Chromite ore is roasted with sodium carbonate in air according to 4Fe(CrO2)2+8Na2CO3+7O2→ 2Fe2O3+8Na2CrO4+8CO2. The number of moles of electrons lost…

In $\mathrm{Fe(CrO_2)_2}$ the oxidation state of $\mathrm{Cr}$ is $+3$ (each $\mathrm{CrO_2^-}$) and that of iron is $+2$. In the products iron is $+3$ in $\mathrm{Fe_2O_3}$ and chromium is $+6$ in $\mathrm{Na_2CrO_4}$. Per formula unit, iron changes $+2\to+3$, losing $1\ e^-$, and the two chromium atoms each change $+3\to+6$, losing $3\ e^-$ each, so $6\ e^-$ in total. The sum is $1+6=7$ electrons per mole of chromite. As a check, $4$ moles lose $28\ e^-$, which equals the electrons gained by $7$ moles of $\mathrm{O_2}$ ($7\times4=28$). Atom balance confirmed with a linear solve: Na, C, Fe, Cr and O all balance. Answer: 7.