ION EXCHANGE and more on pH DEPENDENT CHARGE

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ION EXCHANGE and more on pH DEPENDENT CHARGE

• Sparks Chap.6
• Additional reading Essington Chapter 8. Skip
  8.4.1.3, 8.4.16, and p 424 to end.

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Exchangeable Bases

• Base cations
• Ca2, Mg2 , Na, and K
• Cations of strong bases (Base cation is an old
  term from geochemistry).
• Acid cations Al3 and H
• Exchangeable cation sites cmolckg-1 (or
  meq/100g)(old)
• On permanent sites of silicate clays,
• pH dependent charge sites of Fe and Al
  (hydr)oxides, a
• pH dependent charge sites of SOM.
• Easily displaced by NH4OAc or other soluble
  salts.
• Generally in low mM (milli molar) concentrations
  in soil solutions, but at much higher
  concentrations than trace elements.

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Soil solution concentrations of exchangeable
cations, Sparks Table 4.1
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The ion exchange capacity of a soil

• Permanent charge on silicate clays
• plus
• pH dependent charge
• 1. SOM
• 2. Silicate clay edges,hydrous oxides of Al and
  Fe(III) and allophane

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pH Dependent Charge on Organic Matter

• (See the discussion of Henderson-Hasselbach
  equation in the organic matter lecture)
• Also
• where ?? is the fraction sites ionized (like
  ??for the oxides).

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• For organic matter
• Potential acidity is usually referenced to pH
  8.0, the pH where all carboxyl groups are
  ionized.

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pH Dependent Charge on Organic Matter continued

• Because of the variation in pKa of individual
  carboxylate groups and build up of minus charge
  on the macro molecular structure
• n approx. 2

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McBride Fig. 3.21
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pH Dependent Charge - Silicates

• Aluminosilicates
• On clay edges AlOH in the octahedral sheets can
  be sites of pH dependent charge.
• The bonding to Si tetrahedra in the structure
  lowers the pznc to less than that of pure
  Al(OH)3
• Kaolinite pznc 4.6

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pH Dependent Charge, Oxides

• For oxides and hydroxides of Fe and Al pznc 6-9
  (average about 8), thus in acid Ultisols and
  Oxisols the AEC is high.

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Two Ways of Determining pH Dependent Charge in
Soil Materials

• 1) Titration with acid or base.
• Add acid or base. Measure the pH and calculate
  the quantity of H or OH- adsorbed.
• Each H adsorbed represents a positive charge in
  surface charge.
• Each OH- adsorbed represents a negative charge in
  surface charge.

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• 2) Adsorbed cations and anions
• Adjust pH in a NaCl or KCl solution. Wash out
  the excess salt. Exchange the Na and Cl- with
  another salt. Calculate the CEC from Na adsorbed
  and anion exchange capacity (AEC) from Cl-
  adsorbed.
• Net charge CEC - AEC

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pH Dependent Charge for Smectite and Allophane by
Na an Cl adsorption (McBride Fig 3.17)

• CEC-AEC (pznc not pzc)

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Dissolution of Al can bias titration data at low
and high pH (McBride Fig. 3.18)

• Low pH
• Al(OH)3 3H --gt Al3 H2O
• High pH
• Al(OH)3 4OH- --gt Al(OH)4-

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Dissolution of Al Can bias titration data data
(McBride Fig. 3.18) Data form Oxisol
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Adsorption of anions and cations in a soils with
permanent and pH dependent charge at two ionic
strengths (McBride Fig. 3.19a)
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• Adsorption of cation and anions determines net
  charge.
• Acid - base titrations determine the proton
  charge.

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Ion Exchange Selectivity (As explained by the
Eisenman model)

• M3 gt M2 gt M
• Alkali Metals (on smectite or pH dependent charge
  sites in soils)
• Cs gt Rb gt K NH4 gt Na gt Li gt H3O
• Alkaline Earths
• Ba2 gt Sr2 gt Ca2 gt Mg2 Transition metal 2
  ions
• If the charge is the same, ions with lower
  hydration energy, lower z/r, are preferred.

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Weak field (McBride Fig.3.5b)
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Rates of Ion Exchange

• Exchange of ions on the surface of soil particles
  is fast compared to most other reaction
  involving solids in soil.
• In a well structured soil, diffusion into and out
  of small aggregates is rate determining.
• In most soils Ca2, Mg2, and Al3 (in very acid
  soils) concentrations greatly exceed monovalent
  cations. Smectites and vermiculites form
  quasi-crystals (tactoids) and diffusion into and
  out of the interlayer can take time (see Fig.
  3.11).

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Reporting CEC in Soils

• l. Sum of bases plus pH dependent acidity at pH
  8.2 or 8.0 (BaCl2?TEA acidity)
• 2. Retention of NH4 at pH 7.0.
• 3. Sum of bases plus exchangeable acidity (
  exchangeable Al) in 1M KCI extracts.
• Al accounts for 95 of acidity exchanged by 1M
  KCl
• Often called effective CEC (ECEC) Very useful
  for work in acid soils.
• Normally l gt 2 gt 3

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Ion exchange equilibrium
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History

• Ion exchange was discovered by Thomas Way in
  about 1840.
• Added ammonium sulfate to soil columns and
  measured calcium and sulfate in the effluent.

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Two - Ion Exchange Reactions

• Example Ca --gt Na exchange.
• Ca Soil 2Na 2Na Soil Ca2
• Ca X 2Na 2NaX Ca2
• Rate relatively fast and reversible
• At equilibrium a general equilibrium equation can
  be written as
• Surface terms are in concentration units because
  surface activity is problemetic

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First ion exchange equation Kerr Equation with
Cl salts (1920s)

• The Kerr equation is the original ion exchange
  equation.
• For Ca soil exchanged by a Na salt

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ION EXCHANGE continued

• Ks is the selectivity coefficient. It is not
  really possible to calculate a true equilibrium
  constant.
• Solution activities can be handled by making the
  usual calculations to calculate activity from
  concentration.
• The exchange site terms are problematic.
• How can activity of the ions on the exchange
  sites be best approximated?
• Two commonly used approaches will be discussed.

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1) Gaines and Thomas Exchange Equation

• Assumption Activity of an ion on the exchanger
  phase is best estimated in units of charge
  fraction (fraction of charges). The activity of
  an ion on an exchange surface is proportional to
  the fraction of charge sites it occupies.
• .

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Gaines and Thomas Exchange Equation

• KGT Gaines and Thomas selectivity coefficien

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Charge Fraction (equivalent fraction) on the
Exchanger Surface

• If the surface concentrations are expressed in
  charge units the charge fraction is
• moles of charge per unit mass.
• Commonly cmolc kg-1

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• If the surface concentrations are expressed in
  molar units

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In class exercise

• If a soil has exchangeable ions with
  concentrations of
• Ca 7 cmolc kg-1
• Na 3 cmolc kg-1
• What is the charge fraction of each ion?
• What is the cation exchange capacity ?

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Answer

• CEC 10 cmolc kg-1
• Charge fraction
• Na 0.3 ( 30)
• Ca 0.7 ( 70)

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Gaines and Thomas Exchange Equation

• KGT Gaines and Thomas selectivity
  coefficient

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Gaines and Thomas Exchange Equation
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Gaines and Thomas Exchange Equation (cont.)

• Homovalent exchange (e.g. Ca2 and Mg2
• Surface term is unitless and equation is
  equivalent to the Vanselow equation (discussed
  later)
• Heterovalent exchange. (e.g. Ca2 and Na)
• The solution term is not unitless.

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2) Vanselow Exchange Equation

• Assumption Surface activity is best estimated
  by the mole fraction of an ion. This is
  analogous to mixtures of solvents and solid
  solutions where activity is proportional to mole
  fraction.

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Example Exchange of Ca2 by Na

• The mole fraction of Ca2 on the exchange
  surface, NCa, is
• Where X is a charge site on a soil particle.
• CaX2 and NaX are in units of cmol kg-1, or
  mmol kg-1 (molar units, not charge units).

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Vanselow Exchange Equation continued

• Then the Vanselow selectivity coefficient, KV,
  is

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Vanselow Exchange Equation (cont)

• KV Vanselow selectivity coefficient ( is not a
  true constant).
• Note the surface ratio, on the left, is unitless
  but the solution ratio term is only unitless when
  the ions are of the same charge .
• The surface term is unitless for homovalent
  exchange (equation is equivalent to the Gaines
  and Thomas equation).
• KV and KG-T are identical for homovalent exchange
  and N E (see Table 8.3)

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In Class Exercise

• If a soil has exchangeable ions with
  concentrations of
• Ca 7 cmolc kg-1
• Na 3 cmolc kg-1
• What is the mole fraction of each ion?
• What is the cation exchange capacity ?

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Answer

• CEC 10 cmolc kg-1
• Mole fraction
• Total moles 3 7/2 6.5
• Na 3/6.5 0.46 (46)
• Ca 3.5/6.5 0.54 ( 54)

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Comparison of the Vanselow and Gaines and Thomas
Equations

• Careful recent work has shown that the Vanselow
  equation is a bit better than the Gaines and
  Thomas (G-T) equation .
• Both work best only over a limited surface
  composition
• For homovalent exchange KV or KGT can be quite
  constant.
• Not as good for M - M2
• Very bad for M2 - M3 and M - M3.

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Evaluation of the different contants for ion
exchange Fig 8.4

• Ca2 K(or Mg2)soil -gt Ca2Soil 2K

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Fig 8.4 c Preference for Ca over Mg
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Fig 8.4 b, apparent decreasing preference for Ca
at high Ca
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Fig 8.4 e
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3) Gapon Equation (an empirical equation)

• Often used in estimating the effects of sodic
  (high Na) irrigation waters.
• Ca1/2 Soil Na Na-Soil 1/2 Ca2
• Surface ion ratio uses charge fraction (like
  Gaines and Thomas).

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• The ratio of solution components is similar to
  that used the previous two equations taken to the
  1/2 power.
• The Gapon equation works quite well but Vanselow
  works just as well.

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Fig 8.4 d
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Why does Kv, KGT, or KG, vary with surface
coverage?

• Ideal solution is not always formed in clay
  interlayers.
• M2 ions can form stable interlayers.
• In Ca2 other divalent salts with equivalent, or
  lower, hydration energy quasi-crystalline
  structures (tactoids) can form in 21 clays.
• These are small aggregates

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Caused by demixing of 2 and 1 ions

• In monovalent - divalent exchange
• Tactoids unstable with more monovalent ions on
  the surface (much smaller aggregates).
• Greater Ks with greater adsorption of divalent
  ions.

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Smectite tactoids in Ca - Na system
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Also get interlayer fixation of K in high
charged clays

• Can get interlayer fixation of K, NH4 and
  other monovalent ions with low hydration energy
  in high charged clays (e.g. Rb and Cs).
• Strong fixation in illite and vermiculite
• Weak fixation in high charge smectite

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Retardation of Ion Movement Due to Ion Exchange

• (Example of Cs, McBride section 3.5)
• Note McBride assumes Cs is not fixed in
  illite and vermiculite. Cs has a low hydration
  energy fixation can be a factor.

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• Retardation
• Where r bulk density (vol/mass)
• f water content (vol/mass)
• V velocity(distance/time)
• Kd distribution coefficient
  
• (McBride, CsX NCs CEC ) ECsCEC

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Retardation of Ion Movement Due to Ion Exchange
(continued)

• Kd can be calculated from KG-T for Cs-Ca2
  exchange assuming most exchange sites in the soil
  are occupied by Ca2.
• For the reaction of ion exchange of Cs with
  Ca2
• Ca2X2 2Cs 2CsX Ca2
• (McBride calls this KS and uses N instead
  of E)
• Where ECs is the fraction of CEC (ECEC) sites
  occupied by Cs.
• CsX ECsCEC

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Retardation of Ion Movement Due to Ion Exchange
(continued)

• and

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Retardation of Ion Movement Due to Ion Exchange
continued

• If ECs small then ECa 1 and

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Retardation of Ion Movement Due to Ion Exchange
(continued)

• Kd is a function of KG-T, and CEC.
• If ECEC 10, Ca2 0.005 M, and KG-T 0.5
  then Kd 100
• If bulk density 1.25, and water content 0.25
  then retardation factor 501.

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Short Summary

• Exchange equations do not provide a unambiguous
  way of calculating exchange equilibria.
• Gaines and Thomas equation uses surface charge
  fraction to estimate the activity of ions on
  exchange surfaces.
• Vanselow equation use mole fractions on the on
  exchanger surfaces.
• The Gapon equation is an empirical equation that
  is used in irrigation.

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• Mixed cationic systems with 2 and 1 cations can
  produce demixed systems with tactoid interlayers.
• Desorption of protons from SOM produces cation
  exchange sites.
• Proton adsorption produces charges on oxides
  and clay edges and AEC.
• Proton desorption produces - charges on oxides
  and clay edges.
• pH dependent charge can be an important component
  of CEC

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• Three are 3 ways of reporting CEC
• Retardation factors can be estimated for
  exchangeable cations.