Addition of an electrolyte to water

Transcription

1 Addition of an electrolyte to water Na + Na + Cl - Cl - Cl - Na + Cl - NaCl (s) Na + (aq) + Cl - (aq) ΔH rx = kj/mole (endothermic reaction) Na + Na + NaCl Cl - 1/54

2 Addition of an electrolyte to water ΔH 1 Na + (g) + Cl - (g) NaCl (solid) ΔH 3 ΔH 2 = kj/mole Na + (aq) + Cl - (aq) ΔH 1 = lattice heat = kj/mole ΔH 3 = heat of hydration = ΔH 1 + ΔH 2 = kj/mole 2/54

3 Bonds resulting from the polarity of molecules Water is a very good solvent 3/54

4 Solvated ions by water Charge density of an ion (Zé/volume) and the formation of a hydration sphere: Hydrated ions 1) Cations are generally more hydrated than anions. 2) The greater the charge of the ion, the more heavily hydrated are the ions (ex: Mg 2+ >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 + ). H (kcal mol -1 ) M 2+ La 3+ Y 3+ Cr 3+ Sc 3+ Be 2+ Fe 3+ Al M Z 2 /r 4/54

5 Hydration Numbers Ion n h Ion n h Li F Na Cl K Br Mg I Ca OH Cu SO La CO /54

6 Electrostriction + = 0.5 mole NaCl = g ρ = g/cm cm g of water ρ = g/cm cm g of solution V = cm 3 but ~ cm 3 6/54

7 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 a i = chemical potential a i = activity of species i 7/54

8 Electrostriction 8/54

9 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

10 Salting-out FIZZZZZZ 10/54

11 Salting-out Number of available water molecules in 1 liter (or ~1 kg) = (1000g l -1 )/(18g mol -1 ) = 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: c i = ion concentration in mole l -1 n h = hydration number of the ion Σ c i n h 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/S o = ( Σ c i n h )/55.55 S o = solubility of the non-electrolyte in pure water S = solubility of the non-electrolyte after the addition of an electrolyte 11/54

12 Salting-out 2, 4 dinitrophenol 1 mole KClO 4 (potassium perchlorate) + nk + = 2.9 and nclo 4- = 6 S/S o = (55.55 (1 * * 6))/55.55 = ( )/55.55 = 46.65/55.55 = 0.84 (S/S o ) Exp = /54

13 Salting-in and Salting-out log S k is negative Salting-in log (S/S o ) = k I k is positive Salting-out Ionic strength, I 13/54

14 Ion-ion interactions The non-ideal behaviour of solutes 14/54

15 Ion-ion interactions The non-ideal behaviour of solutes The deviation from ideality is given by the activity coefficient (γ): a i = activity or effective or thermodynamic concentration = γ i [i] γ i = 1 when Σ[i] = 0. or, in terms of free energy or chemical potential, (dg/dn i ) T,P = μ i = μ o i + RT ln a i = μ o i+ RT ln γ i + RT ln [i] Coulombic interactions are proportional to the charge concentration of the ions involved. The charge concentration is given by the ionic strength (I): I = ½ Σ([i]Z 2 i ) 0.7 m in seawater at S P = 35 where [i] is in molal units (mole of ions/kg H 2 O) and Z i is the charge of the ion i. 15/54

16 Debye-Hückel Theory log γ i = AZ 2 i I 1/2 /(1 + a i BI 1/2 ) where A and B are constants that depend only on the temperature and dielectric constant of the system. For water at 25 o C and 1 atm total pressure: A = x 10 6 (εt) 2/3 = mol -1/2 l 1/2 and B = x 10 8 /(εt) 1/2 = x 10 8 cm -1 mol -1/2 l 1/2 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. a i = adjustable size parameter (in angstroms or 10-8 cm) which corresponds roughly to the distance of closest approach between the centre of adjacent ions or the radius of the hydrated ion 16/54

17 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

18 Davies Equation For higher ionic strengths, the Debye-Hückel equation was modified by adding a term which takes into account non-coulombic interactions and the increase of γ with I. log γ i = AZ 2 i (I1/2 /1+BaI 1/2 ) +bi where b is a general constant ( ) 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

19 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

20 Colloids 20/54

21 Operational definition of the dissolved fraction 21/54

22 Operational definition of the dissolved fraction 0.45 µm 22/54

23 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 0.45 µm filter 23/54

24 Free vs complexed solutes (bio-assay) Effect of Cu on Bacteria Effect of Cu on Bacteria 3 H-Amino Acid Incorpotation (%) µm NTA 2 µm NTA 0 µm NTA log [Cu] T 3 H-Amino Acid Incorpotation (%) µm 2 µm 0 µm 10 9 pcu 8 7 = NTA nitrilotriacetic acid -log a(cu 2+ ) 24/54

25 Free vs complexed solutes Polarography Potentiometry/ specific ion electrodes 25/54

26 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

27 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 0.45 µm filter 27/54

28 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 H 2 CO 3 and H 3 BO 3, for which the dissociation is ph dependent. CO 2(g) + H 2 O H 2 CO 3 H 2 CO 3 H + + HCO 3 - HCO 3- H + + CO 3 2- K 1 = (H + ) (HCO 3- ) = or pk 1 = 6.38 (H 2 CO 3* ) 28/54

29 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

30 Associated electrolytes (true complexes /stability) Sequential Global constant M + A MA K 1 = [MA] = β 1 = global constant [M] [A] MA + A MA2 K 2 = [MA 2 ] & β 2 = [MA 2 ] [MA] [A] [M] [A] 2. MA n + A MA n+1 K n+1 = [MA n+1 ] & β n+1 = [MA n+1 ] [MA n ] [A] [M] [A] n+1 30/54

31 Associated electrolytes (ion-pairs) Ion-pairs result from purely electrostatic attraction between oppositely charged ions. ex: Cd 2+ + Cl - CdCl + (positive ion-pair) Hg Cl - HgCl 3- (negative ion-pair) Mg 2+ + SO 4 2- MgSO 4o (neutral ion-pair) Contact ion-pair Solvent-shared ion-pair + Solvent-separated ion-pair 31/54

32 Associated electrolytes (ion-pairs / stability) Mg 2+ + SO 4 2- MgSO 4 o K o (MgSO 4o ) = (MgSO 4o ) = [MgSO 4o ] γ(mgso 4o ) (Mg 2+ ) (SO 4 2- ) [Mg 2+ ] F [SO 4 2- ] F γ F (Mg 2+ ) γ F (SO 4 2- ) = K * (MgSO 4o ) γ(mgso 4o ) γ F (Mg 2+ ) γ F (SO 2-4 ) = 165 at 25 o C and S P = 0 32/54

33 Associated electrolytes (ion-pairs in seawater) H + Cl - Na + SO 4 2- M g 2+ H C O 3 - K + Br - Ca 2+ CO 3 2- Sr 2+ F - 33/54

34 Associated electrolytes (major ion speciation in seawater) From: Garrels and Thomson (1962) Amer. J. Science 260, /54

35 Associated electrolytes (major ion speciation in seawater) γ T (Mg 2+ ) = [Mg 2+ ] F γ F (Mg 2+ ) [Mg 2+ ] T From: Millero and Schreiber (1982) Amer. J. Science 282: /54

36 Associated electrolytes (speciation calculation) Mg 2+ + SO 4 2- MgSO 4 o K o (MgSO 4o ) = (MgSO 4o ) = [MgSO 4o ] γ(mgso 4o ) (Mg 2+ ) (SO 4 2- ) [Mg 2+ ] F [SO 4 2- ] F γ F (Mg 2+ ) γ F (SO 4 2- ) = K * (MgSO 4o ) γ(mgso 4o ) γ F (Mg 2+ ) γ F (SO 2-4 ) where (Mg 2+ ) = [Mg 2+ ] T γ T (Mg 2+ ) = [Mg 2+ ] F γ F (Mg 2+ ) from which γ T (Mg 2+ ) = [Mg 2+ ] F γ F (Mg 2+ ) [Mg 2+ ] T D-H 36/54

37 Associated electrolytes (speciation calculation) [Mg 2+ ] T = [Mg 2+ ] F + [MgSO 4o ] + [MgCO 3o ] + [MgHCO 3+ ] + [MgX1] + [MgX2] + = [Mg 2+ ] F + K*(MgSO4 o ) [Mg 2+ ] F [SO 4 2- ] F + K*(MgCO3 o ) [Mg 2+ ] F [CO 3 2- ] F + K*(MgHCO3 + ) [Mg 2+ ] F [HCO 3- ] F + K*(MgX1) [Mg 2+ ] F [X1] F + + K*(MgX2) [Mg 2+ ] F [X2] F + K*(MgX3) [Mg 2+ ] F [X3] F + [Mg 2+ ] F = 1/ ( 1 + K*(MgSO4 o ) [SO 4 2- ]F + K*(MgCO3 o ) [CO 3 2- ] F + K*(MgHCO3 + ) [HCO 3- ] F + [Mg 2+ ] T + K*(MgX1) [X1] F + K*(MgX2) [X2] F + K*(MgX3) [X3] F + ) In addition, = 1/ ( 1 + Σ K*(MgY i ) [Y i ] F ) [Y i ] F = 1/ ( 1 + Σ K*(M j Y i ) [M J ] F ) [Y i ] T K*(M j Y i ) are a function of the true ionic strength (I true ), I true < I total 37/54

38 Associated electrolytes (speciation in seawater) KSO 4 - CaHCO 3 + H + Na + HF NaSO - 4 HSO 4 - SO 4 2- MgSO 4 NaSO 4 - CaSO 4 HCO 3 - NaHCO 3 MgHCO 3 + Mg 2+ MgHCO 3 + MgSO 4 K + KSO 4 - MgCO 3 CaCO 3 NaCO 3 - MgB(OH) + 4 CaB(OH) + 4 CO 2-3 B(OH) - 4 NaB(OH) 4 Ca 2+ CaSO 4 CaHCO 3 + CaCO 3 Sr 2+ SrCO 3 SrSO 4 SrHCO + 3 F - NaF MgF + CaF + MgOH + OH - CaOH + NaOH Cations and cation ion-pairs Anions and anion ion-pairs 38/54

39 Associated electrolytes (river water vs seawater/dominant species) Metal ions River Water Seawater Cd 2+ CdCO 3 o CdCl +, CdCl 2 o Pb 2+ PbCO 3 o PbCO 3o, Pb 2+, PbCl 2o, PbCl + Zn 2+ ZnCO 3 o ZnOH +, ZnCl +, Zn 2+ Cu 2+ CuCO 3 o CuCO 3o, Cu(CO 3 ) 2 2-, Cu 2+, CuOH + PbCO 3 PbCl 2 Pb PbCl PbCl 3 PbOH CdCl CdCO HgCl 3 3 Cu CuCO 3 HgCl 2 Cu(OH) CdCl 2 3 HgCl4 CuOH CdCl 2 Cu(CO 3 ) 2 39/54

40 Associated electrolytes (speciation as a function of ph) Speciation of Fe(III) in NaCl Speciation of Al(III) in NaCl Fe 3+ FeOH 2+ Fe(OH) Al(OH) 3 - Al(OH) Al 3+ 4 Fraction Fe(OH) 2 + Fe(OH) 3 Fraction AlOH Al(OH) ph ph 40/54

41 X Metal classification X X X X X X X X 41/54

42 Metal classification These d 0 cations are ions with high spherical symmetry and electron clouds which 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. Pearsons classification 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

43 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 d 0 counterparts, they form strong complexes because they form largely covalent bonded complexes and the stability of these complexes decreases with increasing ΔEN. Pearsons classification For example, the halide complexes increase in stability with decreasing EN (or increasing atomic weight or ionic size) of the ligand. Complex log K o AgF o -0.3 AgCl o 3.0 AgBr o 4.3 AgI o 8.1 They coordinate preferentially with bases containing I, S or N as donor atoms. They form insoluble sulfides and soluble complexes with S 2- and HS - with stabilities increasing: S 2- > SH - > OH - > F -. 43/54

44 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. Pearsons classification Mn 2+ (d 5 s 2 ) < Fe 2+ (d 6 s 2 ) < Co 2+ (d 7 s 2 ) < Ni 2+ (d 8 s 2 ) < Cu 2+ (d 10 s 1 ) > Zn 2+ (d 10 s 2 ) With the exception of Cu 2+, this corresponds to the order of increasing Ip. 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

45 Interactions between metallic cations and ligands Complex log K o AgF o -0.3 AgCl o 3.0 AgBr o 4.3 AgI o /54

46 Interaction with organic ligands 46/54

47 Gibbsite solubility in the presence of oxalate From: Fein (1991: Geology 19, ) log [Al] Al 3+ Al(OH) 2+ Al(OH) + 2 Al(OH) 4 - Al(OH) ph Ʃ[Al] = [Al 3+ ] + [AlOH 2+ ] + [Al(OH) 2+ ] + [Al(OH) 3 ] + [Al(OH) 4- ] + [Al(Ox) 3 3- ] 47/54

48 Associated electrolytes (speciation of Cu(+II) in seawater) Inorganic speciation of Cu 2+ Speciation of Cu Organic speciation 2+ of Cu 2+ CuCO3 CuCO 3 CuOH + CuSO4 CuL 1 CuL 2 Cu 2+ Cu(OH)2 Cu(CO3)2 2- Cu 2+ + L1 = CuL1 K1 = Cu 2+ + L 2 = CuL 2 K 2 = a/54

49 Interaction with organic ligands 48b/54

50 Specific Interaction or Pitzer Equation ln γ M = D.H. + M-X + M-N + M-N-X MX = M-Cl + M-SO 4 + M-HCO 3 + M-N = M-Na, M-Mg, M-Ca M-N-X = M-Na-Cl, M-Na-SO 4, /54

51 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: f γ = [(I 1/2 /1+1.2I 1/2 ) + (2/1.2) ln ( I 1/2 )] 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/ 50/54

52 Single ion activity coefficients log γm 2+ γm 2+ 51/54

53 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 γ i is proportional to the ionic strength and can be represented by the Setchenow equation: log γ i = K i I 52/54

54 Activity coefficients of Neutral Species (the Setchenow (salting-out) equation) log γ i = K i I 53/54

55 Associated electrolytes (speciation in seawater) KSO 4 - CaHCO 3 + H + Na + HF NaSO - 4 HSO 4 - SO 4 2- MgSO 4 NaSO 4 - CaSO 4 HCO 3 - NaHCO 3 MgHCO 3 + Mg 2+ MgHCO 3 + MgSO 4 K + KSO 4 - MgCO 3 CaCO 3 NaCO 3 - MgB(OH) + 4 CaB(OH) + 4 CO 2-3 B(OH) - 4 NaB(OH) 4 Ca 2+ CaSO 4 CaHCO 3 + CaCO 3 Sr 2+ SrCO 3 SrSO 4 SrHCO + 3 F - NaF MgF + CaF + MgOH + OH - CaOH + NaOH Cations and cation ion-pairs Anions and anion ion-pairs 54/54