How Many Molecules?StoichiometryChemical FormulasGoldschmidt’s rules of SubstitutionSlide 5Slide 6Compositional diagramsSlide 8Minor, trace elementsNormalizationSlide 11Normalization exampleSlide 13How Many Molecules?•Pyrite Cube weighs 778 g – how many molecules is that??About 4,000,000,000,000,000,000,000,000Are they ALL Iron and Sulfur?Stoichiometry•Some minerals contain varying amounts of 2+ elements which substitute for each other•Solid solution – specific elements substitute for each other in the mineral structure, defined in terms of the end members – species which contain 100% of one of the elementsChemical Formulas•Subscripts represent relative numbers of elements present•(Parentheses) separate complexes or substituted elements that go into a particular place–Fe(OH)3 – Fe bonded to 3 separate OH groups–(Mg, Fe)SiO4 – Olivine group – mineral composed of 0-100 % of Mg, 100-Mg% FeGoldschmidt’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 charge density forms a stronger bond with the anions surrounding the site4. Substitution may be limited when the electronegativities of competing ions are different, forming bonds of different ionic characterGoldschmidt’s rules of Substitution•KMg3(AlSi3O10)(OH)2 - phlogopite•K(Li,Al)2-3(AlSi3O10)(OH)2 – lepidolite•KAl2(AlSi3O10)(OH)2 – muscovite•Amphiboles:•Ca2Mg5Si8O22(OH)2 – tremolite•Ca2(Mg,Fe)5Si8O22(OH)2 –actinolite•(K,Na)0-1(Ca,Na,Fe,Mg)2(Mg,Fe,Al)5(Si,Al)8O22(OH)2 - HornblendeActinolite series mineralsCompositional diagramsFe OFeOwustiteFe3O4magnetiteFe2O3hematiteA1B1C1xA1B2C3ACBxFeMgSifayalite forsteriteenstatiteferrosilitePyroxene solid solution MgSiO3 – FeSiO3 Olivine solid solution Mg2SiO4 – Fe2SiO4Fe MgforsteritefayaliteMinor, trace elements•Because a lot of different ions get into any mineral’s structure as minor or trace impurities, strictly speaking, a formula could look like:•Ca0.004Mg1.859Fe0.158Mn0.003Al0.006Zn0.002Cu0.001Pb0.00001Si0.0985Se0.002O4•One of the ions is a determined integer, the other numbers are all reported relative to that one.Normalization•Analyses of a mineral or rock can be reported in different ways:–Element weight %- Analysis yields x grams element in 100 grams sample–Oxide weight % because most analyses of minerals and rocks do not include oxygen, and because oxygen is usually the dominant anion - assume that charge imbalance from all known cations is balanced by some % of oxygen–Number of atoms – need to establish in order to get to a mineral’s chemical formula•Technique of relating all ions to one (often Oxygen) is called normalizationNormalization•Be able to convert between element weight %, oxide weight %, and # of atoms•What do you need to know in order convert these?–Element’s weight atomic mass (Si=28.09 g/mol; O=15.99 g/mol; SiO2=60.08 g/mol)–Original analysis–Convention for relative oxides (SiO2, Al2O3, Fe2O3 etc) based on charge neutrality of complex with oxygen (using dominant redox species)Normalization example•Start with data from quantitative analysis: weight percent of oxide in the mineral•Convert this to moles of oxide per 100 g of sample by dividing oxide weight percent by the oxide’s molecular weight•‘Fudge factor’ is process called normalization – where we divide the number of moles of one thing by the total moles all species/oxides then are presented relative to one anotherFeldspar analysis(Ca, Na, K)1(Fe, Al, Si)4O8oxideAtomic weight of oxide (g/mol)# cations in oxide# of O2- in oxideOxide wt % in the mineral (determined by analysis)# of moles of oxide in the mineralmole % of oxides in the mineralCationmoles of cations in samplemoles of O2- contributed by each cationNumber of moles of ion in the mineralSiO260.08 1 2 65.90 1.09687 73.83Si4+73.83 147.66 2.95Al2O3101.96 2 3 19.45 0.19076 12.84Al3+25.68 38.52 1.03Fe2O3159.68 2 3 1.03 0.00645 0.43 Fe3+ 0.87 1.30 0.03CaO 56.08 1 1 0.61 0.01088 0.73 Ca2+ 0.73 0.73 0.03Na2O 61.96 2 1 7.12 0.11491 7.73 Na+ 15.47 7.73 0.62K2O 94.20 2 1 6.20 0.06582 4.43 K+ 8.86 4.43 0.35SUM 1.48569 100 125.44 200.38# of moles Oxygen choosen: 8Ca0.73Na15.47K8.86Fe0.87Al25.68Si73.83O200.38Ca0.03Na0.62K0.35Fe0.03Al1.03Si2.95O8to get here from formula above, adjust by 8 /
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