Chemistry - Why do they use graphite electrodes in the Hall–Héroult process?
Solution 1:
According to this source, graphite is used as anode material because carbon is easier to oxidize than $\ce{O^2-}$. The anodic oxidation of carbon
$$\ce{C + 2O^2- \rightarrow CO2 + 4e-}$$
proceeds more efficiently than the oxidation of $\ce{O^2-}$ at an inert anode
$$\ce{2O^2- \rightarrow O2 + 4e-}$$
$\ce{C}$ is a much better reducing agent than $\ce{O^2-}$ whose oxidation state is not changed in the reaction with graphite. As a consequence, anodic current density and the deposition rate of aluminium at the cathode will increase.
Solution 2:
The basic reason for using graphite as an anode is in Hall–Héroult process in the electrolytic reduction of alumina to aluminum metal is because graphite being an allotrope of carbon and an inert electrode reacts with oxygen to give out carbon dioxide which thus prevents the liberation of oxygen as a final product at the anode.
Had there been any other metal oxygen would have been liberated which would have readily reacted with aluminum (as aluminum has a high affinity for oxygen in comparison to other metals, for example, iron—even if iron reacted with oxygen the aluminum will easily displace it) to form aluminum oxide and the whole process will prove to be useless.
Graphite is also a good conductor of electricity.