Adsorption

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Adsorption Measuring Adsorption Adsorption
Kinetics and Equilibria Metal Cation
Adsorption Anion Adsorption Process-based
Adsorption Models
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Measuring Adsorption Adsorption defined as
surface excess with respect to bulk soil
solution mqi ni - VCi where qi is moles
of species i per unit mass of adsorbent ni is
total moles of species i in the system ci is
solution concentration of species i m is mass of
adsorbent V is solution volume Batch and flow
methods for determining In either, reaction time
should be long enough to allow accumulation of
adsorbate but short enough to avoid side
reactions like precipitation / dissolution, redox
or degradation
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• Example
• Soil / solution suspension consisting of 0.010 kg
  soil and 0.040 L water
• contains a total of 0.005 mol Ca and has a Ca
  0.040 M
• q (n VC) / m
• q (0.005 mol 0.040 L x 0.040 M) / 0.010 kg
  0.34 mol kg-1
• Soil / solution suspension consisting of 0.010 kg
  soil and 0.040 L water
• contains a total of 0.010 mol Cl and has a Cl
  0.300 M
• q (0.010 mol 0.040 L x 0.300 M) / 0.010 kg
  -0.20 mol kg-1
• Commonly, adsorption determined from change in
  solution concentration

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Of course, one is never quite sure that a change
in solution concentration is, in fact, due to
adsorption Semi-proof would come from knowledge
of mineralogical composition of soil, together
with spectroscopic data for reaction product(s)
given by pure mineral(s)
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Adsorption Equilibria Equilibrium is not
instantaneous in any case but often effectively
instantaneous Recall earlier example of cation
adsorption in which approach to equilibrium
was limited only by diffusion But for specific
adsorption (with inner-sphere surface complex
formation), approach to equilibrium is much
slower If instantaneous equilibrium does not
occur, general kinetic expression
applicable, dCi / dt Rf - Rr Otherwise,
isotherms, qi F(ci), for constant T and P used
to describe the partition of species i between
adsorbed and solution phases
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General types, S, L, H and C Isotherms S curves
have initially small slope that increases with
increasing adsorptive concentration Possible
explanations include Solution phase complexation
of the adsorptive as with complexation of
dissolved Cu by dissolved organic matter (high
affinity for complexation) Once capacity of
dissolved organic matter to complex Cu reached,
adsorption proceeds Cooperative interactions of
the adsorbed species Increasing extent of
adsorption leads to increased affinity for
adsorption
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L curves have initially steep but decreasing
slope with increasing concentration of the
adsorptive Shape due to initially high affinity
but decreasing area (number of sites)
for continued adsorption as the extent of
adsorption increases Langmuir and Freundlich are
example models S kSMC / (1 kC) S
kCN Langmuir can be developed from above
concept that extent of adsorption is
proportional to the concentration of adsorptive,
C, but decreases with extent of adsorption dS /
dt kfC(SM S) - krS
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Langmuir can be used in conjunction with a site
affinity distribution function to derive other
isotherms qi / Qi ? (Ck(x) / (1 Ck(x)) G(x)
dx where G(x) is the site affinity distribution
function H curve is exaggerated form of
L Often due to inner-sphere surface complex
formation C curve has constant slope, with
neither increasing (S curve) nor decreasing (L or
H curves) slope with increasing concentration of
the adsorptive
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Metal Cation Adsorption
Strength of adsorption Inner-sphere
gt Outer-sphere gt Diffuse ion swarm
Inner-sphere, electronic structure of surface
functional group and metal cation control
adsorption Outer-sphere complexation, similar to
inner-sphere but smeared-out surface charge and
cation valence partly control Diffuse ion swarm
affected only by surface charge and valence
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Inner-sphere complexation For constant Z,
tendency increases as ionic potential, Z / r,
decreases Small Z / r (large r) species will
lose hydration water (easier to de-solvate) and
form inner-sphere complex with surface functional
group Small Z / r (large r) species more easily
polarized by electronic field of surface
functional group, leading to covalent
bonding Cs gt Rb gt K gt Na gt Li Ba2 gt Sr2
gt Ca2 gt Mg2 But trend for transitional
metals Cu2 gt Ni2 gt Co2 gt Fe2 gt Mn2 more
difficult to account for
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pH effects on metal cation adsorption Via
surface charge, sH (pH increases, sH becomes more
-) Adsorption edge, qi F(pH) Generally, if
high pH is necessary for adsorption, affinity
low pH50 ?pH50Na gt pH50Cs but adsorption Na lt
Cs Since hydrolyzed species are more easily
de-solvated, if appreciable hydrolysis occurs
below pH50, M(OH)n(m-n) is involved in
adsorption process
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pH mmole / kg Mg2 / Mg2max

2.48 0.72 0.090
2.73 1.08 0.135
3.05 1.80 0.225
3.20 2.14 0.268
3.36 2.45 0.306
3.80 3.64 0.455
4.10 4.21 0.526
5.00 6.35 0.794
6.00 8.00 1.000

7.
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Role of complexing ligands in solution
M(ad)
ML(ad)
L(ad)
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Anion Adsorption Inner-sphere gt outer-sphere gt
diffuse ion swarm Among common anions in soil
solution, B(OH)4-, (H2PO4-, HPO42- and PO43-)
and COO- tend to form inner-sphere Cl-, NO3-
and, to some extent, HCO3-, CO32- and SO42-,
outer-sphere or to be adsorbed in the diffuse
ion swarm
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Inner-sphere complexation Involves ligand
exchange of the anion for either surface bound
water (protonated hydroxyl) or hydroxyl SOH H
? SOH2 SOH2 Ll- ? SL(l-1)- H2O or SOH
Ll- ? SL(l-1)- OH- Favored by pH lt PZNPC,
however, persists beyond Evidence from
spectroscopic and pH measurements
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Outer-sphere SOH2 Ll- ? SOH2Ll- SMm
Ll- ? SMmLl- In either case, ligand is
hydrated so that there is no direct
contact Evidence that anions like Cl- are either
adsorbed as outer-sphere complexes or in the
diffuse ion swarm These species are readily
displaced (exchanged) Adsorption substantially
decreases as PZNPC approached May exhibit
negative adsorption
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Adsorption (mol / kg) qi (1/ms) ? ci(x) c0i
dV which may be negative as in the previous
example Soil / solution suspension consisting of
0.010 kg soil and 0.040 L water contains a total
of 0.010 mol Cl and has a Cl 0.300 M q
(0.010 mol 0.040 L x 0.300 M) / 0.010 kg
-0.20 mol kg-1 An exclusion volume can also be
calculated, VEX (1/ms) ? ci(x) c0i dV /
c0i -qi / c0i, which for this example would
be VEX -0.20 mol kg-1 / 0.300 M -0.667 L
kg-1 VEX / VH2O 0.667 / 4 0.167 so peak BTC
of pulse at 0.833 PV
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• pH effects on anion adsorption
• Via surface charge, sH (pH decreases, sH becomes
  less -)
• favored at pH lt ZPNPC
• However, for an anion that becomes protonated,
  this effect is offset
• -at low pH protonation of the adsorptive renders
  it non-adsorbed
• Adsorption envelope, qi F(pH)

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Compare adsorption envelopes for monoprotic and
di- / triprotic anions
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Molecular Adsorption Models Gouy-Chapman
(Diffuse Double Layer) Stern Modification Consta
nt Capacitance Models
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• Gouy-Chapman
• For space normal to a planar charged surface and
  non-interacting point charges
• in solution with only two species of same
  valance, c and c-
• 1. Beginning by equating electrochemical
  potentials of a species in the
• diffuse ion swarm and bulk solution, derive the
  Boltzmann distribution relating
• concentration, c/- at any position x to the
  electric potential at x, ?(x),
• c(x) c0 exp(-z?(x) / RT)
• c-(x) c-0 exp(z-?(x) / RT)
• Relate charge density, ?(x) S ciziF, to
  potential using the Poisson equation
• for this one-dimensional space,
• d2? / dx2 F(?) G(c(x), c-(x))

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More explicitly, d2? / dx2 -4p? / e -(4p /
e) zFc0 exp(-zF? / RT) exp(zF? /
RT) Derivations combine parameters to simplify
operations but arrive at (d? / dx) d (d? / dx)
-(4p / e) zFc0 exp(-zF? / RT) exp(zF? / RT)
d? which is integrated to (d? / dx)2 (8p / e)
RT c0 exp(-zF? / RT) exp(zF? / RT)
B or d? / dx -(8p / e) RT c0 exp(-zF? / RT)
exp(zF? / RT) 21/2 where B - 2 (8p / e)
RT c0 since if x is large, both d? / dx and ? are
0 This is the same as Sposito Eq. 8.16 if the
exponentials were expressed as concentrations as
per Boltzman and since 4p / e 1 / e0D
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This expression is then integrated, i.e., d? /
(8p / e) RT c0 exp(-zF? / RT) exp(zF? / RT)
2 -dx using hyperbolic identities to
simplify the matter and a constant of integration
is determined as zF?0 / RT at x 0. But to
obtain an explicit dependence of ? on x, more
identities are needed to finally arrive at, ?
(2RT / zF) ln exp(?x) tanh(zF?0 / 4RT)
(2RT / zF) ln exp(?x) - tanh(zF?0 /
4RT) where ? 8pz2F2c0 / eRT
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• This establishes c/- (x)
• c(x) c0 exp(-z?(x) / RT)
• c-(x) c-0 exp(z-?(x) / RT)
• Surface charge density, s, is found by
  integrating ?(x) from the surface
• outward, since s is equal but opposite to this
  integral
• s - ??(x) dx
• where ?(x) - (e / 4p) d2? / dx2 and the
  integration is from the surface to
• a distance far away. This gives
• s -(e / 4p) (d? / dx) at the surface, since far
  away d? / dx 0.
• From previously,

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So that s (e / 4p) (8p / e) RT c0 exp(-zF?0
/ RT) exp(zF?0 / RT) 21/2 s (e RT c0 /
2p) exp(-zF?0 / RT) exp(zF?0 / RT) 21/2
which is the same as Sposito 8.17 since e / 2p
2 / e0D, except for the coefficient S / F. s
is charge per unit area here. Multiplying by S /
F (m2 kg-1 / C mol-1) converts units of s to mol
(/-) kg-1 as used in Chapter 7.
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Stern Modification Accounts for
specific adsorption of finite-size ions (not
point charges) Application to Variable Surface
Charge Soils
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Stern Modification Allows for surface
adsorption, beyond which exists the diffuse layer
of ions. s sS sD sS NizF / 1 (NA?w /
Mwc) exp(-(zF?d F) / RT) where Ni is number
of adsorption sites per area ? is density of
water Mw is mass of water ?d is potential at the
thickness of the Stern layer, d F is specific
adsorption potential sD is as before but with ?d

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Application to Variable Surface Charge
Soils Unlike the Gouy-Chapman (double layer)
system in which the surface charge is constant,
surface charge variability arises due to
adsorption / desorption of H relative zero
surface charge. As with Gouy-Chapman, s (e
RT c0 / 2p) exp(-zF?0 / RT) exp(zF?0 / RT)
21/2 but ?0 (RT / F) ln (H) / (H0)
where (H0) is that for ?0 0 Thus, s (e
RT c0 / 2p) (H0)z / (H)z (H)z / (H0)z
21/2 s (e RT c0 / 2p) 10-z(pH0 pH)
10z(pH0-pH) 21/2
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Surface Complexation Consider the surface
complexation reaction SO-(s) Cu2(aq)
SOCu(s) K (SOCu) / (SO-) (Cu2) however,
what can be measured is cK SOCu / SO-
(Cu2) which varies with SOCu and
SO- This approach models surface phase
activity as (SOCu) SOCu exp(zF?o / RT)
and (SO-) SO- exp(-zF?o / RT) where z 1
in this case
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So K SOCu exp(zF?o / RT) / SO- exp(-zF?o
/ RT) (Cu2) or K cK exp(2zF?o / RT) The
constant capacitance model assumes that sP
SC?o / F K cK exp(2zF2sP / SCRT) sP s0
sIS s0 2SOCu But the permanent charge is
-(SO- SOCu) so sP -SO- SOCu
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• If in a solution of Ca2 and Cl- there is an
  adsorbent with non-protonated
• SOH sites, and sites SOH2, SO-, SOCa, and
  SOH2Cl-, where each
• refers to a mole of such sites, define sH, sIS,
  sOS and sD in terms of
• concentrations of the surface species, i.e,
  SOH2 etc. The surface
• complex SOCa is inner-sphere.
• sH qH - qOH SOH2 SOH2Cl- SO-
  SOCa
• sIS 2SOCa
• sOS - SOH2Cl-
• Since, sD -(sH sIS sOS), assuming s0 0
• sD -SOH2 - SOCa SO-

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• A variably charged soil contains 0.40 µmol
  SOHTotal / m2 and
• 0.25 µmol SOH2 / m2. If F- is adsorbed at
  pH lt ZPNPC, show that the
• molar ratio of adsorbed H to adsorbed F- is
  0.6.
• qH 0.25 µmol m-2 so qOH 0.0 to 0.15
  µmol m-2
• Assuming adsorption at all possible sites,
  qF 0.25 to 0.40 µmol m-2
• ? (qH / qF) (0.25 / 0.40) to (0.25 /
  0.25) or 0.625 to 1
• Unlikely that no SOH sites exist, i.e.,
  likely that qOH gt 0 so that
• (qH / qF) 0.625 to lt 1
• Also, adsorption of F- by displacement of
  OH- or H2O raises the pH
• which reduces qH and increases qOH. The
  latter limits qF to lt 0.40.

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Do problems 5, 12 and 19.