$(a)$ What are molecules? Using examples, differentiate between the molecules of an element and a compound.
$(b)$ Derive the chemical formulae of the molecules formed between the following ions:
$(i)$ $Al^{3+}$ and $SO_{4}^{2-}$
$(ii)$ $Ba^{2+}$ and $NO_{3}^{-}$

(N/A) molecule is defined as the smallest particle of an element or a compound that is capable of independent existence and exhibits all the properties of that substance.
The molecule of an element is constituted by the same type of atoms, e.g., $O_{2}$, while the molecule of a compound is constituted by different types of atoms, e.g., $CO_{2}$.
$(b)$ To derive the chemical formula, we cross the valencies of the ions:
$(i)$ For $Al^{3+}$ and $SO_{4}^{2-}$:

Symbol	$Al$	$SO_{4}$
Charge	$3+$	$2-$
Formula	$Al_{2}(SO_{4})_{3}$

$(ii)$ For $Ba^{2+}$ and $NO_{3}^{-}$:

Symbol	$Ba$	$NO_{3}$
Charge	$2+$	$1-$
Formula	$Ba(NO_{3})_{2}$