2. Stoichiometry Chemical Analyses and Formulas

3. Stoichiometry Chemical 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.

4. Oxides of Lithophile Cations SiO 2 TiO 2 (4+) Al 2 O 3 Cr 2 O 3 Fe 2 O 3 (3+) MgOMnOFeO (2+) CaO (2+) Na 2 OK 2 OH 2 O (1+)

6. Example 1 Weight percents to formula OxideWt%MolWtMolesMolesMoles OxideOxideCationOxygen SiO 2 59.8560.086.9960.99601.9920 MgO40.1540.312.9960.9960.9960 100.02.9980 Mole ratios Mg : Si : O = 1 : 1 : 3 MgSiO 3

7. Example 2 Formula to weight percents Kyanite is Al 2 SiO 5 Calculate the weight percents of the oxides SiO 2 Al 2 O 3

8. Example 2 Formula to weight percents: Kyanite: Al 2 SiO 5 OxideMolesMolWtGramsWt% PFUOxideOxidePercent SiO 2 160.08660.08637.08 Al 2 O 3 1101.963101.96362.92 Formula weight162.049

9. Example 3: Solid Solutions Weight percents to formula Alkali Feldspars may exist with any composition between NaAlSi 3 O 8 and KAlSi 3 O 8. Formula has 8 oxygens: (Na,K)AlSi 3 O 8 The alkalis may substitute in any ratio, but total alkalis to Al is 1 to 1.

10. Example 3: Solid Solutions Weight percents to formula OxideWt%MolWtMolesMolesMoles OxideOxideCationOxygen SiO 2 68.2060.0861.13501.13502.2701 Al 2 O 3 19.29101.9630.18920.3784.5676 Na 2 O10.2061.97960.16460.3291.1646 K 2 O2.3294.2040.02460.0493.0246 100.003.0269 x 2.6430= 8.000 Mole ratios Na 0.87 K 0.13 Al 1.00 Si 3.00 O 8 calculated as cations per 8 oxygens

11. Simple Solid Solutions NaAlSi 3 O 8 - KAlSi 3 O 8 Alkali Feldspars MgSiO 3 - FeSiO 3 Enstatite-Ferrosilite (pyroxene) MgCaSi 2 O 6 -FeCaSi 2 O 6 Diopside-Hedenbergite Mg 2 SiO 4 - Fe 2 SiO 4 Forsterite-Fayalite Mg 3 Al 2 Si 3 O 12 - Fe 3 Al 2 Si 3 O 12 Pyrope - Almandine

12. Example 4 Weight Percent Oxides from Formula Given the formula En 70 Fs 30 for an orthopyroxene, calculate the weight percent oxides. En = enstatite = Mg 2 Si 2 O 6 Fs = ferrosilite = Fe 2 Si 2 O 6 Formula is (Mg 0.7 Fe 0.3 ) 2 Si 2 O 6 = (Mg 1.4 Fe 0.6 )Si 2 O 6

13. Example 4 (Mg 1.4 Fe 0.6 )Si 2 O 6 Weight Percent Oxides from Formula OxideMolesMolWtGramsWt% PFUOxideOxidePercent SiO 2 260.086120.17254.69 MgO1.440.31256.43725.69 FeO0.671.84643.10819.62 Formula weight219.717100.00

14. Example 5 Weight Percent Oxides from Formula A pyroxene is a solid solution of 40% jadeite (NaAlSi 2 O 6 ) and 60% acmite (NaFeSi 2 O 6 ). Calculate the weight percent oxides Formula is Na(Al 0.4 Fe 0.6 )Si 2 O 6

15. Formula is Na(Al 0.4 Fe 0.6 )Si 2 O 6 Calculate Weight Percent Oxides OxideMolesMolWtGramsWt% PFUOxideOxidePercent SiO 2 2.060.086120.17254.76 Al 2 O 3 0.2101.96320.3939.29 Fe 2 O 3 0.3159.69247.90821.83 Na 2 O0.561.98030.99014.12 Formula weight219.463100.00

16. Coupled Substitutions Plagioclase feldspar NaAlSi 3 O 8 - CaAl 2 Si 2 O 8 Jadeite-diopside NaAlSi 2 O 6 - CaMgSi 2 O 6

17. Coupled Substitution 40% Anorthite; 60% Albite Calculate Weight percent Oxides First write the formula Anorthite is CaAl 2 Si 2 O 8 Albite is NaAlSi 3 O 8 An 40 Ab 60 is Ca.4 Na.6 Al 1.4 Si 2.6 O 8

18. OxideMolesMolWtGramsWt% PFUOxideOxidePercent SiO 2 2.660.086156.2258.17 Al 2 O 3 0.7101.96371.3726.57 CaO0.455.9622.388.33 Na 2 O0.361.98018.596.92 Formula weight268.58100.00

19. Example Given Analysis Compute Mole percents of Jadeite and Diopside Jadeite is NaAlSi 2 O 6 Diopside is CaMgSi 2 O 6

20. Jadeite - Diopside OxideWt%MolWtMolesMolesMoles OxideOxideCationOxygen SiO 2 56.64 60.086.9426.94261.8852 Al 2 O 3 7.21101.963.0707.1414.2121 MgO13.30 40.312.3299.3299.3299 CaO18.46 55.96.3299.3299.3299 Na 2 O 4.38 94.204.0246.0493.0246 99.992.8278 x 2.6430= Normalize to 8 oxygens8.000 Na.3 Ca.7 Al.3 Mg.7 Si 2 O 6 = 30% Jadeite 70% Diopside

21. Unit Cells and Mineral Density Unit cell is basic repeat unit of structure. Parallel-piped box: a, b, c (Å),  º) Å = 10 -8 cm Avogadro’s number (# atoms/mole)=6.02 x10 23 If you know the contents of the box and the size of the box you can calculate the density

22. Cell Volume (1Å 3 =10 -24 cm 3 ) CubicV = a 3 TetragonalV = a 2 c Hex/TrigonalV = a 2 c sin 120º OrthorhombicV = abc MonoclinicV = abc sin  Triclinic V = abc (1 + 2cos  cos  cos  - cos 2  - cos 2  - cos 2  ) 1/2

23. Density Volume of Avogadro’s number of unit cells = AV The number of formula units per unit cell = Z –Z is a small integer 1 to about 16. Weight of Avogadro’s number of unit cells = Z* FW

24. Example Density Calculation Calculate the density of ferberite (FeWO 4 ), which is monoclinic with a = 4.73; b = 5.70; c = 4.95;  = 90.01; Z = 2. Calculate the gram formula weight: –1 Fe (55.847) = 55.847 –1 W (183.85) = 183.85 –4 O (15.9995) 63.998 –FW =303.695 g

25. Example Density Calculation: Ferberite FeWO 4 V = abc sin  = (4.73)(5.70)(4.95)(sin 90.01º) V = 133.46 Å 3 V = 1.335 x 10 -22 cm 3  = ZFw/AV = 2 (303.70) / 6.02 10 23 *1.335 10 -22  = 7.56 g/cm 3