Idea of ionisation isomerism:
Two coordination compounds having the same overall composition but differing in the counter-ion outside the coordination sphere (which can be interchanged with a ligand inside) are called ionisation isomers.
Given pair:
\([\,\mathrm{Co(NH_3)_5Cl}\,]\mathrm{SO_4}\) \(\;\leftrightarrow\;\) \([\,\mathrm{Co(NH_3)_5SO_4}\,]\mathrm{Cl}\)
In the first salt, \(\mathrm{SO_4^{2-}}\) is the counter-ion and \(\mathrm{Cl^-}\) is bound to Co(III) inside the sphere.
In the second, \(\mathrm{Cl^-}\) is the counter-ion and \(\mathrm{SO_4^{2-}}\) is coordinated to Co(III).
Experimental proof by precipitation tests:
\underline{Test for free sulphate (BaCl$_2$ test):}
\[
[\,\mathrm{Co(NH_3)_5Cl}\,]\mathrm{SO_4(aq)} + \mathrm{Ba^{2+}(aq)} \longrightarrow \mathrm{BaSO_4(s)\downarrow} + [\,\mathrm{Co(NH_3)_5Cl}\,]^{2+}
\]
White precipitate of \(\mathrm{BaSO_4}\) confirms free \(\mathrm{SO_4^{2-}}\).
\underline{Test for free chloride (AgNO$_3$ test):}
\[
[\,\mathrm{Co(NH_3)_5SO_4}\,]\mathrm{Cl(aq)} + \mathrm{Ag^{+}(aq)} \longrightarrow \mathrm{AgCl(s)\downarrow} + [\,\mathrm{Co(NH_3)_5SO_4}\,]^+
\]
Curdy white precipitate of \(\mathrm{AgCl}\) confirms free \(\mathrm{Cl^-}\).
\[
\boxed{\text{Hence the pair are ionisation isomers since the counter-ion and a coordinated ligand exchange positions.}}
\]