SME
Physical Geology · Problem type
A silicate structure’s formula and charge
Use this for “Amphiboles are double chains sharing 2.5 oxygens per tetrahedron. Find the unit with 4 Si and its charge.”
Diagram
A double chain (amphiboles): each tetrahedron shares 2.5 of its 4 oxygens.
O
per
Si
=
4
−
2.5
2
=
2.75.
In the box: O = 4 × 2.75 = 11.
Charge = −4 × (4 − 2.5) = −6: Si₄O₁₁⁶⁻.
This is an example. Choose your own values to start a new problem.
O
=
n
(4
−
s
÷
2)
z
=
−
n
(4
−
s
)
k
Oxygens per Si
worked out (not typed)
Formulas
k
=
4
−
s
2
2.75
=
4
−
2.5
2
O
=
n
×
k
11 = 4 × 2.75
z
=
−
n
×
(4
−
s
)
−6 = −4 × (4 − 2.5)
Assumptions
•
Each shared O is split between two tetrahedra, so it counts ½ in each.
•
Si is +4 and O is −2; sharing more oxygens leaves less charge for metal ions to balance.
•
Ring and single-chain silicates both share 2 oxygens per tetrahedron.
Step-by-step
WE KNOW
s = 2.5, n = 4
FIND
oxygens per Si (k), oxygens in the unit (O), charge of the unit (z)
Step 1 · Find oxygens per Si (k)
Use k = 4 − s ÷ 2
Each tetrahedron keeps its unshared oxygens whole and half of each shared one.
k
=
4
−
2.5
2
k
=
4
−
1.25
k
=
2.75
Step 2 · Find oxygens in the unit (O)
Use O = n × k
The
unit
holds
n
tetrahedra’
s
worth
of
oxygens.
O
=
4
×
2.75
O
=
11
Step 3 · Find charge of the unit (z)
Use z = −n × (4 − s)
Each
Si
is
+4
and
its
oxygens
−2
×
(4
−
s
2
),
which
leaves
−(4
−
s
)
per
Si.
z
=
−4
×
(4
−
2.5)
z
=
−4
×
1.5
z
=
−6
Check
Put the numbers back in. Both sides should match.
2.75
=
4
−
2.5
2
✓
11 = 4 × 2.75 ✓
−6 = −4 × (4 − 2.5) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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