GEO 421 Petrology

Take Home Set #1

Method of calculating mole% of mineral endmembers (Question 3):

Use this diagram to plot compositions

Given a chemical analysis of a mineral, in this case plagioclase:

SiO2 = 54.4 wt.%

Al2O3=28.9

CaO=10.5

Na2O=5.57

K2O=0.35

Total: 99.7(2)

Note that you only have to deal with the cations (expressed as oxides) that define the endmembers, i.e. in this example CaO (An), Na (Ab), and K (Or). For olivine only FeO (Fa) and MgO (Fo) are used, and pyroxene uses only CaO (Wo), FeO (Fs), and MgO (En).

1. Calculate the weight of each oxide by adding up the atomic weights of that oxide:

for CaO: weight of CaO (use chemistry book or periodic table to find atomic weights) is

40.08 + 16 = 56.08 [note: weight of one Ca is 40.08; one oxygen is about 16]

for Na2O: weight of Na2O is 2(22.9) + 16 = 62 [note: Na weight must be doubled because there are 2 atoms of Na in the molecule, same for K2O below]

for K2O: weight of K2O is 2(39) + 16 = 94

2. Calculate the moles of each oxide by dividing the weight percent of each respective oxide from the analysis by the weight calculated above:

CaO: 10.5/56.08 = 0.19

Na2O: 5.57/62 = 0.09

K2O: 0.35/94 = 0.004

3. To calculate the mole fraction of each oxide, simply add the three mole values together to get a total (0.28), then divide each mole by that total:

0.19 / 0.28 = 0.68 CaO

0.09 / 0.28= 0.32 Na2O

0.004 / 0.28= 0.01 K2O

Those numbers should add up to 1.0, or close to it. Do they?

4. Write the molecular endmember values (mole fractions x 100):

An₆₈Ab₃₂Or_0.01 What name could you put on this plagioclase composition (An₆₈)?