Transcript Thermodynamics and kinetics

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
12-1
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
[C]c [D]d
K
[A]a [B]b
• Conditions under which the constant is measured
should be listed
 Temperature, ionic strength
12-2
Complete picture: Activities
• Strictly speaking, activities, not concentrations should be used
 C [C ]c  D [ D]d
K
 A [ A]a  B [ B]b
• 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))
0.5085Z 2a 
 log A 
1  0.3281R A 
ZA = charge of species A
µ = molal ionic strength
RA = hydrated ionic radius in Å (from 3 to 11)
First estimation of activity
12-3
Activities
• Debye-Hückel term can be written as:
0.5107 
D
1  1.5 
• Specific ion interaction theory
 Uses and extends Debye-Hückel
long range Debye-Hückel
Short range ion interaction term
ij = specific ion interaction term log  i  Z 2D  ij
log ß()  logß(0)  Z2i D   ij
• Pitzer
 Binary (3) and Ternary (2) interaction
parameters
12-4
Experimental Data shows change in
stability constant with ionic strength
6.6
Ion Specific Interaction Theory
Cm-Humate at pH 6
6.5
logß
6.4
6.3
6.2
K+
6.1
6.0
0.0
0.5
1.0
1.5
2.0
2.5
sqrt Im
Ca2+
Al3+
Fe(CN)6412-5
3.0
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!
12-6
Using Equilibrium Constants
• Constants and balanced equation can be used to evaluate
concentrations at equilibrium
2
[
H
][
L
]
 2 HL <--> H2 + 2L,
K 2 2
[ HL]
 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,
2
2
[
x
][
2
x
]
[
x
][
2
x
]
x =1E-5, 2x=2E-5
K

[1  2 x]
2
1
12-7
Realistic Case: Uranium in Aquifer
• 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
Species
UO2 OH+
UO2(OH)2
UO2(OH)3UO2(OH)42(UO2)2OH3+
(UO2)2(OH)2+
UO2CO3
UO2(CO3)22UO2(CO3)34UO2HA(II)
UO2(OH)HA(I)
logß
8.5
17.3
22.6
23.1
11.0
22.0
8.87
16.07
21.60
6.16
14.7±0.5
12-8
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
12-9
U speciation with different CO2 partial
pressure
0% CO2
1.0
UO (OH)
2
1.0
-
UO HA(II)
3
UO
2
UO OHHA(I)
2
UO (OH)
2
Mole Fraction of U(VI) Species
0.8
UO 2HA(II)
2
0.6
0.4
0.2
0.0
2.0
4.0
6.0
8.0
0.8
2
2+
2
UO OHHA(I)
2
43 3
UO (CO )
2
0.6
0.4
23 2
UO (CO )
2
0.2
0.0
10.0
2.0
4.0
pH
6.0
8.0
10.0
pH
1.0
UO
Mole Fraction of U(VI) Species
Mole Fraction of U(VI) Species
UO
2+
1% CO2
0.8
2+
2
UO 2HA(II)
UO 2OHHA(I)
43 3
UO (CO )
2
0.6
10% CO2
0.4
23 2
UO (CO )
2
0.2
0.0
2.0
4.0
6.0
pH
8.0
10.0
12-10
Comparison of measured and calculated
uranyl organic colloid
1.0
0.8
10%
1%
total
[U(VI)]
[U-colloid]
100%
0.6
0.4
0%
0.035%
0.2
0.0
2.0
4.0
6.0
pH
8.0
10.0
12-11
Energy terms
Rlnß
• 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
Temperature effect on Np-Humate stability
Temp (°C)
56
48
40
32
24
16
76
74
72
70
²H = -22.2 ± 2.8 kJ/mol
²G 298=-21.7 kJ/mol
²S=1.2±1.4 J/molK
68
66
64
0.003
0.0031
0.0032
0.0033
0.0034
1/T (K)
12-12
0.0035