Chapter 5: Aqueous Solubility

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Chapter 5Aqueous Solubility

• equilibrium partitioning of a compound between
  its pure phase and water

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KH PoL/Csatw
Kow Csato/Csatw
Air
Koa Csato/PoL
A gas is a gas is a gas T, P
Koa
KH
Octanol
PoL
Water
NOM, biological lipids, other solvents T,
chemical composition
Fresh, salt, ground, pore T, salinity, cosolvents
Kow
Pure Phase (l) or (s)
Csato
Csatw
Ideal behavior
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• water
• covers 70 of the earths 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

for the organic liquid phase
for the organic chemical in the aqueous phase
at equilibrium (maximum solubility)
At saturation!
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The relationship between solubility and activity
coefficient is
Assume xiL 1 and giL 1
Solubility excess free energy of solubilization
(comprised of enthalpy and entropy terms) over RT
for liquids
or
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

At any given temperature
Recall Prausnitz
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Phase change costsorWhy bother with the
hypothetical liquid?
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Melting point vs. boiling point
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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

theoretical partial pressure of the gas at that
T (i.e. gt 1 atm)
Actual partial pressure of the gas in your system
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concentration dependance of g

• In reality,
• g at saturation ? g at infinite dilution
• However, for compounds with g gt 100 assume
• at saturation g 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 liquids

• The 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 -T?Smix RT ln (Xf/Xi)
•  ?Gs ,?Gmix Gibbs molar free energy of
  solution, mixing (kJ/mol)
• -T?Smix 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 lt10-3
  M)

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dissolution
solute
solvent
two-phase form - low disorder
solution form - high disorder
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 - T?Ss ?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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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
Enthalpy For small molecules, enthalpy term is
small ( 10 kJ/mol) Only for large molecules is
enthalpy significant (positive)
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Solubility Process

• A 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 technique

• Activity 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

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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
molar volume describes vdW forces
refractive index describes polarity
VP describes selfself interactions
additional polarizability term
cavity term
H-bonding
Note that this is similar to the equation we used
to estimate vapor pressure, but is much more
complicated! Also, introduced p, 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).
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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 solubility

• Generally
• 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.

recall from thermodynamic lecture
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What DH is this?
the energy (enthalpy) needed to get the liquid
(real or hypothetical) compound into aqueous
solution
Liquids
Solids
OR
gas
aqueous
liquid
solid
Note sometimes energy states are higher/lower,
so some of these enthalpy terms could be negative!
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Solids, liquids, gases
Solids Liquids Gases
Parameters for this plot
liquid
gas
solid
Tb
Tm
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Salinity effects on solubility

• As 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.

typical seawatersalt 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 DOMKDOM)
•  
• DOM concentration of DOM in water, kg/L
• KDOM DOM/water partition coefficient
• Again, 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
  propanolgtethanolgtmethanol

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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)
if fv1 0, then we are describing the solubility
enhancement relative to the standard aqueous
solubility
sic 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)

• isoctane
• r 0.692 g/mL
• 1-heptene
• r 0.697 g/mL
• Characteristic volumes
• H 8.71
• C 16.35
• -per bond 6.56