Q.The compounds $[Co(SO_4)(NH_3)_5]Br$ and $[Co(SO_4)(NH_3)_5]Cl$ represent

The key idea is that isomers must share the same molecular formula — only then does it make sense to ask what type of isomerism relates them.

Reasoning:

1. Both compounds have the identical coordination sphere, $[Co(SO_4)(NH_3)_5]^{+}$, with sulfate acting as a ligand in both.
2. The only difference is the counter-ion: bromide in the first compound, chloride in the second — so the two compounds have different overall molecular formulas (one contains Br, the other Cl). …

Isomers, by definition, must have the same molecular formula but a different arrangement of atoms or ions. Before deciding which kind of isomerism relates two compounds, you must first check whether they are isomers at all.

Step-by-step reasoning

1. Identify the coordination sphere in each compound.

   In $[Co(SO_4)(NH_3)_5]Br$, the square brackets enclose $Co^{3+}$ bonded to one sulfate ion ($SO_4^{2-}$, acting as a ligand) and five ammonia molecules. Bromide sits outside the sphere as the counter-ion.

   In $[Co(SO_4)(NH_3)_5]Cl$, the coordination sphere is identical — same metal, same ligands (one sulfate, five ammines), same charge on the complex ion. Only the counter-ion is chloride instead of bromide.

2. Compare the overall molecular formulas.

   The first compound's formula contains one bromine atom; the second contains one chlorine atom instead. These are simply two different chemical formulas — a bromide salt and a chloride salt of the same complex cation.

3. Check each isomerism type against this pair:

   • Linkage isomerism requires an ambidentate ligand (like $NO_2^-/ONO^-$ or $SCN^-/NCS^-$) bonding through a different atom in the two compounds. No ambidentate ligand is present here.
   • Ionisation isomerism requires the same overall molecular formula, with an anion exchanging roles — a ligand in one compound, a free counter-ion in the other — e.g. $[Co(NH_3)_5Br]SO_4$ vs. $[Co(NH_3)_5SO_4]Br$ (both compounds share the formula $CoBrSO_4(NH_3)_5$). In our pair, sulfate stays a ligand in both compounds — nothing ever moves in or out of the coordination sphere. Only the identity of the free halide itself changes ($Br^-$ vs. $Cl^-$), which makes the overall formula different between the two compounds — this fails the basic requirement for ionisation isomerism.
   • Coordination isomerism requires both the cation and the anion to be complex ions that exchange ligands between them (e.g. $[Co(NH_3)_6][Cr(CN)_6]$ vs. $[Cr(NH_3)_6][Co(CN)_6]$). Here the counter-ions ($Br^-$, $Cl^-$) are simple monatomic anions, not complex ions — this is impossible. …

Method: Check Molecular Formula Equality BEFORE Naming the Isomerism Type

Steps

1. Write out the coordination sphere and counter-ion for each compound.

   • $[Co(SO_4)(NH_3)_5]Br$ → sphere: $[Co(SO_4)(NH_3)_5]^{+}$; counter-ion: $Br^-$
   • $[Co(SO_4)(NH_3)_5]Cl$ → sphere: $[Co(SO_4)(NH_3)_5]^{+}$; counter-ion: $Cl^-$

2. Compare the coordination spheres. Identical in both — same metal, same ligands (one sulfate, five ammines), same charge.

3. Compare the overall molecular formulas. They are not the same — one compound contains a bromine atom, the other a chlorine atom. Isomers must share an identical molecular formula; these two compounds fail this basic test.

4. Rule out each isomerism type:

   • Linkage isomerism needs an ambidentate ligand bound through different atoms in the two compounds — none is present here.
   • Ionisation isomerism needs the identical overall formula, with an anion swapping between a ligand role and a counter-ion role — this fails here because the counter-ions themselves differ ($Br^-$ vs. $Cl^-$), so sulfate never leaves the coordination sphere in either compound, and the overall formula isn't the same to begin with. …

Here are the common mistakes students make on this exact question, along with the conceptual fixes to avoid them.

Mistake 1: Confusing the Counter Ion with the Ligand

The Error: Students see $SO_4$ inside the coordination sphere and immediately think "sulfate is a ligand." They then compare the two compounds and think the sulfate is different in each, leading them to choose linkage isomerism (option i).

Why it’s wrong: In these complexes, sulfate ($SO_4^{2-}$) is acting as a monodentate ligand (bonded through one oxygen). It is inside the square brackets, so it is part of the coordination sphere. The difference between the two compounds is the ion outside the brackets: $Br^-$ vs $Cl^-$.

How to avoid: Always draw a vertical line mentally at the square brackets. Everything inside is the complex ion; everything outside is the counter ion. Ask: "What is different?" Here, the complex ion $[Co(SO_4)(NH_3)_5]^+$ is identical in both. Only the counter ion changes.

Mistake 2: Forgetting the Definition of Ionisation Isomerism

The Error: Students know the counter ion is different, but they think "ionisation isomerism" means the ligand changes its bonding mode (like $SO_4$ switching from inside to outside). They don't realize that ionisation isomerism specifically refers to the exchange of an ion between the coordination sphere and the outside.

Why it’s wrong: Ionisation isomerism occurs when a compound can be written in two ways: one where an anion is a ligand, and another where that same anion is the counter ion. For example:

• $[Co(NH_3)_5Br]SO_4$ (bromide is ligand, sulfate is counter ion)
• $[Co(NH_3)_5SO_4]Br$ (sulfate is ligand, bromide is counter ion)

In the given question, both compounds have sulfate as a ligand and halide as counter ion. No exchange has occurred. The complex ion is the same; only the counter ion is different.

How to avoid: Memorise the definition: Ionisation isomerism = exchange of an ion between the coordination sphere and the outside. If the complex ion is identical, it cannot be ionisation isomerism.

Mistake 3: Assuming "Different Counter Ions" Means Isomerism

The Error: Students see $Br$ and $Cl$ and think "different atoms = isomerism." They then pick coordination isomerism (option iii) because they vaguely remember that coordination compounds with different ligands can be isomers.

Why it’s wrong: Coordination isomerism occurs when the ligands are exchanged between the cation and anion in a coordination compound. For example:

• $[Co(NH_3)_6][Cr(CN)_6]$ vs $[Cr(NH_3)_6][Co(CN)_6]$

Here, the cation and anion are both complex ions, and ligands swap between them. In the given question, the counter ions ($Br^-$ and $Cl^-$) are simple ions, not complex ions. So coordination isomerism is impossible.

How to avoid: Check if both the cation and anion are complex ions (containing a metal). If one is a simple ion (like $Br^-$, $Cl^-$, $NO_3^-$), coordination isomerism is ruled out. …