Chapter 9; Solid-Aqueous Solution Exchange
Sorption:
1. Adsorption: phase transfer to a surface
2. Absorption: phase transfer to a 3-d matrix (liquid, large humic molecules)
Sorption is important because it may dramatically influence the fate and impact of chemicals in the environment.
Reactions of chemicals dissolved in water may be different then if they are buried in a particle- shielded from light
In the sub-layer the immediate environment of a film, surrounding silicate surfaces are more acidic than the surrounding bulk solution
Micro organisms can biodegrade organics that are dissolved and hence solubulized compounds are more easily reacted on by bacteria than sorbed molecules
Can we predict the amt. in the solid phase from Ciw? What are the basic relationships???
Figure 11.1 p 256 (new book 9.1 p 278)
Fig 11.2 p 257 (Fig 9.2 new book)
Langmuirian sorption (1918)
Assume that a surface is surrounded by a liquid and the surface has a certain number of sorption sites. Trace molecules in the liquid phase sorb onto the surface.
The rate of adsorption will be a function of if the number of available sites.
Let q be the fractional # of occupied sites so (1- q) = fraction of available sites
rateon = ka x (1- q) x Ciw
Ciw Ciw
Ciw
C=0 C=0
rateoff= kd q
kd q = ka Ciw (1-q)
ka = rate of adsorb
kd = rate of desorb
q = fract # of occupied
sites or fractional
surface coverage
at equilibrium ka/kd= Keq
so substituting ka/kd= Keq into
kd q = ka Ciw (1- q)
gives
q = KeqCiw (1- q)
and
q + KeqCiw q = KeqCiw
Langmuirian isotherm
if Keq x Ciw < 1
q = KeqCiw linear isotherm
What kind of plot would we expect from these equations as Ciw increases? Can we change q into a solid loading?
Adsorption of mineral associated peat humic
acid (PHA) on kaolinite (clay); Ellyn M. Murphy et al. ES&T, 28, 1291-1299, 1994
going back to:
q is the moles of occupied sites of compound i compared to total sites. This is really Cis moles of sorbed i/mass of solids, divided by the total moles of available sites / mass of sorbant (Gmax);
Keq= KiL
(note the fine print!!! assumes a uniform density of sites/mass)
inverting gives
1/Cis
1/Ciw
In the gas phase Yamasaki ES&T,1982 uses a linear “Langmurian” Isotherm
To characterize partitioning
Fractional coverage of particles in the gas phase
q = Keq x [C i gas], where [Cgas] is in moles/liter
The total moles of sites on the surface of particles/m3 is assumed to be a function of the particle mass concentration, TSP in ug/m3
Total surface site moles/m3 = Kox TSP,
the fractional coverage q is also
q = [Ci part]/ (Kox TSP), where TSP is in ug/m3,
Keq x [Ci gas] = [Ci part]/ (Kox TSP)
Isolating the constants and 1/( Keq Kox )= Ky
Ky = [Ci gas] xTSP/ [Ci part]
[Ci part] àß [Ci gas] +TSP
ln([Ci gas] xTSP/ [Ci part])= -a 1/T +b
what about simple rates of reaction?
rate = krate x q q = fract. of sites occupied
Substituting
rate krate Keq iCw
0.0238 0.5 0.05 1
0.0455 0.5 0.05 2
0.0652 0.5 0.05 3
0.0833 0.5 0.05 4
0.1000 0.5 0.05 5
0.1154 0.5 0.05 6
0.1296 0.5 0.05 7
0.1552 0.5 0.05 9
0.1667 0.5 0.05 10
0.2143 0.5 0.05 15
0.2500 0.5 0.05 20
0.3000 0.5 0.05 30
0.3571 0.5 0.05 50
0.4000 0.5 0.05 80
0.4286 0.5 0.05 120
0.4545 0.5 0.05 200
Another isotherm is the Freudlich isotherm
Cis = KiFCiwni (old book iCs = KiCwn)
concentrations ideally should be in dimensionless activities but in practice are not.
This relationship assumes there are multiple sites acting in parallel with each site type exhibiting a different sorption free energy and total site abundance.
The exponent is an index of the diversity of the free energies associated with the sorption of the solute by multiple components of a heterogeneous sorbent.
When ni is equal to one a linear isotherm is defined, and one may infer that constant sorption free energies at all sorbate concentrations; when n <1, added sorbates are bound with weaker and weaker free energies.
When n> 1, added sorbates enhances the free energy of further adsorption
log Cis= log KiF + ni log Ciw
There are times when a mixture of Langmuir, Fruendlich and linear forms fit the data.
mixed Fruendlich and Linear (Cis = KipCiw)
or
mixed Langmuir and Linear
Almost like Henry’s law, a distribution coefficient Kid can be defined for a compound i between the water and solid/sediment phase
Kid = Cis /Ciw
Note Cis is in moles per mass of solids
Kid is assumed to be constant over a certain range…
Is this really the case?
Substituting for Cis from the Freunlich isotherm
Cis = KiF Cwni
Kid = KiF Ciwni/ Ciw
Kid = KiF Ciwni-1
Differentiating Kid with respect to Ciw
d Kid/d Ciw = KiF (n-1) Ciw n-2
and
d Kid/d Ciw = KiF (n-1) Ciw n-1/Ciw
substituting Kid = KiF Ciwni-1
so
Determining Kid from experimental data
Kid values are often determined by in bulk phase batch experiments where an aqueous phase compound is allowed to come to equilibrium with a given mass of solids
For 1,4 dinitrobenzene the following data were recorded in a K+-illite water suspension (pH 7 at 20 C; see page 284 new book)
Ciw 0.06 0.17 0.24 0.34 0.85 1.8 2.8 3.6 19.5
mmol L-1
CIs 97 241 393 493 915 1640 2160 2850 6100
mmol kg-1
Estimate the Kid values at 0.2 mM and 15 mM
At 0.2 mM a linear isotherm is suggested; according to your book a regression of Cis vs Ciw gives:
Cis = 1424 Ciw r2 à1
Kid = Cis / Ciw =1424
At 15 mM we are into the curved or Freundlich part of the plot
A regression of log Cis= log KiF + ni log Ciw
Gives log Cis= 2.97 + 0.7 log Ciw
Kid = KiF Ciw1-ni ; for 15 m Kid = 102.97 151-0.7 = 450 L /kg
Dissolved and Sorbed Fractions of a compound in surface and ground water;
The fraction of Ciw in the water solution is:
Ms= the mass of solids in this same volume; Cis= moles/mass solids
(1-fiw = fractional amount in the solids)
substituting Kid = Cis /Ciw for Cis
dividing by CiwVw
The solid to water phase ratio is Ms/Vw is defined as rsw, so
when Kid is high (Kid = Cis /Ciw) or rsw is large (high solids/vol. of water) the fraction of a compound i in the water phase will be low.
The fraction of water volume to the total volume Vtot , is called the porosity, f,
f = Vw / Vtot = Vw/ (Vw+Vs)
density x volume = mass
rs Vs= Ms
where rsw= Ms/ Vw
solving for rsw
where, f ,porosity = Vw/Vtot
Let’s compare fiw (the fraction of Ciw in a water solution) of 1,4 dimethylbenene (DMB)for two situations; in a lake and in flowing ground water.
In a lake the solid-water ratio (rsw) is typically on the order of 10-6kg/L; the Kid for DMB in a lake is on the order of 1L / Kg. (Kid = Cis /Ciw)
In flowing ground water, the density of the aquifer solids, rs, is ~2.65 kg/ L
The porosity,f, {we said f = Vw/(Vw+Vs) }
the porosity of flowing ground water is ~0.2, and the solid-water ratio rsw, (where rsw= Ms/ Vw)
the fractional mass in the water phase is
Why are the two fiw values different?
1/fiw is often call the retardation factor Rfi
see Figure 9.6 p288 new book
The Complex nature of Kid
Exchange between the water phase and particulate organic matter of 4-chloroaniline for uncharged species can be represented as
Exchange between the water phase and mineral surfaces of 4-chloroaniline
`
It is possible to react with components on the surface of solids
It is also possible to react with ion exchange sites on the surface of solids
Various combinations of these equilibrium processes, will pertain to overall Kid expressions for different compounds
The role of Natural Organic Matter (NOM)
Most of the organics that we have looked at have high activity coefficients in water.
The surface of most natural mineral compounds have surfaces with hydroxy and oxygen groups à favors hydrogen bonding
Non-polar and even some polar compounds can not compete with H2O
Penetration and sorption into natural organic matter is highly possible
Biomolecules
Lignin
Cellulose
Altered natural organic substances are often referred to as Humic Substancesà extractable in aqueous or basic solutions; Called Humin or kerogin if they are not soluble or extractable
Humic substances are divided into fulvic acids if they are soluble in both acidic and basic solutions, and humic acids if they are soluble at only at high pHs.
humic substances are composed of 40-50% carbon by mass and ~the same amount in oxygen.
Fulvic acids can have molecular weights as low as 2000, and some humic acids and kerogens can be much, much higher.
Given their structure they offer an environment for the sorption of non-polar organics such as PAHs, chlorinated organics, etc.
(old book)
25
Since carbon mass in humics is ~ equal to oxygen mass, the fraction of organic carbon is
foc = fom/2 (see page 296 new book)
34
An example structure of soil organic matter (see new book, page 296 for more structures)
Kid, the fraction of organic carbon, foc, and is Kid constant?
The fraction fom of organic matter is defined as the mass of organic matter (om) divided by the mass of the total solids.
We have already said the foc ~ fom/2
The “concentration” of a sorbate (chemical such as pyrene on organic matter or Ci om ) is defined as moles sorbate/kg om, so fom Ciom = Cis
or om/total sorbant mass x moles i/om= Cis
Kid = Cis /Ciw
Kid = fom Ciom / Ciw,neut;
where Ciw,neut here is the
concentration of the neutral species
We can now define a new partitioning coefficient, Kiom between the organic matter phase for a compound i, and the water phase (old literature uses Kiom, while new literature uses Kioc)
hence, Kid = iKi om x fi om
Where Ki om is a property of the organic matter and fI om is a property of the soil or sediment.
Going back to
Ciom x density of humics (in kg/liter) = Ci om,vol in moles/L
From chapters 3 & 5, Ci om,vol in moles/L = xi om / Vom
substituting
One can assume that Vw, Vom and rom are reasonably constant for a given set of humic/soil and water conditions, so Ki om should be reasonably constant
since Kid = Ki om x f iom
and Kid = Cis /Ciw, , one would expect for a given set of conditions for the ratio of Cis /Ciw to be relatively constant
This is what is observed for benzene (old book)
From
and by analogy with log Kiow = -a log Csatiw + b
We could say
log Kiom = -a’ log Csatiw+ b’
log Kom = -75 log Csatw + 0.44
Since Ki om and Kiow vary directly with Ciwsat
it is reasonable to suggest that Ki om can be directly related to Kiow.
34
Table 11.2 page 274 (old book)
34
We could have done all of the above in terms of organic carbon, instead of organic mass
Where foc = Cioc/Cis and we know Kid = Cis/Ciw
What the new book uses is Kioc and not Kiom
Kioc = Cioc/ Ciw in kg kg-1 / kg L-1 = Kid/foc
Figure 9. 7 page 292 new book; t= dichlorobenzene
O = tetrachloro methane
Figure 9.11 new book p 301
so now we have
log Kioc = a log Kiow + b as well as
log Ki om = a’ log Kiow + b’ regression lines
Returning to Mixed isotherms and now thinking about Kioc
Can we calculate the amount in the solid phase if we know something about the content of the soil and the concentration in the water phase?
We said before that mixed linear and Freundlich isotherms often can be used to fit observed data partitioning onto natural organic carbon, oc.
Where
Cis = Kip Ciw +KiF Cniiw
Kip here refers to partitioning onto natural organic carbon and is Kid if only partitioning to humics is considered; thus KiP = focxKioc. In the case of humics KiF may be related to the fraction of black carbon in the humic matrix. KiF= fbcxKibc
Your book gives values for the Freundlich exponent, ni, of 0.7
This gives
Cis = focxKioc Ciw + fbcxKibc C0.7iw
On page 306, new book, phenanthrene has a log Kiow =4.7 and log Kioc = 4.3 and it asks you to estimate Cis values from different Ciw concentrations of phenanthrene. You are also given an foc of 0.056 kg oc kg-1 for the soil of interest, and fbc is between 1 and 10% of foc.
Kibc is given as function of Kiow
log Kibc = 1.6 log Kiow –1.4 = 5.9
For Ciw = 1 ug/L and Kioc = 104.3
Cis = focxKioc Ciw + fbcxKibc C0.7iw
Cis= 1540 to5500 ug/kg for fbc = 1 and 10% of foc
Cis measured =3200ug/kg
If only Cis = focxKioc Ciw, Cis is underestimated by a factor of 3 and this suggest that the Freudlich term or absorption to back carbon is important at these concentrations
At high the high concentration of 100 ug/L phenanthrene, 121,000 to 220,000 ug/kg solids is estimated for fbc = 1 and 10% of foc, while only 91,000 is observed. The linear part of the isotherm accounts for all of this and suggest that at high concentrations of Ciw adsorption to black carbon (the Freundlich portion) is not important
Reversibility, Competitive and Temperature Effects (Can we use temperature to our advantage to clean up the sub layer??)