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StoichiometryChemical Analyses and Formulas

StoichiometryChemical analyses of oxygen bearing minerals are given as weight percents of oxides.

We need to be able to recalculate oxide analyses to cations per given number of oxygens to derive a chemical formula.

Oxides of Lithophile CationsSiO2TiO2 (4+)Al2O3Cr2O3Fe2O3 (3+)MgOMnOFeO (2+)CaO (2+)Na2OK2OH2O (1+)

Example 1Weight percents to formulaOxideWt%MolWtMolesMolesMoles OxideOxideCationOxygen

SiO259.8560.086.9960.99601.9920MgO40.1540.312.9960.9960.9960 100.02.9980

Mole ratios Mg : Si : O = 1 : 1 : 3MgSiO3

Example 2 Formula to weight percentsKyanite is Al2SiO5Calculate the weight percents of the oxidesSiO2Al2O3

Example 2 Formula to weight percents:Kyanite: Al2SiO5OxideMolesMolWtGramsWt% PFUOxideOxidePercentSiO2160.08660.08637.08Al2O31101.963101.96362.92Formula weight162.049

Example 3: Solid SolutionsWeight percents to formulaAlkali Feldspars may exist with any composition between NaAlSi3O8 and KAlSi3O8.Formula has 8 oxygens: (Na,K)AlSi3O8The alkalis may substitute in any ratio, but total alkalis to Al is 1 to 1.

Example 3: Solid SolutionsWeight percents to formulaOxideWt%MolWtMolesMolesMoles OxideOxideCationOxygen

SiO268.2060.0861.13501.13502.2701Al2O319.29101.9630.18920.3784.5676Na2O10.2061.97960.16460.3291.1646K2O2.3294.2040.02460.0493.0246 100.003.0269 x 2.6430= 8.000Mole ratios Na 0.87 K 0.13 Al 1.00 Si 3.00 O8calculated as cations per 8 oxygens

Simple Solid SolutionsNaAlSi3O8 - KAlSi3O8 Alkali Feldspars

MgSiO3- FeSiO3 Enstatite-Ferrosilite (pyroxene)MgCaSi2O6-FeCaSi2O6 Diopside-HedenbergiteMg2SiO4- Fe2SiO4 Forsterite-FayaliteMg3Al2Si3O12- Fe3Al2Si3O12 Pyrope - Almandine

Example 4 Weight Percent Oxides from FormulaGiven the formula En70Fs30 for an orthopyroxene, calculate the weight percent oxides.En = enstatite = Mg2Si2O6Fs = ferrosilite = Fe2Si2O6Formula is (Mg0.7Fe0.3)2Si2O6 = (Mg1.4Fe0.6)Si2O6

Example 4 (Mg1.4Fe0.6)Si2O6 Weight Percent Oxides from FormulaOxideMolesMolWtGramsWt% PFUOxideOxidePercentSiO2260.086120.17254.69MgO1.440.31256.43725.69FeO0.671.84643.10819.62

Formula weight219.717100.00

Example 5Weight Percent Oxides from FormulaA pyroxene is a solid solution of 40% jadeite (NaAlSi2O6) and 60% acmite (NaFeSi2O6). Calculate the weight percent oxidesFormula is Na(Al0.4Fe0.6)Si2O6

Formula is Na(Al0.4Fe0.6)Si2O6Calculate Weight Percent OxidesOxideMolesMolWtGramsWt% PFUOxideOxidePercentSiO22.060.086120.17254.76Al2O30.2101.96320.3939.29Fe2O30.3159.69247.90821.83Na2O0.561.98030.99014.12Formula weight219.463100.00

Coupled SubstitutionsPlagioclase feldspar NaAlSi3O8 - CaAl2Si2O8Jadeite-diopside NaAlSi2O6 - CaMgSi2O6

Coupled Substitution40% Anorthite; 60% Albite Calculate Weight percent OxidesFirst write the formulaAnorthite is CaAl2Si2O8Albite is NaAlSi3O8An40 Ab60 is Ca.4Na.6Al1.4Si2.6O8

An40 Ab60 is Ca.4Na.6Al1.4Si2.6O8

OxideMolesMolWtGramsWt% PFUOxideOxidePercentSiO22.660.086156.2258.17Al2O30.7101.96371.3726.57CaO0.455.9622.388.33Na2O0.361.98018.596.92Formula weight268.58100.00

Example Given AnalysisCompute Mole percents of Jadeite and DiopsideJadeite is NaAlSi2O6Diopside is CaMgSi2O6

Jadeite - DiopsideOxideWt%MolWtMolesMolesMoles OxideOxideCationOxygen

SiO256.64 60.086.9426.94261.8852Al2O3 7.21101.963.0707.1414.2121MgO13.30 40.312.3299.3299.3299CaO18.46 55.96.3299.3299.3299Na2O 4.38 94.204.0246.0493.0246 99.992.8278 x 2.6430=Normalize to 8 oxygens8.000Na.3Ca.7Al.3Mg.7 Si2O6 =30% Jadeite 70% Diopside

Unit Cells and Mineral DensityUnit cell is basic repeat unit of structure.Parallel-piped box: a, b, c (), a, b, g () = 10-8cmAvogadros number (# atoms/mole)=6.02 x1023If you know the contents of the box and the size of the box you can calculate the density

Cell Volume (13=10-24 cm3)CubicV = a3TetragonalV = a2cHex/TrigonalV = a2c sin 120OrthorhombicV = abcMonoclinicV = abc sin bTriclinicV = abc (1 + 2cos a cos b cos g - cos2a - cos2b - cos2g)1/2

DensityVolume of Avogadros number of unit cells = AVThe number of formula units per unit cell = ZZ is a small integer 1 to about 16. Weight of Avogadros number of unit cells = Z* FW

Example Density Calculation Calculate the density of ferberite (FeWO4), which is monoclinic with a = 4.73; b = 5.70; c = 4.95; b = 90.01; Z = 2.Calculate the gram formula weight:1 Fe (55.847) = 55.8471 W (183.85) = 183.854 O (15.9995) 63.998FW =303.695 g

Example Density Calculation:Ferberite FeWO4V = abc sin b = (4.73)(5.70)(4.95)(sin 90.01)V = 133.46 3V = 1.335 x 10-22 cm3 r = ZFw/AV = 2 (303.70) / 6.02 1023 *1.335 10-22 r = 7.56 g/cm3