Problem 51 - Chemistry The Molecular Science

Question

Write a structural formula for the coordination compound \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{I}_{2}\right],\) and give the coordination number for the central \(\mathrm{Cr}^{2+}\) ion.

Step-by-Step Solution

Answer

The coordination number of \( \mathrm{Cr}^{2+} \) in the compound is 6.

Step 1: Understand the components

The complex given is \( \left[ \mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{I}_{2}\right] \). Here, \( \mathrm{Cr}^{2+} \) is the central metal ion, \( \mathrm{en} \) stands for ethylenediamine, a bidentate ligand, \( \mathrm{NH}_{3} \) is ammonia, and \( \mathrm{I} \) is iodide. The coordination compound consists of ligands \( \mathrm{en} \), \( \mathrm{NH}_{3} \), and \( \mathrm{I}^{-} \) bonding with the central metal ion \( \mathrm{Cr}^{2+} \).

Step 2: Assign the coordination number

The coordination number of a metal in a complex is the total number of ligand attachment points. Ethylenediamine (\( \mathrm{en} \)) is a bidentate ligand, meaning it forms two bonds, contributing 2 coordination points. \( \mathrm{NH}_{3} \) is a monodentate ligand with each \( \mathrm{NH}_{3} \) contributing one coordination point, totaling 2 from \( (\mathrm{NH}_{3})_{2} \). \( \mathrm{I}^{-} \) is also a monodentate ligand, contributing 1 coordination point per atom, totaling 2 from \( \mathrm{I}_{2} \). Therefore, the coordination number is the sum: \( 2 + 2 + 2 = 6 \).

Step 3: Draw the structural formula

In the structural formula, the central \( \mathrm{Cr}^{2+} \) is connected to each of its ligands based on the determined coordination points. Start by connecting one bidentate \( \mathrm{en} \) (which connects at two sites). Then attach two \( \mathrm{NH}_{3} \) molecules (one connection each), and finally, connect two \( \mathrm{I}^{-} \) ions (one connection each). This ensures the correct coordination number (6) and the structural integrity of the complex.

Key Concepts

Understanding the Coordination Number

In coordination chemistry, the coordination number is a crucial concept as it defines the number of ligand attachment points around a metal ion. For instance, in the compound \( \left[ \mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{I}_{2}\right] \), we have Chromium \( \mathrm{Cr}^{2+} \) as the central metal ion. The coordination number here is calculated by counting the total attachment points provided by all ligands surrounding the metal ion.

• Ethylenediamine (\( \mathrm{en} \)) is a bidentate ligand, meaning it can bond at two points, contributing 2 coordination points.
• Ammonia (\( \mathrm{NH}_{3} \)) is a monodentate ligand, providing 1 point each, summed up to 2 points for two \( \mathrm{NH}_{3} \) molecules.
• Iodide (\( \mathrm{I}^{-} \)) is also monodentate, with one iodide contributing 1 point, totaling to 2 points for two \( \mathrm{I}^{-} \).

Adding these gives us a coordination number of 6, indicating six points of attachment for the central \( \mathrm{Cr}^{2+} \) ion.

Exploring Bidentate Ligands

Bidentate ligands are fascinating because they form two bonds with a central metal atom or ion, contributing significantly to the stability and geometry of coordination complexes.

• Ethylenediamine (\( \mathrm{en} \)) is a classic example of a bidentate ligand. It possesses two donor atoms which can each form a coordinate bond with the metal center.
• This dual bonding ability allows bidentate ligands to "chelate" the metal, forming a more stable ring-like structure due to the chelate effect. This enhances the stability of the coordination compound compared to those with monodentate ligands.

In the context of our compound \( \left[ \mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{I}_{2}\right] \), the ethylenediamine wraps around the \( \mathrm{Cr}^{2+} \) ion, establishing two connections which count towards the coordination number.

Structural Formula of Coordination Compounds

Creating a structural formula in coordination chemistry involves illustrating the connections between the central metal ion and its surrounding ligands to reflect physical arrangements and bonding.
For the compound \( \left[ \mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{I}_{2}\right] \), the central \( \mathrm{Cr}^{2+} \) ion is encircled by:

• A bidentate ligand \( \mathrm{en} \), connected at two sites, forming a (nearly) closed loop with \( \mathrm{Cr}^{2+} \).
• Two \( \mathrm{NH}_{3} \) molecules, each connecting at one point, represented by simple lines radiating from the chromium ion.
• Two \( \mathrm{I}^{-} \) ions, each making a single connection line to the metal center.

The structural formula showcases these interactions, ensuring the overall coordination number is upheld, and visually communicating the spatial arrangement of the ligands.

Decoding Metal-Ligand Bonding

Metal-ligand bonding is at the heart of coordination chemistry, and it accounts for the way in which ligands attach to a central metal ion, such as \( \mathrm{Cr}^{2+} \) in our example compound. These bonds form through a mechanism known as coordinate or dative bonding.

• In a coordinate bond, the ligand donates a pair of electrons to the metal ion which can accept those electrons due to its nature.
• Bidentate ligands like ethylenediamine can use two pairs of lone electrons to form coordinate bonds, effectively surrounding the metal ion and stabilizing the complex.
• Monodentate ligands such as \( \mathrm{NH}_{3} \) or \( \mathrm{I}^{-} \) involve a single pair of electrons to form a bond with the metal center.

This bonding is illustrated in our compound, showing how each ligand type contributes to the overall structure and stability of the coordination complex, relying on their capacity to share electron pairs for bond formation.