Presentation on theme: "Aqueous Complexes Why do we care??"— Presentation transcript:
1 Aqueous Complexes Why do we care?? Complexation of an ion also occuring in a mineral increases solubilitySome elements occur as complexes more commonly than as free ionsAdsorption of elements greatly determined by the complex it resides inToxicity/ bioavailability of elements depends on the complexation
2 Defining Complexes Use equilibrium expressions: DG0R = -RT ln Keq cC + lHL CL + lH+Where B is just like Keq!
3 Closer look at complexation Stability of complexes generally increases with increasing charge or decreasing radius ratio (i.e. factors increasing bond strength)Cations forming strong complexes with certain ligands also tend to form minerals with low solubilitiesComplexation tends to increase mineral solubility that contain the species being complexedMore salinity = more multinuclear complexes
4 Outer Sphere Complexes d+..Water’s polar nature is key:Cations are usually surrounded by H2O’sOuter-sphere complexes (aka ion pairs) – Cation complexed with an anion BUT the anion does NOT displace a water:Ca(H2O)6SO40Long-range electrostatic interactionCommonly involve mono and di-valent cations and anions like Cl-, HCO3-, SO42-, and CO32-Draw the Ca(H2O)6 ion on the board, then put in SO4…
5 Inner Sphere Complexes Inner-sphere complexes – ligand does displace the waterM(H2O)n + L- ML(H2O)n-1 + H2On for any complex is based on Pauling’s first rule (radius ratio, close packed structures)Cations get more inner-sphere as charge increases and radius decreases scales as Ionic potential, I=z/r
6 Ionization Potentialz/r (charge/radius) also relates to a surface charge density on a cation ‘surface’With increasing IP, charge density repulses H+ on H2O and forms oxycations (UO22+), hydroxycations (Fe(H2O)5OH2+), and hydroxyanions (Fe(OH)4-)This effectively displaces the equilibrium distribution as a function of pH when comparing cations of varying IP
7 Electronegativities The power of an atom or ion to attract electrons High EN (>2) = Lewis bases (nonmetals and ligands; e- donor)Low EN (<2) = Lewis acids (metal cations; e- acceptor)DEN determines bonding – covalent as DEN approaches 0 (more inner sphere), as DEN > 1.7, more ionic and outer-sphereLewis acid = e-pair-acceptor; base= e-pair donor
8 HSABClassification of cations and ligands as hard or soft acids and basesSoft species electron cloud is polarizable (deformable, soft) which prefers to participate in covalent bondingHard low polarizability, e- cloud is rigid and prefers ionic bondingHard-hard = ionic (outer sphere)Soft-soft = covalent (inner sphere)Opposite Weak bonds, rare complexes
9 Schwarzenbach Classification Considers the electronic structure of individual cations divided into 3 classes:Class A noble gas configurations (highest orbital level filled) spherical symmetry and low polarizablity – hard spheres (Na+, Al3+, Ca2+)Class B electron configurations Ni0, Pd0, Pt0, highly polarizable – soft spheres (Ag+, Zn2+, Cd2+, Hg2+, Sn4+)Class C Transition metals with 0-10 e- in the d shell, intermediate polarizabilityPolarizability – ease to which the cation’s e- cloud is deformed (ease to which the e- easily move in response to an attractive/repulsive force (presumably electrostatic)
10 ToxicityToxicity of a particular contaminant is partly based on complexation reactions Hg2+ for instance is a soft acid, forming strong bonds with sulfur sites in amino acids like methionine and cysteine, breaking down enzyme function
11 Speciation Plus more species gases and minerals!! Any element exists in a solution, solid, or gas as 1 to n ions, molecules, or solidsExample: Ca2+ can exist in solution as:Ca CaCl CaNO3+Ca(H3SiO4) CaF CaOH+Ca(O-phth) CaH2SiO CaPO4-CaB(OH) CaH3SiO CaSO4CaCH3COO CaHCO CaHPO40CaCO30Plus more species gases and minerals!!
12 Mass Action & Mass Balance mCa2+=mCa2++MCaCl+ + mCaCl20 + CaCL3- + CaHCO3+ + CaCO30 + CaF+ + CaSO40 + CaHSO4+ + CaOH+ +…Final equation to solve the problem sees the mass action for each complex substituted into the mass balance equation
13 Coupling mass action and mass balance governing equations Start with a set of basis speciesMass balance for each of those basis species (includes all complexes of one basis species with other possible basis species – Cd2+ with Cl-, OH+, SO42- for example)Using mass action for each complex in each mass balance – get an equation using only basis species to determine activity of each basis species – each secondary species then calculated based on the solution for the basis
15 Non-linearityUnknown variables (species activities and activity coefficients) are products raised to reaction coefficientsMultiple basis species – multiple equations need to be solved simulaneouslySet of values that satisfies a set of equations is called a rootIterative procedures guess at the root value and tries to improve it incrementally until it satisfies the equations to a desired accuracy
16 Newton’s Method Newton’s method – for a function f(x)=a An initial guess (x0) will yield a residual (R(x)), which is the amount that guess is still ‘off’Subsequent guesses ideally improve, resulting in a smaller residual – keep going to the root!Start atR(x)BUT – what if there is more than one root????
17 Newton - Raphson Multi-dimensional counterpart to Newton’s method Used for the multiple governing equation for each basis speciesResults in a matrix of functions where the residuals are recalculated iteratively to a small number (epsilon value in GWB, default=5e-11), the matrix, called the Jacobian matrix is n x n (where n are the number of basis species)
18 UniquenessAny set of equations that has more than one possible root can become a non-unique situationThere are several geochemical examples where 2 roots are physically realistic
19 Ionic StrengthDealing with coulombic interaction of selected ions to each other in a matrix (solution) of many ionsIonic strength is a measure of how many of those ions are in the matrix which affect how selected ions interactIonic strength (I):Where m is the molality of species i and z is the charge of species i
20 Debye-HückelAssumes ions interact coulombically, ion size does not vary with ionic strength, and ions of same sign do not interactA, B often presented as a constant, but:A= x106r01/2(T)-3/2, B=50.3 (T)-1/2Where is the dielectric constant of water and r is the density
21 Iteration and activity example Speciate a simple mix of Fe3+ and Cl-Starting analysis of Fe3+ and Cl-Calculate ICalculate gi for each ion (Fe3+, Cl-, FeCl++)Calculate activity for each ionRecalculate IRecalculate gi for each ion (Fe3+, Cl-, FeCl++)Recalculate activity for each ionUntil the residual for these reduces…
22 Geochemical ModelsStep 1: Defining the problem Define basis species, used to then distribute between all species for that element or groupAl3+ = Al3+ + Al(OH)2+ + Al(OH)2+ + Al(OH)30 + Al(NO3)2- +… OR Fe2+ = Fe2+(H2O)6 + FeCl+ + FeCl20 + FeCl3- + FeNO3+ + FeHCO3+ + …)Step 2 – Calculate the distribution of speciesStep 3 – Calculate mineral and gas equilibria, find S.I.THEN many models continue with a reaction titration (T, +/- anything), mineral +/-, gas +/-,
23 Charge BalancePrinciple of electroneutrality For any solution, the total charge of positively charged ions will equal the total charge of negatively charged ions.Net charge for any solution must = 0Charge Balance Error (CBE)Tells you how far off the analyses are (greater than 5% is not good, greater than 10% is terrible…)Models adjust concentration of an anion or cation to make the charges balance before each iteration!
24 Activity Coefficients No direct way to measure the effect of a single ion in solution (charge balance)Mean Ion Activity Coefficients – determined for a salt (KCl, MgSO4, etc.)g±KCl = [(gK)(gCl)]1/2Ksp= g±KCl2(mK+)(mCl-)MacInnes Convention gK = gCl= g±KClMeasure other salts in KCl electrolyte and substitute g±KCl in for one ion to measure the other ion w.r.t. g±KCl and g±saltDirect measurement of g can be made from solubility measurments as well as freezing point lowering, boiling point elevation, water-vapor pressure, osmotic pressure, transport properties (including conductivity and diffusion)
25 Ionic StrengthDealing with coulombic interaction of selected ions to each other in a matrix (solution) of many ionsIonic strength is a measure of how many of those ions are in the matrix which affect how selected ions interactIonic strength (I):Where m is the molality of species i and z is the charge of species i
26 Mean Ion Activity Coefficients versus Ionic Strength
27 Debye-HückelAssumes ions interact coulombically, ion size does not vary with ionic strength, and ions of same sign do not interactA, B often presented as a constant, but:A= x106r01/2(T)-3/2, B=50.3 (T)-1/2Where is the dielectric constant of water and r is the density
28 Higher Ionic Strengths Activity coefficients decrease to minimal values around m, then increasethe fraction of water molecules surrounding ions in hydration spheres becomes significantActivity and dielectric constant of water decreases in a 5 M NaCl solution, ~1/2 of the H2O is complexed, decreasing the activity to 0.8Ion pairing increases, increasing the activity effects
29 Extended Debye-Hückel Adds a correction term to account for increase of gi after certain ionic strengthTruesdell-Jones (proposed by Huckel in 1925) is similar:
30 Davies EquationLacks ion size parameter –only really accurate for monovalent ionsOften used for Ocean waters, working range up to 0.7 M (avg ocean water I)
31 Specific Ion Interaction theory Ion and electrolyte-specific approach for activity coefficientsWhere z is charge, i, m(j) is the molality of major electrolyte ion j (of opposite charge to i). Interaction parameters, (i,j,I) describes interaction of ion and electrolyte ionLimited data for these interactions and assumes there is no interaction with neutral species
32 Pitzer ModelAt ionic strengths above 2-3.5, get +/+, -/- and ternary complexesTerms above describe binary term, fy describes interaction between same or opposite sign, terms to do this are called binary virial coefficientsTernary terms and virial coefficients refine this for the activity coefficient
33 Setchenow Equation log gi=KiI For molecular species (uncharged) such as dissolved gases, weak acids, and organic speciesKi is determined for a number of important molecules, generally they are low, below 0.2 activity coefficients are higher, meaning mi values must decline if a reaction is at equilibrium “salting out” effect