Question

The cation exchange equilibrium reaction between end-member components of orthopyroxene and ilmenite is given below: \[ \text{MgSiO}_3 + \text{FeTiO}_3 = \text{FeSiO}_3 + \text{MgTiO}_3 \] (Enstatite) (Fe-Ilmenite) (Ferrosilite) (Mg-Ilmenite)
Considering ideal mixing of Fe and Mg in orthopyroxene and ilmenite solid solutions, the mole fractions are \( X_{\text{Orthopyroxene}}^{\text{Mg}} = 0.60 \) and \( X_{\text{Ilmenite}}^{\text{Mg}} = 0.40 \). The equilibrium constant of the above reaction is ............. (Round off to two decimal places)

Hint:

For ideal mixing, the equilibrium constant can be simplified to the ratio of the products of mole fractions of the components on either side of the reaction.

Answer 1

Step 1: Understanding the equilibrium constant expression.
For the reaction, the equilibrium constant \( K \) can be written as: \[ K = \frac{X_{\text{Ferrosilite}} \cdot X_{\text{Mg-Ilmenite}}}{X_{\text{Enstatite}} \cdot X_{\text{Fe-Ilmenite}}} \] where:
- \( X_{\text{Ferrosilite}} = 1 - X_{\text{Orthopyroxene}}^{\text{Mg}} = 1 - 0.60 = 0.40 \)
- \( X_{\text{Mg-Ilmenite}} = 1 - X_{\text{Ilmenite}}^{\text{Mg}} = 1 - 0.40 = 0.60 \)
Step 2: Calculate the equilibrium constant.
\[ K = \frac{(0.40) \cdot (0.60)}{(0.60) \cdot (0.40)} = 1 \] Final Answer: \[ \boxed{1.00} \]