Question

The mole fraction of jadeite in the pyroxene of composition (Ca$_{0.667}$Na$_{0.333}$Fe$^{2+}_{0.12}$Fe$^{3+}_{0.125}$Mg$_{0.546}$Al$_{0.208}$)Si$_2$O$_6$ is .................. [round off to 3 decimal places]

Hint:

In pyroxenes, jadeite content is estimated from Na in the formula. If Na = 0.33 pfu, the mole fraction of jadeite is 0.333.

Answer 1

Step 1: Recall jadeite formula.
Jadeite = NaAlSi$_2$O$_6$ → requires Na in M2 site and Al in M1 site.

Step 2: Given composition.
(Ca$_{0.667}$Na$_{0.333}$Fe$^{2+}_{0.12}$Fe$^{3+}_{0.125}$Mg$_{0.546}$Al$_{0.208}$)Si$_2$O$_6$.

Step 3: Identify Na and Al contributions.
- Na = 0.333 mol. - Al = 0.208 mol. Jadeite component is controlled by Na occupancy since jadeite requires 1 Na and 1 Al per formula unit.

Step 4: Calculate mole fraction.
Na = 0.333 → fraction = 0.333.

Final Answer: \[ \boxed{0.333} \]