Question

An eclogite consists of garnet (60%) and omphacite (40%), where the mineral abundances are in mole %. \( X_Mg \) [=Mg/(Mg+Fe\(^2+\))] of garnet and omphacite is 0.50 and 0.75, respectively. The \( X_{Mg} \) of eclogite is .............

Hint:

To calculate the overall mole fraction of a component in a mixture, multiply the mole fraction in each phase by its abundance, then divide by the total abundance.

Answer 1

Correct Answer: 0.6

Step 1: Understand the Calculation of \( X_{Mg} \).
To calculate the overall mole fraction of magnesium (\( X_{Mg} \)) in the eclogite, we use the mole fractions of magnesium in garnet and omphacite, and their respective mineral abundances. The total mole fraction \( X_{Mg} \) of the eclogite is given by: \[ X_{Mg} = \frac{X_{Mg,garnet} \times W_{garnet} + X_{Mg,omphacite} \times W_{omphacite}}{W_{garnet} + W_{omphacite}} \] Where: - \( X_{Mg,garnet} = 0.50 \), - \( X_{Mg,omphacite} = 0.75 \), - \( W_{garnet} = 60 \) (percentage of garnet), - \( W_{omphacite} = 40 \) (percentage of omphacite).

Step 2: Apply the Formula.
Substitute the values into the formula: \[ X_{Mg} = \frac{(0.50 \times 60) + (0.75 \times 40)}{60 + 40} = \frac{30 + 30}{100} = \frac{60}{100} = 0.60 \] Thus, the \( X_{Mg} \) of eclogite is 0.60.