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Chemical Speciation. Use of constants to model chemical form Thermodynamic and kinetic Determine property of radioelement based on speciation Chemical species in system Review Equilibrium constants Activity Use of constants in equation. Reaction Constants. For a reaction

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chemical speciation
Chemical Speciation
  • Use of constants to model chemical form
    • Thermodynamic and kinetic
    • Determine property of radioelement based on speciation
      • Chemical species in system
  • Review
    • Equilibrium constants
    • Activity
    • Use of constants in equation
reaction constants
Reaction Constants
  • For a reaction
    • aA + bB <--> cC + dD
  • At equilibrium ratio of product to reactants is a constant
    • Constant can change with conditions
      • Not particularly constant
    • By convention, constants are expressed as products over reactants
  • Conditions under which the constant is measured should be listed
    • Temperature, ionic strength
complete picture activities
Complete picture: Activities
  • Strictly speaking, activities, not concentrations should be used
  • Activities normalize concentration to amount of anions and cations in solution
  • At low concentration, activities are assumed to be 1
  • constant can be evaluated at a number of ionic strengths and overall activities fit to equations
  • Debye-Hückel (Physik Z., 24, 185 (1923))

ZA = charge of species A

µ = molal ionic strength

RA = hydrated ionic radius in Å (from 3 to 11)

First estimation of activity

activities
Activities
  • Debye-Hückel term can be written as:
  • Specific ion interaction theory
    • Uses and extends Debye-Hückel
      • long range Debye-Hückel
      • Short range ion interaction term

ij = specific ion interaction term

  • Pitzer
    • Binary (3) and Ternary (2) interaction parameters
slide5

Experimental Data shows change in stability constant with ionic strength

Ion Specific Interaction Theory

Cm-Humate at pH 6

K+

Ca2+

Al3+

Fe(CN)64-

constants
Constants
  • Constants can be listed by different names
    • Equilibrium constants (K)
      • Reactions involving bond breaking
        • 2 HL <--> H2 + 2L
    • Stability constants (ß), Formation constants (K)
      • Metal-ligand complexation
        • Pu4+ + CO32- <--> PuCO32+
        • Ligand is written in deprotonated form
    • Conditional Constants
      • An experimental condition is written into equation
        • Pu4+ + H2CO3 <--> PuCO32+ +2H+
          • Constant can vary with concentration, pH

Must look at equation!

using equilibrium constants
Using Equilibrium Constants
  • Constants and balanced equation can be used to evaluate concentrations at equilibrium
    • 2 HL <--> H2 + 2L,
    • K=4E-15
    • With one mole of HL initially, what are the concentration of the species at equilibrium?
    • write species in terms of one unknown
      • Start with species of lowest concentration
      • [H2] =x, [Y]=2x, [HY]=1-2x
    • Since K is small, x must be small, 1-2x ≈ 1
    • K=4E-15=4x3,
      • x =1E-5, 2x=2E-5
realistic case uranium in aquifer
Realistic Case: Uranium in Aquifer

Species logß

UO2 OH+ 8.5

UO2(OH)2 17.3

UO2(OH)3- 22.6

UO2(OH)42- 23.1

(UO2)2OH3+ 11.0

(UO2)2(OH)2+ 22.0

UO2CO3 8.87

UO2(CO3)22- 16.07

UO2(CO3)34- 21.60

UO2HA(II) 6.16

UO2(OH)HA(I) 14.7±0.5

  • Species to consider include
    • free metal ion: UO22+
    • hydroxides: (UO2)x(OH)y
    • carbonates: UO2CO3
    • humates: UO2HA(II), UO2OHHA(I)
  • Need to get stability constants for all species
    • UO22++ CO32- <--> UO2CO3
  • Know or find conditions
    • Total uranium, total carbonate, pH, total humic concentration
  • If total U concentration is low binary or tertiary species can be excluded
equations
Equations
  • Write concentrations in terms of species
    • [UO2]tot= UO2free+U-carb+U-hydroxide+U-humate
    • [CO32-]free=f(pH)
    • [OH-] = f(pH)
    • [HA]tot = UO2HA + UO2OHHA+ HAfree
  • Write the species in terms of metal, ligands, and constants
    • [(UO2)xAaBb] = 10-(xpUO2+apA+bpB-log(UO2)xAaBb)
    • pX = -log[X]free
      • [(UO2)2(OH)22+]=10-(2pUO2+2pOH-22.0)
  • Set up equations and solve for known terms
  • Can use excel, incorporate solver
  • CHESS example
energy terms
Energy terms
  • Constants can be used to evaluate reaction thermodynamics
  • From Nernst equation
    • ∆G=-RTlnK
  • ∆G=∆H-T∆S
    • -RTlnK = ∆H-T∆S
    • RlnK= - ∆H/T + ∆S
      • Plot RlnK vs 1/T