Q.Predict conditions under which Al might be expected to reduce MgO. (Hint: See Intext question 6.4)

As established (Intext 6.4), below ~1623 K the Mg,MgO Ellingham line lies below the Al,Al$_2$O$_3$ line, so Mg reduces $Al_2O_3$; above ~1623 K the lines cross and Al$_2$O$_3$ becomes the more stable oxide, so the reverse reaction becomes favourable: $2Al + 3MgO \rightarrow Al_2O_3 + 3Mg$. …

Step 1 – Recall the relevant Ellingham lines and their crossover

As discussed in Intext Question 6.4, the Mg,MgO and Al,Al$_2$O$_3$ lines on the Ellingham diagram intersect at approximately 1623 K (about 1350°C):

• Below ~1623 K, the Mg,MgO line lies below the Al,Al$_2$O$_3$ line (MgO more stable) → Mg reduces $Al_2O_3$.
• Above ~1623 K, the lines cross and the Al,Al$_2$O$_3$ line drops below the Mg,MgO line ($Al_2O_3$ more stable) → the situation reverses.

Step 2 – Apply this to the reverse direction: Al reducing MgO

For aluminium to reduce magnesium oxide,

to be thermodynamically favourable, $Al_2O_3$ must be the more stable (lower $\Delta_fG^\circ$) oxide at the operating temperature. From Step 1, this is exactly the condition that holds above the crossover temperature of about 1623 K.

Step 3 – State the condition …

Use the same Mg/Al Ellingham crossover established in Intext 6.4 (~1623 K), but apply it in the OPPOSITE direction: above this temperature, $Al …

• Repeating the Intext 6.4 condition for Mg reducing Al$_2$O$_3$ (below 1623 K) instead of correctly inverting it for the reverse reaction (Al reducing MgO requires ABOVE 1623 K). …