Chapter 5:Aqueous Solubility

equilibrium partitioning of a compound between its pure phase 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

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

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!

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

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

Phase change costs

or

Why bother with the

hypothetical liquid?

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

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)

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

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.

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)

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

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

  

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

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

 

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

Molar volume here must be estimated by the atom fragment technique (see p. 149)

This type of LFER is only applicable within a group of similar compounds:

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

Factors Influencing Solubility in Water

• Temperature

• Salinity

• pH

• Dissolved organic matter (DOM)

• Co-solvents

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

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!

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

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

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 

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.

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

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?

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

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

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

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