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

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

2/54

Bonds resulting from the polarity of molecules

Water is a very good solvent

3/54

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

4/54

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

5/54

=+

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

Electrostriction

8/54

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

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

11/54

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

12/54

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

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,(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.

15/54

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

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 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. …

18/54

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

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 solidsII- Colloidal materialIII – Truly dissolved

a) non-associated (free)b) associated (complexed)

i) Weak electrolytesii) Complexesiii) Ion-pairs

0.45 µm filter

23/54

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+)

=

24/54

Free vs complexed solutes

Potentiometry/ specific ion electrodes

Polarography

25/54

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

26/54

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

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 H2CO3H2CO3 H+ + HCO3-HCO3- H+ + CO32-

K°1 = (H+) (HCO3-) = 10-6.38 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] [MAn] [A] [M] [A]n+1

30/54

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

(

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

32/54

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 -

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)

From: Millero and Schreiber (1982) Amer. J. Science 282: 1508-1540.

γT(Mg2+) = [Mg2+]F γF(Mg2+) [Mg2+]T

35/54

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

36/54

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

37/54

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

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+

39/54

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)

40/54

Metal classificationXX

XX X X X

X X

41/54

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,

42/54

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-.

43/54

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

44/54

Interactions between metallic cations and ligands

Complex log Ko

AgFo -0.3AgClo 3.0AgBro 4.3AgIo 8.1

45/54

Interaction with organic ligands

46/54

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-]

47/54

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+

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

Single ion activity coefficientslo

g γM

2+

γM2+

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 γiis 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)

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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