SME
Mineralogy · Problem type
Plagioclase An content and charge balance
Use this for “A plagioclase has 0.6 Ca and 0.4 Na per 8 oxygens. Name it and balance its charge.”
Diagram
Or = 0%, Ab = 40%, An = 60% of Or + Ab + An.
An
Ab + An
=
60%.
The point's field: labradorite (plagioclase, An₅₀–An₇₀).
This is an example. Type your own values to start a new problem.
An
%
=
100
×
Ca
÷
(
Ca
+
Na
)
Al
Aluminum per 8 O
worked out (not typed)
Si
Silicon per 8 O
worked out (not typed)
charge
Cation charge
worked out (not typed)
Formulas
Ca + Na = 1
0.6 + 0.4 = 1
An
=
100
×
Ca
Ca + Na
60
=
100
×
0.6
0.6 + 0.4
Al = 1 + Ca
1.6 = 1 + 0.6
Si = 3 − Ca
2.4 = 3 − 0.6
charge = Na + 2 × Ca + 3 × Al + 4 × Si
16 = 0.4 + 2 × 0.6 + 3 × 1.6 + 4 × 2.4
Assumptions
•
Plagioclase runs from NaAlSi₃O₈ to CaAl₂Si₂O₈: Ca and Na share one site, so Ca + Na = 1 per 8 oxygens.
•
Ca²⁺ for Na⁺ is paid for by Al³⁺ for Si⁴⁺ (coupled substitution), so the cations stay at +16.
•
The plagioclase names split the An scale at 10, 30, 50, 70 and 90%.
Step-by-step
WE KNOW
Ca = 0.6
FIND
sodium per 8 O (Na), anorthite content (An), aluminum per 8 O (Al), silicon per 8 O (Si), cation charge (charge)
Step 1 · Find sodium per 8 O (Na)
Use Ca + Na = 1
Ca and Na fill one site between them.
Na = 1 − Ca
Na = 1 − 0.6
Na = 0.4
Step 2 · Find anorthite content (An)
Use An = 100 × Ca ÷ (Ca + Na)
The anorthite content is the calcium share of the site.
An
=
100
×
0.6
0.6 + 0.4
An = 100 × 0.6
An = 60% → 50 < 60 ≤ 70: labradorite.
Step 3 · Find aluminum per 8 O (Al)
Use Al = 1 + Ca
Each Ca brings one more Al in place of Si.
Al = 1 + 0.6
Al = 1.6
Step 4 · Find silicon per 8 O (Si)
Use Si = 3 − Ca
Each Ca takes one Si away.
Si = 3 − 0.6
Si = 2.4
Step 5 · Find cation charge (charge)
Use charge = Na + 2 × Ca + 3 × Al + 4 × Si
The cations’ charge must balance 8 oxygens at −2 each: 16.
charge = 0.4 + 2 × 0.6 + 3 × 1.6 + 4 × 2.4
charge = 0.4 + 1.2 + 4.8 + 9.6
charge = 16
Check
Put the numbers back in. Both sides should match.
0.6 + 0.4 = 1 ✓
60
=
100
×
0.6
0.6 + 0.4
✓
1.6 = 1 + 0.6 ✓
2.4 = 3 − 0.6 ✓
16 = 0.4 + 2 × 0.6 + 3 × 1.6 + 4 × 2.4 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.