Question

Which of the following crystal field diagram(s) is(are) correct for the complex given? a. \(\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\) (tetrahedral) b. \(\operatorname{Mn}(\mathrm{CN})_{6}^{3-}\) (strong field) c. \(\mathrm{Ni}(\mathrm{CN})_{4}^{2-}\) (square planar, diamagnetic)

Short answer

All three options (a, b, and c) have the correct crystal field diagrams for their respective complexes. The Zn(NH3)4^2+ complex has a tetrahedral geometry, the Mn(CN)6^3- complex has an octahedral geometry with a strong field ligand, and the Ni(CN)4^2- complex has a square planar geometry and is diamagnetic.

Step-by-step solution

Determine the geometry of each complex

We first need to determine the geometry of each complex, which will help us understand the splitting diagram. a. \(\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\): The central atom Zn has a d10 configuration, and with Ammonia acting as a ligand, forms a tetrahedral complex. b. \(\operatorname{Mn}(\mathrm{CN})_{6}^{3-}\): Mn has a d4 configuration, and with Cyanide acting as a ligand, forms an octahedral complex. c. \(\mathrm{Ni}(\mathrm{CN})_{4}^{2-}\): Ni has a d8 configuration, and with Cyanide acting as a ligand, forms a square planar complex.

Determine the crystal field splitting diagram for each complex

Now, we can determine the crystal field splitting diagrams for each complex: a. Tetrahedral complex: The crystal field splitting diagram for a tetrahedral complex has the following energy levels, from lowest to highest: \(e^2t^2\). b. Octahedral complex with strong field ligand: The crystal field splitting diagram for an octahedral complex with a strong field ligand (such as Cyanide) has the following energy levels, from lowest to highest: \(t^2g^4e^2g^0\). c. Square planar complex: The crystal field splitting diagram for a square planar complex has the following energy levels, from lowest to highest: \(d_z^2xy^3z^2-x^2\).

Check if the complex is diamagnetic (for option c)

To determine if the Ni(CN)4^2- complex is diamagnetic, we need to review the electron configuration and the crystal field splitting diagram. As mentioned earlier, Ni has a d8 configuration, and the square-planar splitting for this complex would show that all d orbitals (d8) are completely filled, with no unpaired electrons. Thus, this complex is indeed diamagnetic.

Compare the properties of each complex to the options given

Here, we compare the properties (geometry and splitting) of each complex with the information given in each option: a. \(\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\) (tetrahedral): The geometry matches, so this option is correct. b. \(\operatorname{Mn}(\mathrm{CN})_{6}^{3-}\) (strong field): The complex has an octahedral geometry with a strong field ligand, causing large crystal field splitting. Therefore, this option is correct. c. \(\mathrm{Ni}(\mathrm{CN})_{4}^{2-}\) (square planar, diamagnetic): The complex has the correct geometry and is also diamagnetic. So this option is correct. All three options (a, b, and c) have the correct crystal field diagrams for their respective complexes.

Key concepts

Tetrahedral Complex

In a tetrahedral complex, the central metal atom is surrounded by four ligands positioned at the corners of a tetrahedron. This setup is different from other geometries because the ligands approach the metal in a way that does not align directly with its d-orbitals. As a result, there is less influence on the d-orbitals, causing smaller splitting compared to octahedral complexes.

Key points about tetrahedral complexes:

• Four ligands form a tetrahedral shape around a central metal.
• Ligands do not face d-orbitals directly, resulting in small crystal field splitting.
• The energy levels follow the order: lower energy for the e orbitals and higher for the t₂ orbitals, denoted as \(e^2t^2\).
• Common in ions with full or nearly full d-orbitals.

Octahedral Complex

An octahedral complex is the most common type of coordination complex, where six ligands surround the central metal atom at the vertices of an octahedron. This setup leads to significant splitting of the d-orbitals due to direct interaction between the ligands and the orbitals.

Important aspects of octahedral complexes:

• Six ligands form an octahedral shape around the metal atom.
• Significant splitting occurs, represented by two levels: lower energy t_2g and higher energy e_g orbitals.
• The splitting pattern for a strong field ligand is \(t^2g^4e^2g^0\), indicating a large energy gap.
• Complexes often exhibit different optical properties based on splitting.

Square Planar Complex

Square planar complexes are less common and typically involve central metal atoms with a d⁸ configuration. Here, four ligands are arranged in a square around the metal atom. This geometry results in unique splitting of the d-orbitals, creating a stable electronic configuration.

Features of square planar complexes:

• Four ligands positioned at the corners of a square.
• Significant rearrangement of d-orbitals leads to a specific splitting pattern.
• Involves orbitals \(d_{z^2}\), \(d_{xy}\), and others, often represented as \(d_z^2xy^3z^2-x^2\).
• Typically diamagnetic due to complete pairing of electrons in their low-energy orbitals.

Crystal Field Splitting

Crystal field splitting describes how the presence of ligands affects the energy levels of d-orbitals in a metal complex. When ligands approach the metal, the electrostatic interactions cause the d-orbitals to split into different energy levels

Understanding crystal field splitting:

• The nature of ligands (strong or weak field) influences the extent of splitting.
• In tetrahedral complexes, the splitting is less due to non-direct interaction with d-orbitals.
• In octahedral complexes, stronger interactions lead to greater splitting into t_2g and e_g orbitals.
• Square planar complexes result in unique rearrangements, affecting both energy and magnetic properties.
• Splitting helps predict properties like color and magnetism, influencing complex behaviors.