Consider the following reaction and statements :
[Co(NH3)4Br2]+ + Br- - [Co(NH3)3Br3] + NH3
I. Two

Q: Why does the trans isomer only give one product?

In the trans isomer, the two $Br$ ligands are at axial positions (180 degrees apart). This forces all four $NH_3$ ligands into the equatorial square plane. Because of this high symmetry, all four $NH_3$ ligands are chemically equivalent. Replacing any one of them with a $Br^-$ will result in the exact same 3D structure (the meridional isomer).

Q: What exactly are facial (fac) and meridional (mer) isomers?

These terms describe $MA_3B_3$ octahedral complexes. In a facial (fac) isomer, the three identical ligands occupy the corners of one triangular face of the octahedron (they are all 90 degrees to each other). In a meridional (mer) isomer, the three identical ligands form a T-shape, lying on the same plane or 'meridian' of the octahedron.

Q: Can the facial (fac) isomer be formed from the trans reactant?

No, it cannot. In the trans reactant, the two $Br$ ligands are already 180 degrees apart. A facial isomer requires all three $Br$ ligands to be at 90 degrees to one another. Since a simple substitution only replaces one ligand and doesn't rearrange the existing ones, the 180-degree $Br-Co-Br$ bond remains, making it impossible to form a facial isomer.

Q: Are these resulting $MA_3B_3$ isomers optically active?

No, neither the facial nor the meridional isomer of an $MA_3B_3$ complex is optically active. Both possess planes of symmetry, which means their mirror images are superimposable on themselves.

Q: How do I quickly know if ligands are equivalent without drawing everything?

Look for symmetry elements! If you can rotate the molecule or reflect it across a mirror plane such that one ligand perfectly swaps places with another, those ligands are equivalent. In trans-$[Co(NH_3)_4Br_2]^+$, a 90-degree rotation around the Br-Co-Br axis swaps all the $NH_3$ ligands, proving they are all equivalent.

Question

Consider the following reaction and statements :
$[Co(NH_3)_4Br_2]^+ + Br^- \longrightarrow [Co(NH_3)_3Br_3] + NH_3$
I. Two isomers are produces if the reactant complex ion is a cis-isomer.
II. Two isomers are produced if the reactant complex ion is a trans-isomer.
III. Only one isomer is produced if the reactant complex ion is a trans-isomer.
IV. Only one isomer is produced if the reactant complex ion is a cis-isomer.
The correct statements are

Options:

(A) (I) and (II)

(B) (I) and (III)

(C) (III) and (IV)

(D) (II) and (IV)

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Welcome to a fascinating exploration of coordination chemistry! We are tasked with analyzing a substitution reaction where a bromide ion ($Br^-$) replaces an ammonia ($NH_3$) ligand in an octahedral cobalt complex, specifically $[Co(NH_3)_4Br_2]^+$.

The core of the problem lies in understanding how the geometry of the starting material dictates the number of possible products. Our reactant is an octahedral complex of the type $MA_4B_2$. This specific stoichiometry allows for two distinct geometrical isomers: the **cis-isomer** and the **trans-isomer**.

In the cis-isomer, the two bromide ligands are positioned adjacent to each other, forming a $90^\circ$ angle. Conversely, in the trans-isomer, the two bromide ligands are situated directly opposite one another, creating a $180^\circ$ angle.

### The Reaction of the Cis-Isomer

Let's first examine what happens when the cis-isomer undergoes substitution. Imagine a bromide ion approaching the complex to kick out one of the four ammonia ligands. A crucial question arises: are all four ammonia ligands in identical chemical environments?

If we look closely at the 3D structure of the cis-isomer, the answer is a resounding no! Two of the ammonia ligands are positioned opposite to each other, while the remaining two are positioned opposite to the bromide ligands. Because these environments are chemically distinct, replacing different ammonia molecules will inevitably lead to different isomeric products.

If the incoming bromide replaces an ammonia that is opposite to another ammonia, the resulting complex will have three bromides occupying the corners of one triangular face of the octahedron. This is known as the **facial (fac)** isomer.

On the other hand, if the incoming bromide replaces an ammonia that is opposite to a bromide, the three bromides will end up forming a T-shape, lying on the same meridian of the octahedron. This is the **meridional (mer)** isomer. Therefore, the cis-isomer yields **two distinct isomers**.

### The Reaction of the Trans-Isomer

Now, let's shift our focus to the trans-isomer. In this highly symmetric configuration, the two bromide ligands are at the top and bottom (axial positions), directly opposite each other. The four ammonia ligands all lie in the square equatorial plane.

Because of this high degree of symmetry, all four ammonia ligands are in exactly the same chemical environment. They are all adjacent to two bromides and two other ammonias.

Since all four ammonia ligands are equivalent, it does not matter which one the incoming bromide replaces. The result will always be structurally identical: the three bromides will form a T-shape. As we established earlier, this arrangement is the **meridional (mer)** isomer. Consequently, the trans-isomer yields **only one single product**.

### Final Conclusion

Let's match our structural findings with the given statements:
- **Statement I:** "Two isomers are produced if the reactant complex ion is a cis-isomer." This is **correct** (we get fac and mer).
- **Statement II:** "Two isomers are produced if the reactant complex ion is a trans-isomer." This is incorrect.
- **Statement III:** "Only one isomer is produced if the reactant complex ion is a trans-isomer." This is **correct** (we only get mer).
- **Statement IV:** "Only one isomer is produced if the reactant complex ion is a cis-isomer." This is incorrect.

Thus, statements I and III are the true statements, making option (b) the correct answer. Always remember that visualizing the 3D symmetry of coordination complexes is the master key to unlocking isomerism problems!

Select Answer:

Visualized Solution

$T h e R e a c t i o n S e t u p$

$U n d er s t an d in g t h e R e a c t an t s$

$R e a c t i o n o f t h e C i s - I so m er$

$P r o d u c t s f r o m C i s - I so m er$

$R e a c t i o n o f t h e T r an s - I so m er$

$P r o d u c t f r o m T r an s - I so m er$

$C o n c l u s i o n$

$F oo d f or T h o ug h t$

The Sigma Insight: Nomenclature, Isomerism, Importance and Werner's Theory

Analyzing the Setup

The Reaction of the Cis-Isomer

The Reaction of the Trans-Isomer

Final Conclusion

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Indicate the complex/complex ion which did not show any geometrical isomerism.

Select Answer:

Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The Reaction Setup

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Understanding the Reactants

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Reaction of the Cis−Isomer

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Products from Cis−Isomer

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Reaction of the Trans−Isomer

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Product from Trans−Isomer

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Conclusion

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Food for Thought