Mineralogy Exercise 1: Calculating Mineral Formulas
The chemical compositions of minerals as reported in their chemical formulas are really Ideal compositions, based only on the proportions of their Major Element constituents. [Major elements are defined as any element occurring at >1% wt. in a mineral, and/or any element which predominantly fills a structural site in a mineral]. In the real world, however, minerals include both Minor Elements (1.0 – 0.1% wt. abundance) and Trace Elements (>0.1% wt in abundance) in their structures, and often it is very useful to know how these other elements are distributed in the mineral structure. Unfortunately, when mineral compositions are analyzed chemically and reported, the values are traditionally reported in wt.% oxides and in ppm (parts per million, = µg/g: 10,000 ppm = 1% wt.), which isn’t very enlightening as to mineral structure.
However, if we know a little bit about element valences, and the atomic structures of minerals (ala Pauling’s Rules), we can calculate their formulas from wt % data. Box 1.5 in Perkins (page 22) goes over how we do this. Below is a simplified “cookbook” for getting mineral formulas from wt% data. [Warning! The Professor is a touch dyslexic regarding multiplication and division! Did I do this right? Check it against what Perkins recommends!!]
1) Divide each oxide constituent by the formula weight of the oxide. This gives you the Molar Proportions of each oxide.
2) Multiply the molar proportions of each oxide by the number of cations in the oxide. This gives you the molar proportions of cations in your mineral.
3) Multiply the molar proportions of each oxide by the number of oxygens in each. This gives you the molar proportions of Oxygen in your mineral.
4) Sum the Molar proportions of Oxygen, and correct this sum to the number of oxygens in the mineral’s ideal chemical formula (i.e., 4 oxygens for olivine; 8 oxygens for feldspar). The value you use to make your summed oxygens equal the formula oxgyens is a Correction factor (really, a “fudge factor”) that will allow you to obtain formula units.
5) Now, multiply the Molar Proportions of each Cation by the Correction Factor. This will give you the proportions of each cation with respect to oxygen (or the “Oxygen units” of each cation) in your mineral. At this point, one can group your cations by valence and calculate the REAL mineral formula.
- A) Here are some mineral compositions in wt.% oxides. What I want you to do is use the cookbook above to generate their mineral formulas.
Oxide, %wt. | Olivine
(4 oxygens) |
Pyroxene
(6 Oxygens) |
K – Feldspar
(8 Oxygens) |
Magnesite
(6 oxygens) |
Kyanite
(20 oxygens) |
SiO_{2} | 40.65 | 52.70 | 64.28 | — | 37.46 |
TiO_{2} | — | 0.34 | — | — | 0.03 |
Al_{2}O_{3} | — | 1.84 | 19.19 | — | 61.52 |
Cr_{2}O_{3} | .007 | — | — | — | 0.08 |
Fe_{2}O_{3} | — | 2.12 | 0.09 | — | 0.71 |
FeO | 10.56 | 5.42 | — | 0.56 | — |
MgO | 48.62 | 15.15 | 0.10 | 46.62 | 0.03 |
MnO | 0.115 | 0.16 | — | 0.12 | 0.006 |
NiO | .297 | — | — | — | — |
BaO | — | — | 0.11 | 0.06 | — |
CaO | 0.019 | 21.58 | 0.11 | 0.43 | 0.02 |
K_{2}O | — | 0.01 | 15.3 | — | 0.01 |
Na_{2}O | — | 0.49 | 0.92 | — | 0.03 |
CO2 | — | — | — | 51.93 | — |