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How do ionization isomers differ in the ions located inside and outside a coordination sphere?

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Structural diagram of the vitamin B12 coenzyme molecule, highlighting its organometallic core with five nitrogen-cobalt bonds and one cobalt-carbon bond at the center, surrounded by complex organic groups. — coordination compound Coordination compounds contain a central metal atom surrounded by nonmetal atoms or groups of atoms, called ligands. For example, vitamin B₁₂ is made up of a central metallic cobalt ion bound to multiple nitrogen-containing ligands.

Ionization isomers are a type of coordination compound isomer that differ based on the exchange of ionic groups between the primary coordination sphere and the area outside of it.1

In these isomeric pairs, an ionic group that is coordinated directly to the central metal atom (inside the coordination sphere) swaps positions with an ion located outside the coordination sphere.1

For example, consider the pair consisting of:
* Pentaamminebromocobalt sulfate: $[C o B r (N H_{3})_{5}] S O_{4}$ , where the bromide ion is coordinated to the cobalt(3+) ion, while the sulfate ion remains outside the coordination sphere.1
* Pentaamminesulfatocobalt bromide: $[C o (S O_{4}) (N H_{3})_{5}] B r$ , where the sulfate ion is located within the coordination sphere, and the bromide ion is outside it.1

Because these isomers result in different ions being available to dissociate in solution, they exhibit distinct chemical properties despite having the same molecular formula.1