Explain the following reactions:
$(a)$ Silicon is heated with methyl chloride at high temperature in the presence of copper;
$(b)$ Silicon dioxide is treated with hydrogen fluoride;
$(c)$ $CO$ is heated with $ZnO$;
$(d)$ Hydrated alumina is treated with aqueous $NaOH$ solution.

(N/A) When silicon reacts with methyl chloride in the presence of copper catalyst at about $570 \, K$,a mixture of methyl-substituted chlorosilanes like $(CH_3)_2SiCl_2$ is formed.
$2CH_3Cl + Si \xrightarrow[570 \, K]{Cu} (CH_3)_2SiCl_2$
$(b)$ Silicon dioxide $(SiO_2)$ reacts with hydrogen fluoride $(HF)$ to form silicon tetrafluoride $(SiF_4)$.
$SiO_2 + 4HF \longrightarrow SiF_4 + 2H_2O$
$SiF_4$ can further react with $HF$ to form hydrofluorosilicic acid $(H_2SiF_6)$.
$SiF_4 + 2HF \longrightarrow H_2SiF_6$
$(c)$ Carbon monoxide $(CO)$ acts as a reducing agent and reduces zinc oxide $(ZnO)$ to zinc $(Zn)$.
$ZnO_{(s)} + CO_{(g)} \stackrel{\Delta}{\longrightarrow} Zn_{(s)} + CO_{2_{(g)}}$
$(d)$ Hydrated alumina $(Al_2O_3 \cdot 2H_2O)$ dissolves in aqueous $NaOH$ to form sodium meta-aluminate $(NaAlO_2)$.
$Al_2O_3 \cdot 2H_2O + 2NaOH \longrightarrow 2NaAlO_2 + 3H_2O$