An element $X$ belongs to the $3rd$ period and group $13$ of the Modern Periodic Table.
$(a)$ Determine the valence electrons and the valency of $X$.
$(b)$ Determine the molecular formula of the compound formed when $X$ reacts with an element $Y$ (atomic number $= 8$).
$(c)$ Write the name and formula of the compound formed when $X$ combines with chlorine.

(N/A) Since $X$ is in group $13$,it has $3$ valence electrons. Its valency is $3$.
$(b)$ Element $Y$ has an atomic number of $8$,so its electronic configuration is $2, 6$. It needs $2$ electrons to complete its octet,so its valency is $2$. Element $X$ has a valency of $3$. By criss-crossing the valencies,the molecular formula is $X_2Y_3$. Since $X$ is Aluminum $(Al)$ and $Y$ is Oxygen $(O)$,the compound is $Al_2O_3$ (Aluminum oxide).
$(c)$ Chlorine $(Cl)$ has a valency of $1$. Element $X$ has a valency of $3$. By criss-crossing the valencies,the formula is $XCl_3$. Since $X$ is Aluminum,the compound is $AlCl_3$ (Aluminum chloride).