Question

Give the geometry or geometries for coordination number (a) \(2,\) (b) 4 , and (c) 6 .

Short answer

The geometry for coordination number 2 is linear, for coordination number 4 is either tetrahedral or square planar, and for coordination number 6 is octahedral.

Step-by-step solution

Understand Coordination Number

Coordination number refers to the number of atoms, ions, or molecules that a central atom or ion can bind to. For example, in a coordination complex, the central metal cation can bind to a certain number of ligands. This number is its coordination number.

Determine Geometry for Coordination Number 2

When the coordination number is 2, the shape that minimizes repulsions between the ligands is linear. This means the central atom and its two ligands will lie along a straight line.

Determine Geometry for Coordination Number 4

For a coordination number of 4, there are two common geometries. These are tetrahedral, where ligands are arranged in a tetrahedron around the central atom, and square planar, where ligands are arranged in a square on the same plane around the central atom.

Determine Geometry for Coordination Number 6

When the coordination number is 6, the most common geometry is octahedral. In this arrangement, the six ligands are positioned at the corners of an octahedron with respect to the central atom.

Key concepts

Coordination Complex

When delving into the fascinating world of chemistry, one of the intriguing concepts you'll encounter is the coordination complex. This is an array where a central metal atom or ion is surrounded by a group of molecules or ions known as ligands. These ligands are essentially 'sponsors' that donate electron pairs to the central entity, forming what we call coordinate covalent bonds.

The coordination number plays a pivotal role in these complexes as it denotes the exact count of ligands that are snugly attached to the central metal. For instance, in a silver complex with two ammonia molecules, the coordination number would be two, because that's how many ammonia molecules are cozying up to our central silver ion.

Linear Geometry

Now picture this: just two ligands bonded to a central atom. This is the simplest form called linear geometry. Visualize them in a game of 'tug-of-war' with the central atom as the prize—they stand opposite each other, forming a straight line. It's essentially a game where everyone's a winner because they're in harmony. This structure is often the mark of a coordination number of 2, reflecting how the ligands want to keep as far away from each other as possible to minimize any squabbles (or what chemists call 'repulsion').

Tetrahedral Geometry

Scaling up the complexity, we encounter tetrahedral geometry. Imagine sending four ligands to the corners of a pyramid with a triangular base—that's the tetrahedral shape for you. With a coordination number of 4, each ligand ideally gives the others space, staying at an angle of about 109.5 degrees apart. This shape is often found in compounds where the central atom likes to share attention equally among its four partners, promoting harmony all around.

Square Planar Geometry

Also in the league of a coordination number of 4, is the trendy square planar geometry. Here, the central atom becomes a royal figure, with four ligands as its knights guarding it from the four corners of a square. This plan makes sure all the knights are equidistant from each other, maintaining peace in the molecular kingdom. This arrangement is not only stylish but also crucial for certain chemical behaviors and is often showcased by d8 metal ions.

Octahedral Geometry

Last but not least, for the grand coordination number of 6, the octahedral geometry takes the stage. With six ligands, this shape is essentially two square planar geometries stacked on top of each other to form a shape resembling a diamond. Each ligand is equidistant from its adjacent peers, forming a 90-degree angle at all intersections. This is a highly symmetrical arrangement and favored by central atoms that are social butterflies, wanting to be surrounded by as many ligands as possible without favoritism.