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Complete the following table of radicals.
Name of radical Molecular representation
sulphate
${{N}_{3}}^{-}$
nitrate
Bisulphate
$C{{O}_{3}}^{2-}$
$O{{H}^{-}}$
phosphate


Answer
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Hint: The name of ions which have negative charge in them, usually end with –ate, and the ions which have positive overall charge in it, tends to end with an –ium.
-Molecular representation of a radical of the radicals requires proper identification of names of molecules in their ionic form.

Complete answer:
The complete table is given below.
Name of radical Molecular representation
sulphate$S{{O}_{4}}^{2-}$
azide${{N}_{3}}^{-}$
nitrate$N{{O}_{3}}^{-}$
Bisulphate$HS{{O}_{4}}^{-}$
carbonate$C{{O}_{3}}^{2-}$
hydroxide$O{{H}^{-}}$
phosphate$P{{O}_{4}}^{3-}$


If we consider the table given in the question, the first column says sulphate. As we know from the name of this ion, that it contains one sulphur group, along with four oxygen groups attached to it. Now the –ate, at the end of the name indicates its anion. And we know that the outermost orbital of an oxygen contains six electrons each, and the sulphur also contains six electrons in its outermost shell. So, the two oxygen will satisfy its valency with four electrons of sulphur, and the rest of the two oxygen would have negative charge in it, producing an overall charge of $-2$.
The name of a radical whose molecular formula is ${{N}_{3}}^{-}$ is azide. This is because it contains $N=N$ bond between three atoms of nitrogen.
In case of nitrate ion, as we know that it contains a nitrogen atom, along with three oxygen atoms. Now the outermost shell of the nitrogen contains five valence electrons, so two of the oxygen would satisfy its valencies with four of the electrons of nitrogen, and one oxygen would get only one electron, hence a negative overall charge will be there.
Bisulphate anion, as the name suggests, it would have a sulphur atom as the central atom. And four oxygen groups attached to it along with a hydrogen atom. As we know sulphate ion has a negative overall of two. And the bisulphate ion differs from sulphate ion, by one hydrogen atom. We know that it has only one electron at the outermost shell. So three of the oxygen would satisfy its valency along with a hydrogen, and one atom of oxygen would get only one electron, leaving an overall negative charge in the ion.
The name of the next radical is carbonate, as the radical contains carbon and oxygen, in its anionic form. We all know that carbon has four outermost electrons, so one of the oxygen would satisfy the valency of its own, and the remaining two oxygen would have one electron each, leaving two negative charges.
Name of the next ion is hydroxide as we could see from the formula, it contains a hydrogen hence the prefix hydro, and an oxygen oxide.
The last ion is phosphate, as we can tell, from the name, that the ion will contain phosphorus as the central atom and oxygens attached to it. We know that phosphorus has five valence electrons, so one oxygen would satisfy the valence totally, and the rest of the three would get one electron each, leaving a \[-3\] overall charge.

Note:The oxygen has six electrons in its outermost shell, it needs two electrons to satisfy its valency, so every radical which has an oxygen atom, which are, phosphate, bisulphate, nitrate, carbonate, sulphate and hydroxide ion, the negative overall charge arises from the negative charge of the oxygen itself.
-The name of ${{N}_{3}}^{-}$ is azide because it contains azide bond in its structure. And one of the valencies of nitrogen is not satisfied, hence the negative charge.