112.2 121.3 2.72-me heptane 114.2 117.6 0.851-nonene 126.3 146.9 1.123-me octane 128.3 143 1.422,2,5-trimethylhexane 128.3 124 1.15
isoctane: = 0.692 g/mL
1-heptene = 0.697 g/mL
Characteristic volumes:H = 8.71C = 16.35-per bond = 6.56