Hello!
The balanced chemical equation for the oxidation of diamonds is the following one:
C(s) + O₂(g) → CO₂(g)
As simple as that! You see, Diamonds are an allotropic form of pure carbon. Allotropic forms are different arrangements of atoms. In graphite, the C atoms are arranged in layers like paper sheets, and in diamond, the C atoms are arranged in a tetrahedral structure, which gives them their hardness and their thermal and electrical properties. Burning diamonds would be the same as burning elemental carbon and the chemical equation is the one shown before.
Have a nice day!
