The Fe-Mg exchange reaction between olivine and spinel is the following:
\[ \mathrm{Mg_2SiO_4 + 2FeAl_2O_4 \rightleftharpoons Fe_2SiO_4 + 2MgAl_2O_4} \]
(Forsterite) (Fe-spinel) (Fayalite) (Mg-spinel)
Assuming ideal solid solutions, the temperature of equilibration between olivine and spinel using the following data is
\(^{\circ}\text{C}\) (round off to nearest integer).
[Assume that \(\Delta H_r^{0}\) and \(\Delta S_r^{0}\) are independent of P and T, and \(K_d\) is independent of P]
\[ K_d = \left[\frac{(X_{Fe}^{Ol})(X_{Mg}^{Sp})}{(X_{Mg}^{Ol})(X_{Fe}^{Sp})}\right]^2 \]
| ΔH0r (kJ/mol) | ΔS0r (J/mol.K) | Kd | R (J/mol.K) |
|---|
| -10.91 | -3.90 | 3.024 | 8.314 |