What is the difference between a cation and an anion?

$(a)$ 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 $NO_{3}^{-}$

State whether the following statement is true or false:
$A$ mole always represents $6.023 \times 10^{22}$ atoms,molecules,or ions of a substance.

$(a)$ What do the following formulae stand for:
$(i)$ $2O$
$(ii)$ $O_{2}$
$(iii)$ $O_{3}$
$(iv)$ $H_{2}O$
$(b)$ Give the chemical formulae of the following compounds:
$(i)$ Potassium carbonate
$(ii)$ Calcium chloride
$(c)$ Calculate the formula unit mass of $Al_{2}(SO_{4})_{3}$.
(Given atomic mass of $Al = 27 \, u, S = 32 \, u, O = 16 \, u$)

Calculate the number of moles of magnesium present in a magnesium ribbon weighing $12 \, g$. The molar atomic mass of magnesium is $24 \, g \, mol^{-1}$. (in $, mol$)

$(a)$ What is the law of constant proportions? Explain with the help of an example.
$(b)$ Which postulate of Dalton's atomic theory is in agreement with this law?