$A$ tetravalent element forms monoxide and dioxide with oxygen. When air is passed over the heated element $(1273 \ K)$,producer gas is obtained. The monoxide of the element is a powerful reducing agent and reduces ferric oxide to iron. Identify the element and write the formulas of its monoxide and dioxide. Write chemical equations for the formation of producer gas and the reduction of ferric oxide with the monoxide.

The element is carbon $(C)$,which is tetravalent and forms monoxide $(CO)$ and dioxide $(CO_2)$.
Producer gas is a mixture of $CO_{(g)}$ and $N_{2_{(g)}}$.
Formation of producer gas:
$2C_{(s)} + O_{2_{(g)}} + 4N_{2_{(g)}} \xrightarrow{1273 \ K} 2CO_{(g)} + 4N_{2_{(g)}}$
Carbon monoxide acts as a strong reducing agent and reduces ferric oxide $(Fe_2O_3)$ to iron $(Fe)$.
Reduction of ferric oxide:
$Fe_2O_{3_{(s)}} + 3CO_{(g)} \xrightarrow{\Delta} 2Fe_{(s)} + 3CO_{2_{(g)}}$