The following table provides the mineral chemistry of a garnet. All oxides are in weight percentage and cations in atoms per formula unit. Total oxygen is taken as 12 based on the ideal garnet formula. Consider Fe as Fetotal and Fe\(^{3+}\) = 0. The Xpyrope of this garnet is _.
Show Hint
To calculate the mole fraction of pyrope, divide the number of Mg atoms by the total number of Mg and Fe atoms in the garnet structure.
Step 1: Determine the mole fraction of pyrope (Xpyrope)
The mole fraction of pyrope (Xpyrope) in garnet is determined by the amount of pyrope (Mg-Fe) component in the garnet. The formula for pyrope is:
\[
{Xpyrope} = \frac{[{Mg in the garnet}]}{[{Mg in the garnet}] + [{Fe in the garnet}]}
\]
Step 2: Calculate the total cations of Mg and Fe
- From the given cation data, the number of atoms per formula unit (apfu) for Mg is 1.221 and for Fe is 1.666.
Step 3: Calculate the mole fraction of pyrope (Xpyrope)
Since Mg and Fe are both in the pyrope component, we use the following relation for Xpyrope:
\[
{Xpyrope} = \frac{1.221}{1.221 + 1.666} = \frac{1.221}{2.887} = 0.400
\]
Step 4: Conclusion
The Xpyrope of this garnet is 0.400.
