Activity IIActivity CoefficientsEquilibrium ConstantEquilibrium constantsSolubility Product ConstantIon Activity ProductSaturation IndexCalculating KeqUsing Keq to define equilibrium concentrationsThis is the law of mass action!Summation of reaction-thermodynamic propertiesSlide 12Mineral ChemistryPauling’s Rules for ionic structuresSlide 15Slide 16Slide 17Isoelectronic seriesSlide 19Goldschmidt’s rules of SubstitutionSlide 21Goldschmidt’s rules updated…FeS2Coupled SubstitutionSlide 25Goldschmidt’s ClassificationsSlide 27Slide 28Activity II•For solids or liquid solutions:ai=Xii•For gases:ai=Pii = fi•For aqueous solutions:ai=miiXi=mole fraction of component iPi = partial pressure of component imi = molal concentration of component iActivity Coefficients•Debye-Huckel approximation:•Where A and B are constants (depending on T, see table 10.3 in your book), and a is a measure of the effective diameter of the ion (table 10.4)21212logaBIIIAz2izmIiiEquilibrium ConstantGR – G0R = RT ln QAT equilibrium, GR=0, therefore:G0R = -RT ln Keqwhere Keq is the equilibrium constantEquilibrium constantsG0R = -RT ln KRearrange:ln K = -G0R / RTFind K from thermodynamic data for any reaction•Q is also found from the activities of the specific minerals, gases, and species involved in a reaction (in turn affected by the solution they are in)RTGReK0ininproductsQ]react ants[][Solubility Product Constant•For mineral dissolution, the K is Ksp, the solubility product constant•Use it for a quick look at how soluble a mineral is, often presented as pK (table 10.1)G0R = -RT ln Ksp•Higher values  more solubleCaCO3(calcite)  Ca2+ + CO32-Fe3(PO4)2*8H2O  3 Fe2+ + 2 PO43- + 8 H2OIon Activity Product•For reaction aA + bB  cC + dD:•For simple mineral dissolution, this is only the product of the products  activity of a solid phase is equal to oneCaCO3  Ca2+ + CO32-IAP = [Ca2+][CO32-]    1dcDCIAP       badcBADCIAP eqRKQRTG lnSaturation Index•When GR=0, then ln Q/Keq=0, therefore Q=Keq.•For minerals dissolving in water:•Saturation Index (SI) = log Q/K or IAP/Keq•When SI=0, mineral is at equilibrium, when SI<0 (i.e. negative), mineral is undersaturatedeqoRKQRTG lneqRKQRTG log303.20Calculating KeqG0R = -RT ln Keq•Look up G0i for each component in data tables (such as Appendix F3-F5 in your book)•Examples:•CaCO3(calcite) + 2 H+  Ca2+ + H2CO3(aq)•CaCO3(aragonite) + 2 H+  Ca2+ + H2CO3(aq)•H2CO3(aq)  H2O + CO2(aq)•NaAlSiO4(nepheline) + SiO2(quartz)  NaAlSi3O8(albite))reactants()(000iiiiiiRGnproductsGnGUsing Keq to define equilibrium concentrationsG0R = -RT ln Keq•Keq sets the amount of ions present relative to one another for any equilibrium conditioninineqreactantspro ductsQK][][AT EquilibriuminineqreactantsproductsK][][•If the system is at equilibrium, then the ratio is a constant •Example: CaCO3(calcite)  Ca2+ + CO32-•pK=8.4, T=25, Ca2+ = CO32-  what’s the concentration of Ca2+??•What if there is already some CO32- there? Ca2+ ≠ CO32- This is the law of mass action!Summation of reaction-thermodynamic properties•Can sum a set of reactions (cancelling out equivalent terms on opposite sides) to form a new reaction, and derive that reaction’s Keq from it’s constituents…•Consider rxn: CaCO3(calcite) + CO2(g) + H2O = Ca2+ + 2 HCO3- –SUM of reactions: •CaCO3(calcite) = Ca2+ + CO32- •CO2(g) + H2O = H2CO30•H2CO30 = H+ + HCO3-•H+ + CO32- = HCO3-log Keq•CaCO3(calcite) = Ca2+ + CO32- -8.48•CO2(g) + H2O = H2CO30-1.47•H2CO30 = H+ + HCO3--6.35•H+ + CO32- = HCO3-+10.33CaCO3(calcite) + CO2(g) + H2O = Ca2+ + 2 HCO3- -5.97Another way to do this is to simply combine the Keq data algebraically:212KKKKKCOcalciteeqStill another way is recompute the G0R for the reaction of interest and calculate KeqMineral ChemistryHow could we describe the complete chemistry of a mineral or rock?What processes affect how this complete chemistry might change?Pauling’s Rules for ionic structures1. Radius Ratio Principle – •cation-anion distance can be calculated from their effective ionic radii•cation coordination depends on relative radii between cations and surrounding anions•Geometrical calculations reveal ideal Rc/Ra ratios for selected coordination numbers•Larger cation/anion ratio yields higher C.N.  as C.N. increases, space between anions increases and larger cations can fit•Stretching a polyhedra to fit a larger cation is possiblePauling’s Rules for ionic structures2. Electrostatic Valency Principle–Bond strength = ion valence / C.N.–Sum of bonds to an ion = charge on that ion–Relative bond strengths in a mineral containing >2 different ions:•Isodesmic – all bonds have same relative strength•Anisodesmic – strength of one bond much stronger than others – simplify much stronger part to be an anionic entity (SO42-, NO3-, CO32-)•Mesodesmic – cation-anion bond strength = ½ charge, meaning identical bond strength available for further bonding to cation or other anionPauling’s Rules for ionic structures3. Sharing of edges or faces by coordinating polyhedra is inherently unstable–This puts cations closer together and they will repel each otherPauling’s Rules for ionic structures4. Cations of high charge do not share anions easily with other cations due to high degree of repulsion5. Principle of Parsimony – Atomic structures tend to be composed of only a few distinct components – they are simple, with only a few types of ions and bonds.Isoelectronic series•Ions of different elements with equal numbers of electrons are said to be isoelectronic•Example: Al3+, Si4+, P5+, S6+, Cl7+ each have how many e-??•Size patterns can be related to the concept of shielding vs. electrostatic interaction•For any element – how would charge and size be related??Goldschmidt’s rules of Substitution1. The ions of one element can extensively replace those of another in ionic crystals if their radii differ by less than about 15%2. Ions whose charges differ by one may substitute readily if electrical neutrality is maintained – if charge differs by more than one, substitution is minimal3. When 2 ions can occupy a particular position in a lattice, the ion with the higher ionic potential