Animated Solution for Chemistry - Coordination Compounds: The isomer (s) of $[Co(N{H}_3{)}_{4}C{l}_2]$ that has/have a $Cl-Co-Cl$ angle of $90^{\circ }$, is/are

The study of coordination compounds is like exploring molecular architecture. Just as the placement of windows and doors defines a building, the spatial arrangement of ligands around a central metal ion defines the chemical and physical properties of a complex.

In this problem, we are dealing with the octahedral complex $[Co(N{H}_3{)}_{4}C{l}_2]$. Let's break down its geometry and understand why bond angles are the key to unlocking its isomeric secrets.

Our given complex is $[Co(N{H}_3{)}_{4}C{l}_2]$. If we look at the number and types of ligands, we have four identical ammonia ($N{H}_3$) ligands and two identical chloride ($Cl$) ligands. This perfectly matches the general formula $M{A}_4{B}_2$, where $M$ is the central metal ion, $A$ represents the four identical ligands, and $B$ represents the two identical ligands.

Because the coordination number is 6 (4 + 2), the geometry of this complex is strictly octahedral. In an octahedral geometry, the ligands are positioned at the six vertices of a regular octahedron, with the metal ion sitting right at the center.

Complexes of the type $M{A}_4{B}_2$ are famous for exhibiting geometrical isomerism. This means that while the chemical bonds are the same, the spatial arrangement of the ligands can be different. Specifically, they can exist in two distinct forms: the $cis$-isomer and the $trans$-isomer.

To differentiate between these two, we focus on the two identical $B$ ligands—in our case, the two chloride ($Cl$) ions. Their relative positioning will dictate the entire geometry of the molecule.

Imagine you are standing inside the octahedron at the position of the Cobalt ion. If you place the two chloride ligands such that they are right next to each other, you have created the $cis$-isomer.

In this adjacent configuration, the two $Cl$ ligands occupy positions that are $90^{\circ }$ apart. Therefore, the $Cl-Co-Cl$ bond angle is exactly $90^{\circ }$. The remaining four positions are filled by the ammonia ligands.

Now, let's rearrange the furniture. If you take those two chloride ligands and place them as far away from each other as possible, they will end up on completely opposite sides of the Cobalt ion. This is the $trans$-isomer.

Because they are diametrically opposite, the $Cl-Co-Cl$ bond angle stretches out to a straight line, making it exactly $180^{\circ }$. The four ammonia ligands will then occupy the square planar equatorial positions.

The question specifically asks for the isomer that possesses a $Cl-Co-Cl$ angle of $90^{\circ }$. As we have beautifully visualized, the $trans$-isomer has an angle of $180^{\circ }$, while the $cis$-isomer proudly holds the $90^{\circ }$ angle.

Therefore, the correct answer is cis only. Understanding these spatial relationships not only helps in solving such problems instantly but also builds a strong foundation for predicting the polarity and reactivity of coordination complexes!