addition of an electrolyte to watercourses/c542/choc_week 3b(electrolyte... · the deviation...
TRANSCRIPT
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Addition of an electrolyte to water
NaCl
Na+
Na+
Na+
Na+
Na+
Cl-
Cl-
Cl-
Cl-
Cl-
NaCl(s) Na+(aq) + Cl-(aq)ΔHrx = + 2.5 kJ/mole(endothermic reaction)
http://eps.mcgill.ca/~courses/c542/ 1/54
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Addition of an electrolyte to water
Na+(g) + Cl-(g) NaCl(solid)
Na+(aq) + Cl-(aq)
ΔH1
ΔH3ΔH2 = + 2.5 kJ/mole
ΔH1 = lattice heat = -757.3 kJ/mole
ΔH3 = heat of hydration = ΔH1 + ΔH2 = -754.8 kJ/mole
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Bonds resulting from the polarity of molecules
Water is a very good solvent
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Z2/r
0 4 8 12 16 20
−∆H
(kca
l mol
-1)
0
200
400
600
800
1000
1200
Be2+
Al3+Fe3+
Cr3+
Sc3+Y3+
La3+
M2+
M+
Solvated ions by waterCharge density of an ion (Zé/volume) and the formation of a hydration sphere:
1) Cations are generally more hydrated than anions.2) The greater the charge of the ion, the more heavily
hydrated are the ions (ex: Mg2+ >Li+, even though they have similar ionic radii).
3) For ions of similar charge, the smaller the ionic radius of the ion, the more heavily hydrated it is (ex: Li+ > Na+ >K+).
Hydrated ions
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Hydration Numbers
Li+ 2.8 F- 5.6Na+ 3.7 Cl- 2.0K+ 2.9 Br- 1.2 Mg2+ 7.8 I- 0.1Ca2+ 6.5 OH- 6.4Cu2+ 7.6 SO42- 8.6La3+ 14.7 CO32- 12.8
Ion nh Ion nh
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=+
Electrostriction
0.5 mole NaCl= 29.22 gρ = 2.165 g/cm3 13.5 cm3 970.78 g of water
ρ = 0.997 g/cm3 973.7 cm3
1000 g of solutionV ≠ 13.5 + 973.7 = 987.2 cm3but ~ 982.5 cm3
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+
Electrostricted Region
Electrostriction
The amount of electrostriction is dependent upon the concentration and nature of the salt. It is related to the partial molal volume (V) of the constituent ions.
(δµ/δP)T = V = partial molal volume
where µ = µ° + RT ln ai = chemical potentialai = activity of species i
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Electrostricted
Region
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Electrostriction
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Non-electrolyte in waterNon-electrolytes are held in solution by weak Van der Waals or dipole-dipole interactions with water.
THF - tetrahydrofuraneSalting-out 9/54
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Salting-out
FIZZZZZZ …
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Salting-outNumber of available water molecules in 1 liter (or ~1 kg) = (1000g l-1)/(18g mol-1)
= 55.55 moles l-1
Upon the addition of an electrolyte (salt), the number of water molecules (per liter of water) available to dissolve a non-electrolyte is given by:
55.55 – Σ cinhci = ion concentration in mole l-1nh = hydration number of the ion
Assuming that the solubility of a non-electrolyte in water is simply proportional to the number of water molecules outside the first hydration layer of the ions, then:
S/So = (55.55 - Σ cinh)/55.55So = solubility of the non-electrolyte in pure waterS = solubility of the non-electrolyte after the addition of an electrolyte
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2, 4 dinitrophenol
Salting-out
+
1 mole KClO4 (potassium perchlorate)
S/So = (55.55 – (1 * 2.9 + 1 * 6))/55.55= (55.55 -8.9)/55.55= 46.65/55.55= 0.84
(S/So)Exp = 0.7
nK+ = 2.9 and nClO4- = 6
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Salting-in and Salting-out(the Setchenow equation)
log S
Ionic strength, I
k is negative
Salting-outk is positive
Salting-in
log (S/So) = k I
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Ion-ion interactions The non-ideal behaviour of solutes
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Ion-ion interactions The non-ideal behaviour of solutes
The deviation from ideality is given by the activity coefficient (γ):ai = activity or “effective or thermodynamic concentration” = γi [i]
γi = 1 when Σ[i] = 0.
or, in terms of free energy or chemical potential,(dG/dni)T,P = μi = μoi + RT ln ai = μoi+ RT ln γi + RT ln [i]
Coulombic (electrostatic) interactions are proportional to the charge concentration of the ions in solution. The charge concentration is given by the ionic strength (I):
I = ½ Σ([i]Z2i) ≈ 0.7 m in seawater at SP = 35
where [i] is in molal units (mole of ions/kg H2O) and Zi is the charge of the ion i.
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Debye-Hückel Theorylog γi = – AZ2i I1/2/(1 + ai BI1/2)
where A and B are constants that depend only on the temperature anddielectric constant of the system.
For water at 25oC and 1 atm total pressure:A = 1.824928 x 106 (εT)2/3 = 0.5085 mol-1/2 l1/2 andB = 50.29 x 108/(εT)1/2 = 0.3281 x 108 cm-1 mol-1/2 l1/2
ε is the dielectric constant of water (a measure of its capacity to holdcharges in solution). Pure water has the highest dielectric constant of allliquids.
ai = adjustable size parameter (in angstroms or 10-8 cm) that correspondsroughly to the distance of closest approach between the centre of adjacentions or the radius of the hydrated ion
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Single ion activity coefficients calculated from the Debye-Hückel Equation
The Debye-Hückel equation predicts that activity coefficients decrease continuously with ionic strength. The model is reasonably accurate to an ionic strength of 0.1 m.
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Davies EquationFor higher ionic strengths, the Debye-Hückel equation was modified by adding a term that takes into account non-coulombic interactions and the increase of γ with I.
log γi = – AZ2i (I1/2/1+BaI1/2) + bIwhere b is a general constant (0.2-0.3) or a specific constant for each individual ion i. This expression is known as the Davies equation. This equation yields reasonably accurate estimates of the individual ion activity coefficients for solutions of ionic strengths up to 0.5 m but is not suitable for seawater or solutions of higher ionic strength. …
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The make up of seawaterI – Particulate or solidsII- Colloidal materialIII – Truly dissolved
a) non-associated (free)b) associated (complexed)
i) Weak electrolytesii) Complexesiii) Ion-pairs
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Colloids
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Operational definition of the dissolved fraction
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Operational definition of the dissolved fraction
0.45 µm
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The make up of seawater
I – Particulate or solidsII- Colloidal materialIII – Truly dissolved
a) non-associated (free)b) associated (complexed)
i) Weak electrolytesii) Complexesiii) Ion-pairs
0.45 µm filter
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Effect of Cu on Bacteria
log [Cu]T
-8 -7 -6 -53H
-Am
ino
Aci
d In
corp
otat
ion
(%)
0
20
40
60
80
100
4 µM NTA2 µM NTA0 µM NTA
Free vs complexed solutes(bio-assay)
Effect of Cu on Bacteria
pCu78910113
H-A
min
o A
cid
Inco
rpot
atio
n (%
)
0
20
40
60
80
100
4 µM2 µM0 µM
NTA – nitrilotriacetic acid -log a(Cu2+)
=
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Free vs complexed solutes
Potentiometry/ specific ion electrodes
Polarography
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Non-associated electrolytesPresumed to exist in the form of simple cations and anions, all of which are probably solvated.
Included in this category are elements that do not exhibit strong covalent bonding or electrostatic association between oppositely charged ions. This behavior is typical of the alkali metal ions: Li+, Na+, K+, Rb+, Cs+.
Free ion
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The make up of seawaterI – Particulate or solidsII- Colloidal materialIII – Truly dissolved
a) non-associated (free)b) associated (complexed)
i) Weak electrolytesii) Complexesiii) Ion-pairs
0.45 µm filter
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Associated electrolytes(weak electrolytes)
Solutes that can exist as undissociated molecules in equilibrium with their ions. This group includes substances that might be regarded as weak acids or bases, such as H2CO3 and H3BO3, for which the dissociation is pH dependent.
CO2(g) + H2O H2CO3H2CO3 H+ + HCO3-HCO3- H+ + CO32-
K°1 = (H+) (HCO3-) = 10-6.38 or pK°1 = 6.38(H2CO3*)
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Associated electrolytes(true complexes)
Formed by interaction between a cationic species and ligands (organic or inorganic), and for which covalent bonding is typically important.The number of linkages attaching ligands to a central atom is known as the coordination number.Complexes in which the ligand attaches itself to the central atom through two or more bonds are known as chelates or multidentate complexes.
Calcium oxalate
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Associated electrolytes(true complexes /stability)
Sequential Global constant
M + A MA K1 = [MA] = β1 = global constant [M] [A]
MA + A MA2 K2 = [MA2] & β2 = [MA2] [MA] [A] [M] [A]2
.…
MAn + A MAn+1 Kn+1 = [MAn+1] & βn+1 = [MAn+1] [MAn] [A] [M] [A]n+1
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Associated electrolytes(ion-pairs)
Ion-pairs result from purely electrostatic attraction between oppositely charged ions.
+
ex: Cd2+ + Cl- CdCl+ (positive ion-pair)Hg2+ + 3Cl- HgCl3- (negative ion-pair)Mg2+ + SO42-MgSO4o (neutral ion-pair)
Contact ion-pair
Solvent-shared ion-pair
Solvent-separated ion-pair31/54
(
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Associated electrolytes(ion-pairs / stability)
Mg2+ + SO42-MgSO4o
Ko(MgSO4o) = (MgSO4o) = [MgSO4o] γ(MgSO4o) (Mg2+) (SO42-) [Mg2+]F [SO42-]F γF(Mg2+) γF(SO42-)
= K*(MgSO4o) γ(MgSO4o) γF(Mg2+) γF(SO42-)
= 165 at 25oC and SP = 0
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Associated electrolytes(ion-pairs in seawater)
H + C l -
N a + S O 4 2 -
M g 2 + H C O 3 -
K + B r -
C a 2 + C O 3 2 -
S r 2 + F -
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Associated electrolytes(major ion speciation in seawater)
From: Garrels and Thomson (1962) Amer. J. Science 260, 57-66. 34/54
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Associated electrolytes(major ion speciation in seawater)
From: Millero and Schreiber (1982) Amer. J. Science 282: 1508-1540.
γT(Mg2+) = [Mg2+]F γF(Mg2+) [Mg2+]T
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Associated electrolytes(speciation calculation)
Mg2+ + SO42-MgSO4o
Ko(MgSO4o) = (MgSO4o) = [MgSO4o] γ(MgSO4o) (Mg2+) (SO42-) [Mg2+]F [SO42-]F γF(Mg2+) γF(SO42-)
= K*(MgSO4o) γ(MgSO4o) γF(Mg2+) γF(SO42-)
where (Mg2+) = [Mg2+]T γT(Mg2+) = [Mg2+]F γF(Mg2+)
from which γT(Mg2+) = [Mg2+]F γF(Mg2+) [Mg2+]T
D-H
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Associated electrolytes(speciation calculation)
[Mg2+]T = [Mg2+]F + [MgSO4o] + [MgCO3o] + [MgHCO3+] + [MgX1] + [MgX2] + …
= [Mg2+]F + K*(MgSO4o) [Mg2+]F [SO42-]F + K*(MgCO3o) [Mg2+]F [CO32-]F+ K*(MgHCO3+) [Mg2+]F [HCO3-]F + K*(MgX1) [Mg2+]F [X1]F +
+ K*(MgX2) [Mg2+]F [X2]F + K*(MgX3) [Mg2+]F [X3]F + …
[Mg2+]F = 1/ ( 1 + K*(MgSO4o) [SO42-]F + K*(MgCO3o) [CO32-]F + K*(MgHCO3+) [HCO3-]F + [Mg2+]T + K*(MgX1) [X1]F + K*(MgX2) [X2]F + K*(MgX3) [X3]F + …)
= 1/ ( 1 + Σ K*(MgYi) [Yi]F )
In addition,
[Yi]F = 1/ ( 1 + Σ K*(MjYi) [MJ]F )[Yi]T
K*(MjYi) are a function of the true ionic strength (Itrue), Itrue < Itotal
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Associated electrolytes(speciation in seawater)
HSO4-
H +
HF NaSO4-
Na +
Mg 2+MgHCO3
+MgSO4
K +
KSO4-
Ca 2+
CaSO4
CaCO3
CaHCO3+
SrSO4
Sr 2+
SrHCO3+
SrCO3
NaSO4-
SO42- MgSO4
KSO4-
CaSO4HCO3
- NaHCO3
MgHCO3+
CaHCO3+
MgCO3
CaCO3NaCO3
-
CO32- B(OH)4
-NaB(OH)4
CaB(OH)4+
MgB(OH)4+
F -
MgF +CaF +NaF
MgOH +
OH -
NaOH CaOH +
Cations and cation ion-pairs Anions and anion ion-pairs38/54
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Associated electrolytes(river water vs seawater/dominant species)
PbCO3Pb
PbClPbCl2
PbCl3PbOH
CdCO3CdCl
CdCl2
CdCl3 HgCl4
HgCl2
HgCl3CuCO3
Cu(CO3)2
CuOH
CuCu(OH)2
Metal ions River Water Seawater
Cd2+ CdCO3o CdCl+, CdCl2o
Pb2+ PbCO3o PbCO3o, Pb2+, PbCl2o, PbCl+
Zn2+ ZnCO3o ZnOH+, ZnCl+, Zn2+
Cu2+ CuCO3o CuCO3o, Cu(CO3)22-, Cu2+, CuOH+
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Speciation of Fe(III) in NaCl
pH0 2 4 6 8 10 12 14
Frac
tion
0.0
0.2
0.4
0.6
0.8
1.0
Fe(OH)2+
Fe(OH)4-
Fe(OH)3
Fe3+FeOH2+
Speciation of Al(III) in NaCl
pH2 4 6 8 10 12
Frac
tion
0.0
0.2
0.4
0.6
0.8
1.0
Al3+Al(OH)4
-Al(OH)3
AlOH2+
Al(OH)2+
Associated electrolytes(speciation as a function of pH)
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Metal classificationXX
XX X X X
X X
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Metal classification
Pearsons’ classification
These d0 cations are ions with high spherical symmetry and electron clouds that are not easily deformed or polarizable by electric fields of other ions. They form few complexes, mostly complexes with strong ionic character, such as with fluoride ions and ligands where oxygen is the donor atom. They basically are complexes that form between elements with the large differences in electronegativity.
Electronegativity is defined as the ability of an atom in a molecule to attract an electron to itself, a Lewis acid. When ΔEN =0, the bonding is purely covalent. Until ΔEN reaches 1.7, covalency predominates. Larger ΔEN values indicate chiefly electrostatic or ionic bonding between the cation and ligand,
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Metal classification
Pearsons’ classification
These metal ions have electron sheets that are easily distorted or polarizable. They tend to share their electrons with large anions. Unlike their d0 counterparts, they form strong complexes because they form largely covalent bonded complexes and the stability of these complexes decreases with increasing ΔEN.
Complex log Ko
AgFo -0.3AgClo 3.0AgBro 4.3AgIo 8.1
For example, the halide complexes increase in stability with decreasing EN (or increasing atomic weight or ionic size) of the ligand.
They coordinate preferentially with bases containing I, S or N as donor atoms. They form insoluble sulfides and soluble complexes with S2- and HS- with stabilities increasing: S2- > SH- > OH- > F-.
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Metal classification
Pearsons’ classification
Although the transition metals (C-type) can be subdivided into different classes according to the order of the affinity for a series of ligands, in general, for almost every ligand, the stability of their complexes increases in the so-called "Irving-Williams" order.
Mn2+(d5s2) < Fe2+(d6s2) < Co2+(d7s2) < Ni2+(d8s2) < Cu2+(d10s1) > Zn2+(d10s2)
With the exception of Cu2+, this corresponds to the order of increasing Ip (Z2/r, propensity to form ionic bonds). This order reflects the enhancement of the stability of complexes resulting from the electronic interaction between the cation and ligand, more specifically the degenerescence of the d orbitals and the distribution of the electrons between various energy levels LFSE
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Interactions between metallic cations and ligands
Complex log Ko
AgFo -0.3AgClo 3.0AgBro 4.3AgIo 8.1
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Interaction with organic ligands
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Gibbsite solubility in the presence of oxalateFrom: Fein (1991: Geology 19, 1037-1040)
log [Al]
2
0
-2
-4
-6
0 2 4 6 8 10 12pH
Al(OH)°3
Al3+
Al(OH)2+
Al(OH)2+
Al(OH)4-
Ʃ[Al] = [Al3+] + [AlOH2+] + [Al(OH)2+] + [Al(OH)3°] + [Al(OH)4-] + [Al(Ox)33-]
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Associated electrolytes(speciation of Cu(+II) in seawater)
Organic Speciation of Cu2+
CuL1
CuCO3CuL2
Cu2+ + L1 = CuL1 K1 = 1012
Cu2+ + L2 = CuL2 K2 = 109
Organic speciation of Cu2+
CuCO3
Cu(CO3)22-
Cu2+
CuOH+
CuSO4
Cu(OH)2
Inorganic speciation of Cu2+
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Interaction with organic ligands
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Specific Interaction or Pitzer Equation
ln γM = D.H. + ∑ M-X + ∑ M-N + ∑ M-N-X
∑ MX = ∑ M-Cl + M-SO4 + ∑ M-HCO3
∑ M-N = M-Na, M-Mg, M-Ca ...
∑ M-N-X = M-Na-Cl, M-Na-SO4, ...
+
+ +
–
+ + –
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Specific Interaction or Pitzer Equation
The first term on the right is a modified Debye-Hückel term which takes into account long range electrostatic interactions:
fγ = -0.392 [(I1/2/1+1.2I1/2) + (2/1.2) ln (1 + 1.2I1/2)]B terms describe the interactions of species of opposite sign and are functions of the ionic strength, much like the ion-pairing stability constants. Interactions between species of like charges (θ terms) are assumed independent of I. Ternary interaction terms (Ψ) in the Pitzer equation are not generally needed for I
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Single ion activity coefficientslo
g γM
2+
γM2+
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Activity coefficients of Neutral Species
Given that non-ideality for ions arises primarily as a result of electrostatic interactions with each other, one would expect that neutral species should behave differently since, with no charge, the electrostatic interactions should be negligible. In general, activity coefficients of uncharged species are near unity in dilute solutions and often rise above unity in concentrated solutions because more water is tied up in the hydration of ions and less water is available to interact with the uncharged species (i.e., salting-out). Irrespective of the behaviour of individual neutral solutes, most of the recent studies indicate that log γiis proportional to the ionic strength and can be represented by the Setchenow equation:
log γi = Ki I
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Activity coefficients of Neutral Species(the Setchenow (salting-out) equation)
log γi = Ki I
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Associated electrolytes(speciation in seawater)
HSO4-
H +
HF NaSO4-
Na +
Mg 2+MgHCO3
+MgSO4
K +
KSO4-
Ca 2+
CaSO4
CaCO3
CaHCO3+
SrSO4
Sr 2+
SrHCO3+
SrCO3
NaSO4-
SO42- MgSO4
KSO4-
CaSO4HCO3
- NaHCO3
MgHCO3+
CaHCO3+
MgCO3
CaCO3NaCO3
-
CO32- B(OH)4
-NaB(OH)4
CaB(OH)4+
MgB(OH)4+
F -
MgF +CaF +NaF
MgOH +
OH -
NaOH CaOH +
Cations and cation ion-pairs Anions and anion ion-pairs54/54
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