MINERAL FORMULA CALCULATIONS. Sarah Lambart
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1 MINERAL FORMULA CALCULATIONS Sarah Lambart
2 RECAP CHAP 7: NON-SILICATE MINERALS Part 1: Native element Part 2: Sulphides and related minerals Part 3 : Oxides, Hydrs and Halides Part 4: Carbonates, Sulphates and Phosphates
3 RECAP CHAP 7: NON-SILICATE MINERALS Part 1: Native elements Rare: 2ppm of Earth s crust Close-packing Metal, semimetal, non metal Metal: gold group, platinum group and iron group Occurrences: Au & Ag hydrothermal; Cu mafic rock; Pt & Diamond: ultramafic; graphite sedimentary metamorphic rock; Sulfur fumaroles & salt domes
4 RECAP CHAP 7: NON-SILICATE MINERALS Part 2: Sulfides and related elements Large group: 600 minerals Most common source: hydrothermal deposits most common ore source M p X r : - M is a metal or semimetal - X can be: S, As, S+As, Te
5 RECAP CHAP 7: NON-SILICATE MINERALS Part3: s, hydrs and halides Oxides: Metals + oxygen X 2 O group (X = H or Cu) Spinel group: XY 2 O 4 (Y= Al, Cr or Fe) X 2 O 3 group: Hematite (Fe 2 O 3 ), Ilmenite (FeTiO 3 ), Corundum (Al 2 O 3 ) XO 2 group: rutile (TiO 2 )
6 RECAP CHAP 7: NON-SILICATE MINERALS Hydrs: Brucite (Mg(OH) 2 ) and gibbsite (Al(OH) 3 ) OH - : arrange in planes Cation (Mg or Al): octahedral sites between the anion planes Halides: Halite (NaCl), Fluorite (CaF 2 ), Sylvite (KCl) NaCl and KCl: isostructural 2 fcc interconnected found in evaporites CaF 2 : layer of anions with cations in cubic sites between the layers found in hydrothermal deposits
7 RECAP CHAP 7: NON-SILICATE MINERALS Part 4: Carbonates, phosphates, sulfates Carbonates: ~170 minerals 4 Groups: calcite & dolomite (= rhombohedral carbonates), aragonite and hydrated carbonates Sulfates: Gypsum, anhydrite and barite Phosphates: Apatite, monazite and xenotime
8 MINERAL FORMULA CALCULATIONS Chemical analyses are usually reported in weight percent of elements or elemental s To calculate mineral formula requires transforming weight percent into atomic percent or molecular percent
9 ION COMPLEXES OF IMPORTANT CATIONS (cation valence in parentheses) SiO 2 TiO 2 (+4) Al 2 O 3 Cr 2 O 3 Fe 2 O 3 (+3) MgO MnO FeO CaO(+2) Na 2 O K 2 O H 2 O (+1)
10 EXAMPLE 1: WEIGHT PERCENT TO FORMULA Oxide wt. % MolWt Moles Moles cation Mole oxygen SiO * *0.996 = MgO Total * 59.85/ Mole ratio Mg:Si:O = 1:1:3 Formula: MgSiO 3 : enstatite
11 EXAMPLE 2: FORMULA TO WEIGHT PERCENTS Kyanite: Al 2 SiO 5 What are the weight percent of the s SiO 2 & Al 2 O 3? Oxide Mole PFU MolWt Gramm wt. % SiO * Al 2 O Total * / *100
12 PROBLEM 1: SOLID SOLUTION WEIGHT PERCENT TO FORMULA Alkali Feldspars may exist with any composition between NaAlSi 3 O 8 (Albite) and KAlSi 3 O 8 (Sanidine, Orthoclase and Microcline) Formula has 8 oxygens: (Na,K)AlSi 3 O 8 The alkalis may substitute in any ratio, but total alkalis (Na + K) to Al is 1 to 1.
13 PROBLEM 1: SOLID SOLUTION WEIGHT PERCENT TO FORMULA Oxide wt. % MolWt Moles Moles cation Mole oxygen SiO Al 2 O Na 2 O K 2 O 2.32 Total 100
14 PROBLEM 1: SOLID SOLUTION WEIGHT PERCENT TO FORMULA Oxide wt. % MolWt Moles Moles cation Mole oxygen SiO Al 2 O Na 2 O K 2 O Total * Mole ratio Si ~3, Al~1, Na~0.87, K~0.13 (Na+K~1) Formula: (Na.87 K.13 )AlSi 3 O8 Moles cations for 8O
15 PROBLEM 1: SOLID SOLUTION WEIGHT PERCENT TO FORMULA Various simple solid solutions: Alkali Feldspars: NaAlSi 3 O 8 - KAlSi 3 O 8 Orthopyroxenes: MgSiO 3 - FeSiO 3 Enstatite - Ferrosilite (opx) MgCaSi 2 O 6 -FeCaSi 2 O 6 Diopside-Hedenbergite (cpx) Olivines: Mg 2 SiO 4 - Fe 2 SiO 4 Forsterite - Fayalite Garnets: Mg 3 Al 2 Si 3 O 12 - Fe 3 Al 2 Si 3 O 12 Pyrope - Almandine
16 EXAMPLE 3: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Given the formula En 70 Fs 30 for an orthopyroxene, calculate the weight percent s En = Enstatite = MgSiO 3 Fs = Ferrosilite = FeSiO 3
17 EXAMPLE 3: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Given the formula En 70 Fs 30 for an orthopyroxene, calculate the weight percent s En = Enstatite = MgSiO 3 Fs = Ferrosilite = FeSiO 3 Formula is (Mg 0.7 Fe 0.3 )SiO 3
18 EXAMPLE 3: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Formula is (Mg 0.7 Fe 0.3 )SiO 3 Oxide Mole PFU MolWt Gramm wt. % MgO FeO SiO Total
19 PROBLEM 2: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Consider a Pyroxene solid solution of 40% Jadeite (NaAlSi 2 O 6 ) and 60% Aegirine (NaFeSi 2 O 6 ). Calculate the weight percent s
20 PROBLEM 3: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Formula is Na(Al 0.4 Fe 0.6 )Si 2 O 6 Oxide Mole PFU MolWt Gramm wt. %
21 PROBLEM 3: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Formula is Na(Al 0.4 Fe 0.6 )Si 2 O 6 Oxide Mole PFU MolWt Gramm Na 2 O wt. % Fe 2 O 3 Al 2 O 3 SiO 2 Total
22 PROBLEM 3: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Formula is Na(Al 0.4 Fe 0.6 )Si 2 O 6 Oxide Mole PFU MolWt Gramm wt. % Na 2 O Fe 2 O Al 2 O SiO Total
23 PROBLEM 4: SOLID SOLUTION WITH COUPLED SUBSTITUTIONS FORMULA TO WT.% Examples: Plagioclase Feldspar CaAl 2 Si 2 O 8 - NaAlSi 3 O 8 Jadeite - Diopside NaAlSi 2 O 6 - CaMgSi 2 O 6 Consider a feldspar composition with 40% Anorthite and 60% Albite. Calculate Weight percent Oxides.
24 PROBLEM 4: SOLID SOLUTION WITH COUPLED SUBSTITUTIONS FORMULA TO WT.% 40% Anorthite and 60% Albite. 1 st step: write the formula 40% CaAl 2 Si 2 O 8 60% NaAlSi 3 O 8 Ca 0.4 Na 0.6 Al 1.4 Si 2.6 O 8 Note: - Silica (0.4 x 2 Silica in Anorthite) + (0.6 x 3 in Albite) = Aluminum (0.4 x 2 Aluminum in Anorthite) + (0.6 x 1 in Albite) = 1.4
25 PROBLEM 4: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Formula is Ca 0.4 Na 0.6 Al 1.4 Si 2.6 O 8 Oxide Mole PFU MolWt Gramm Na 2 O 0.3 wt. % CaO 0.4 Al 2 O SiO Total
26 PROBLEM 3: SOLID SOLUTION - FORMULA TO WEIGHT PERCENTS Formula is Ca 0.4 Na 0.6 Al 1.4 Si 2.6 O 8 Oxide Mole PFU MolWt Gramm wt. % Na 2 O CaO Al 2 O SiO Total
27 PROBLEM 5: SOLID SOLUTION WEIGHT PERCENT TO FORMULA We are given the following chemical analysis of a pyroxene. Compute its formula: (Hint: Jadeite NaAlSi 2 O 6 Diopside: CaMgSi 2 O 6 ) Oxide wt. % MolWt Moles Moles cation Mole oxygen SiO Na 2 O 4.38 Al 2 O MgO CaO Total 100
28 PROBLEM 5: SOLID SOLUTION WEIGHT PERCENT TO FORMULA We are given the following chemical analysis of a pyroxene. Compute its formula: (Hint: Jadeite NaAlSi 2 O 6 Diopside: CaMgSi 2 O 6 ) Oxide wt. % MolWt Moles Moles cation Mole oxygen SiO Na 2 O Al 2 O MgO CaO Prop cations to O6 Total Na.3 Ca.7 Mg.7 Al.3 Si 2 O 6
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