Addition of an electrolyte to water
Cl- Cl-
Na+ + - NaCl(s) Na (aq) + Cl (aq) + Na ΔHrx = + 2.5 kJ/mole Na+ (endothermic reaction) Cl- Cl-
Na+ Na+
NaCl Cl- http://eps.mcgill.ca/~courses/c542/ 1/54 Addition of an electrolyte to water
ΔH1 + - Na (g) + Cl (g) NaCl(solid)
ΔH3 ΔH2 = + 2.5 kJ/mole
+ - Na (aq) + Cl (aq)
ΔH1 = lattice heat = -757.3 kJ/mole
ΔH3 = heat of hydration = ΔH1 + ΔH2 = -754.8 kJ/mole
2/54 Bonds resulting from the polarity of molecules
Water is a very good solvent
3/54 Solvated ions by water Charge 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+).
1200 Cr3+ Al3+ 1000 Fe3+ Y3+ 3+ Hydrated ions ) 3+ Sc La -1 800
600
H (kcal mol H (kcal 400 2+ 2+ Be
−∆ M
200
M+ 0 0 4 8 12 16 20 Z2/r 4/54 Hydration Numbers
Ion nh Ion nh Li+ 2.8 F- 5.6 Na+ 3.7 Cl- 2.0 K+ 2.9 Br- 1.2 Mg2+ 7.8 I- 0.1 Ca2+ 6.5 OH- 6.4 Cu2+ 7.6 SO42- 8.6 La3+ 14.7 CO32- 12.8
5/54 Electrostriction
+ =
0.5 mole NaCl = 29.22 g ρ = 2.165 g/cm3 13.5 cm3 970.78 g of water 3 ρ = 0.997 g/cm 1000 g of solution 3 973.7 cm V ≠ 13.5 + 973.7 = 987.2 cm3 but ~ 982.5 cm3 6/54 Electrostriction
+
Electrostricted Region
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 potential ai = activity of species i 7/54 Electrostriction
8/54 Non-electrolyte in water Non-electrolytes are held in solution by weak Van der Waals or dipole-dipole interactions with water.
THF - tetrahydrofurane Salting-out 9/54 Salting-out
FIZZZZZZ …
10/54 Salting-out
Number 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 cinh -1 ci = ion concentration in mole l nh = 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)/55.55
So = solubility of the non-electrolyte in pure water S = solubility of the non-electrolyte after the addition of an electrolyte 11/54 Salting-out 2, 4 dinitrophenol 1 mole KClO4 (potassium perchlorate)
+ - + nK = 2.9 and nClO4 = 6
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
12/54 Salting-in and Salting-out (the Setchenow equation)
Salting-in log S k is negative
log (S/So) = k I
Salting-out k is positive
Ionic strength, I
13/54 Ion-ion interactions The non-ideal behaviour of solutes
14/54 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, o o (dG/dni)T,P = μi = μ i + RT ln ai = μ i+ 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):
2 I = ½ Σ([i]Z i) ≈ 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. 15/54 Debye-Hückel Theory 2 1/2 1/2 log γi = – AZ i I /(1 + ai BI ) where A and B are constants that depend only on the temperature and dielectric 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 and B = 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 hold charges in solution). Pure water has the highest dielectric constant of all liquids. -8 ai = adjustable size parameter (in angstroms or 10 cm) that corresponds roughly to the distance of closest approach between the centre of adjacent ions or the radius of the hydrated ion
16/54 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. 17/54 Davies Equation For 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. 2 1/2 1/2 log γi = – AZ i (I /1+BaI ) + bI where 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. …
18/54 The make up of seawater I – Particulate or solids II- Colloidal material III – Truly dissolved a) non-associated (free) b) associated (complexed) i) Weak electrolytes ii) Complexes iii) Ion-pairs
19/54 Colloids
20/54 Operational definition of the dissolved fraction
21/54 Operational definition of the dissolved fraction
0.45 µm
22/54 The make up of seawater I – Particulate or solids II- Colloidal material 0.45 µm filter III – Truly dissolved a) non-associated (free) b) associated (complexed) i) Weak electrolytes ii) Complexes iii) Ion-pairs
23/54 Free vs complexed solutes (bio-assay)
Effect of Cu on Bacteria Effect of Cu on Bacteria
100 100
80 80
60 60 4 µM 2 µM 40 µ 40 4 µM NTA 0 M 2 µM NTA 20 20 0 µM NTA H-Amino Acid Incorpotation (%) Incorpotation Acid H-Amino
H-Amino Acid Incorpotation (%) Incorpotation Acid H-Amino 0 0 3 3 -8 -7 -6 -5 11 10 9 8 7 pCu log [Cu]T =
NTA – nitrilotriacetic acid -log a(Cu2+)
24/54 Free vs complexed solutes
Polarography
Potentiometry/ specific ion electrodes
25/54 Non-associated electrolytes
Presumed to exist in the form of simple cations and anions, all of which are probably solvated.
Free ion
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+.
26/54 The make up of seawater I – Particulate or solids II- Colloidal material 0.45 µm filter III – Truly dissolved a) non-associated (free) b) associated (complexed) i) Weak electrolytes ii) Complexes iii) Ion-pairs
27/54 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 H2CO3 + - H2CO3 H + HCO3 - + 2- HCO3 H + CO3
- -6.38 K°1 = (H+) (HCO3 ) = 10 or pK°1 = 6.38 * (H2CO3 )
28/54 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 29/54 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] n+1 [MAn] [A] [M] [A]
30/54 Associated electrolytes (ion-pairs) Ion-pairs result from purely electrostatic attraction between oppositely charged ions. ex: Cd2+ + Cl- CdCl+ (positive ion-pair) 2+ - - Hg + 3Cl HgCl3 (negative ion-pair) 2+ 2- o Mg + SO4 MgSO4 (neutral ion-pair)
Contact ion-pair
Solvent-shared ion-pair
+ Solvent-separated ion-pair 31/54 Associated electrolytes (ion-pairs / stability)
2+ 2- o Mg + SO4 MgSO4
o o o o o K (MgSO4 ) = (MgSO4 ) = [MgSO4 ] γ(MgSO4 )
2+ 2- 2+ 2- 2+ 2- (Mg ) (SO4 ) [Mg ]F [SO4 ]F γF(Mg ) γF(SO4 )
* o o = K (MgSO4 ) γ(MgSO4 )
2+ 2- γF(Mg ) γF(SO4 )
o = 165 at 25 C and SP = 0
32/54 Associated electrolytes (ion-pairs in seawater)
H + Cl-
+ 2- Na SO 4
2+ - Mg HCO3
K + Br-
2+ 2- Ca CO3
Sr2+ F -
33/54 Associated electrolytes (major ion speciation in seawater)
From: Garrels and Thomson (1962) Amer. J. Science 260, 57-66. 34/54 Associated electrolytes (major ion speciation in seawater)
2+ 2+ 2+ γT(Mg ) = [Mg ]F γF(Mg ) 2+ [Mg ]T
From: Millero and Schreiber (1982) Amer. J. Science 282: 1508-1540. 35/54 Associated electrolytes (speciation calculation)
2+ 2- o Mg + SO4 MgSO4
o o o o o K (MgSO4 ) = (MgSO4 ) = [MgSO4 ] γ(MgSO4 )
2+ 2- 2+ 2- 2+ 2- (Mg ) (SO4 ) [Mg ]F [SO4 ]F γF(Mg ) γF(SO4 )
* o o = K (MgSO4 ) γ(MgSO4 )
2+ 2- γF(Mg ) γF(SO4 )
2+ 2+ 2+ 2+ 2+ where (Mg ) = [Mg ]T γT(Mg ) = [Mg ]F γF(Mg )
2+ from which (Mg2+) = [Mg ] (Mg2+) γT F γF D-H 2+ [Mg ]T
36/54 Associated electrolytes (speciation calculation) 2+ 2+ o o + [Mg ]T = [Mg ]F + [MgSO4 ] + [MgCO3 ] + [MgHCO3 ] + [MgX1] + [MgX2] + …
2+ o 2+ 2- o 2+ 2- = [Mg ]F + K*(MgSO4 ) [Mg ]F [SO4 ]F + K*(MgCO3 ) [Mg ]F [CO3 ]F + 2+ - 2+ + K*(MgHCO3 ) [Mg ]F [HCO3 ]F + K*(MgX1) [Mg ]F [X1]F + 2+ 2+ + K*(MgX2) [Mg ]F [X2]F + K*(MgX3) [Mg ]F [X3]F + …
2+ o 2- o 2- + - [Mg ]F = 1/ ( 1 + K*(MgSO4 ) [SO4 ]F + K*(MgCO3 ) [CO3 ]F + K*(MgHCO3 ) [HCO3 ]F + 2+ [Mg ]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 37/54 Associated electrolytes (speciation in seawater)
- KSO4 + CaHCO3 SO 2- MgSO4 H + Na + 4 HCO - NaHCO - 3 3 HF NaSO4 CaSO4 MgHCO + - - 3 HSO4 NaSO4
+ MgCO3 MgB(OH)4 2+ + + Mg K CaB(OH)4 + MgHCO3 KSO - - MgSO4 4 2- B(OH)4 NaB(OH) CO3 4 CaCO3 - NaCO3
- F - OH Ca 2+ Sr 2+ + CaOH + CaHCO3 SrCO3 NaF CaSO SrSO + NaOH 4 4 CaF + + MgF + MgOH SrHCO3 CaCO3
Cations and cation ion-pairs Anions and anion ion-pairs 38/54 Associated electrolytes (river water vs seawater/dominant species)
Metal ions River Water Seawater
2+ o + o Cd CdCO3 CdCl , CdCl2
2+ o o 2+ o + Pb PbCO3 PbCO3 , Pb , PbCl2 , PbCl
2+ o + + 2+ Zn ZnCO3 ZnOH , ZnCl , Zn
2+ o o 2- 2+ + Cu CuCO3 CuCO3 , Cu(CO3)2 , Cu , CuOH
HgCl Pb CdCl CdCO3 3 Cu PbCO 3 CuCO3 HgCl2 Cu(OH) PbOH CdCl 2 3 CuOH PbCl3 HgCl4 CdCl2 Cu(CO3)2 PbCl PbCl2
39/54 Associated electrolytes (speciation as a function of pH)
Speciation of Fe(III) in NaCl Speciation of Al(III) in NaCl
1.0
Al(OH)3 1.0 Al(OH) - 3+ 4 Fe(OH) - Al Fe3+ 4 2+ 0.8 0.8 FeOH
Fe(OH) + 0.6 2 0.6 Fraction Fraction 0.4 0.4 AlOH2+ Fe(OH)3 0.2 + Al(OH)2 0.2
0.0
0.0 0 2 4 6 8 10 12 14 2 4 6 8 10 12 pH pH
40/54 Metal classification
X X X X X X X X X
41/54 Metal 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 Pearsons’ classification ΔEN values indicate chiefly electrostatic or ionic bonding between the cation and ligand,
42/54 Metal 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 For example, the halide complexes increase in Pearsons’ classification AgFo -0.3 stability with decreasing EN (or increasing AgClo 3.0 atomic weight or ionic size) of the ligand. AgBro 4.3 AgIo 8.1
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-.
43/54 Metal 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) Pearsons’ classification 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
44/54 Interactions between metallic cations and ligands
Complex log Ko AgFo -0.3 AgClo 3.0 AgBro 4.3 AgIo 8.1
45/54 Interaction with organic ligands
46/54 Gibbsite solubility in the presence of oxalate
From: Fein (1991: Geology 19, 1037-1040) log [Al] Al3+ 2 - Al(OH)4 0 Al(OH)2+ -2
-4 + Al(OH)2 -6 Al(OH)°3
0 2 4 6 8 10 12 pH
3+ 2+ + - 3- Ʃ[Al] = [Al ] + [AlOH ] + [Al(OH)2 ] + [Al(OH)3°] + [Al(OH)4 ] + [Al(Ox)3 ]
47/54 Associated electrolytes (speciation of Cu(+II) in seawater)
2+ Inorganic speciation of Cu2+ OrganicOrganic Speciationspeciation of Cu of Cu2+
CuCO3 CuCO3 CuL CuOH+ 2 CuL1 CuSO4
Cu(OH)2 Cu2+
2- Cu(CO3)2
2+ 12 Cu + L1 = CuL1 K1 = 10
2+ 9 Cu + L2 = CuL2 K2 = 10
48a/54 Interaction with organic ligands
48b/54 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, ...
+ + –
49/54 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<3.5 mol/kg, they take into account interactions between two-like charged and a third unlike-charged species. They are also assumed to be independent of ionic strength. wwwbrr.cr.usgs.gov/projects/GWC_coupled/phreeqc/ www.ndsu.nodak.edu/webphreeq/ 50/54 Single ion activity coefficients 2+ M γ γM2+ log
51/54 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 γi is proportional to the ionic strength and can be represented by the Setchenow equation:
log γi = Ki I
52/54 Activity coefficients of Neutral Species (the Setchenow (salting-out) equation)
log γi = Ki I
53/54 Associated electrolytes (speciation in seawater)
- KSO4 + CaHCO3 2- + + SO MgSO4 H Na 4 - HCO3 NaHCO3 HF NaSO - 4 CaSO4 MgHCO + - - 3 HSO4 NaSO4
+ MgCO3 MgB(OH)4 Mg 2+ K + CaB(OH) + + 4 MgHCO3 KSO - - MgSO4 4 2- B(OH)4 NaB(OH) CO3 4 CaCO3 - NaCO3
- F - OH Ca 2+ Sr 2+ + CaOH + CaHCO3 SrCO3 NaF CaSO SrSO4 + NaOH 4 CaF + + + MgOH SrHCO3 MgF CaCO3
Cations and cation ion-pairs Anions and anion ion-pairs 54/54