Question

In the garnet formula \( \text{(Fe}_{2.5}\text{Mg}_{0.3}\text{Ca}_x\text{)}\text{Al}_2\text{Si}_3\text{O}_{12} \), x represents the number of atoms of Ca. The mole % of grossular in the garnet is ........... (answer in one decimal place).
 

Hint:

The mole % of a component in a mineral can be calculated by dividing the number of atoms of that component by the total number of atoms and multiplying by 100.

Answer 1

Correct Answer: 6.6 - 6.8

Garnet has 3 divalent cations in the X-site:
\[\text{Fe} + \text{Mg} + \text{Ca} = 3\]

Given:
\[\text{Fe}_{2.5}\text{Mg}_{0.3}\text{Ca}_x\]
\[x = 3 - (2.5 + 0.3) = 0.2\]

So Ca = 0.2 atoms per formula unit.

Mole % of grossular (Ca₃Al₂Si₃O₁₂):

\[\text{Mol \% Gr} = \frac{\text{Ca}}{3} \times 100 = \frac{0.2}{3} \times 100 = 6.67\%\]

Answer: 6.67