Question

Which of the following statement(s) is(are) true? a. The coordination number of a metal ion in an octahedral complex ion is 8 . b. All tetrahedral complex ions are low-spin. c. The formula for triaquatriamminechromium(III) sulfate is \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]_{2}\left(\mathrm{SO}_{4}\right)_{3}\) d. The electron configuration of \(\mathrm{Hf}^{2+}\) is \([\mathrm{Xe}] 4 f^{12} 6 s^{2}\). e. Hemoglobin contains \(\mathrm{Fe}^{3+}\).

Short answer

#tag_title# Statement analysis: Tetrahedral complexes and low-spin #tag_content# Tetrahedral complex ions are formed when four ligands are attached to a central metal ion. The term low-spin refers to the electron spin configuration in a coordination compound where electrons are paired in the lower energy orbitals before they begin to populate the higher energy orbitals. Tetrahedral complexes are associated with high-spin configurations due to the significantly lower crystal field splitting energy compared to the octahedral complexes. Since the statement b states that all tetrahedral complexes are low-spin and that's incorrect, b is false. #tag_title# Statement analysis: Molecular formula #tag_content# The name triaquatriamminechromium(III) sulfate consists of the following parts: - triaqua: indicating 3 water molecules (H₂O) - triammine: indicating 3 ammonia molecules (NH₃) - chromium(III): Chromium with a +3 oxidation state (Cr³⁺) - sulfate: sulfate ion (SO₄²⁻) Based on the name, the correct formula should be \(\left[\mathrm{Cr}\left(\mathrm{H}_{2}\mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]\left(\mathrm{SO}_{4}\right)_{2}\), because the overall charge balance must be conserved. So statement c is false. #tag_title# Statement analysis: Electron configuration #tag_content# Hafnium (Hf) has an atomic number of 72. The electron configuration of a neutral Hf atom is \([\mathrm{Xe}] 4 f^{14} 5 d^{2} 6 s^{2}\). In losing two electrons to form Hf²⁺, its electron configuration will become \([\mathrm{Xe}] 4 f^{14} 5 d^{1}\), which differs from the statement d that claims it to be \([\mathrm{Xe}] 4 f^{12} 6 s^{2}\). Therefore, statement d is false. #tag_title# Statement analysis: Hemoglobin and iron #tag_content# Hemoglobin is a protein responsible for transporting oxygen in the blood. It contains iron (Fe) in its heme group, coordinated to a porphyrin ring. The iron in hemoglobin is predominantly in the +2 oxidation state (Fe²⁺) when binding to oxygen, not in the +3 state (Fe³⁺) as stated in statement e. Therefore, statement e is false. #Short_Answer# All given statements (a, b, c, d, and e) are false.

Step-by-step solution

Statement analysis: Coordination number

The coordination number is the number of ligands attached to the central metal ion in a coordination compound. An octahedral complex ion has six ligands arranged around the central metal ion in a way that the shape resembles an octahedron. Thus, the coordination number for an octahedral complex should be 6, not 8. The statement a is false.

Key concepts

Coordination Number

Understanding the coordination number is crucial in coordination chemistry. A coordination number represents the count of ligand atoms that are directly bonded to the central metal ion in a coordination compound.
In simpler terms, it tells us how many attachments—like hands in a handshake—a metal has with its surrounding atoms or molecules.

• For an octahedral complex, the coordination number is typically 6. This is because the metal is centrally placed and surrounded by six ligands, forming an octahedral shape.
• Other common coordination numbers include 4 for tetrahedral and square planar geometries, and occasionally 2 or more for other shapes.

Knowing the coordination number helps in predicting a compound's geometry and reactivity.

Octahedral Complexes

Octahedral complexes are a common and important type of coordination geometry in transition metal chemistry. As the name suggests, these complexes have a shape that resembles an octahedron. An octahedron has:

• Six vertices
• Eight faces
• Twelve edges

In chemistry, this means there are six points where ligands attach to a central metal atom. This configuration is prevalent among many transition metals due to its stability and symmetry. Examples of octahedral complexes include

• extit{Hexaamminecobalt(III) chloride} with the formula exttt{[Co(NH$_3$)$_6$]Cl$_3$}
• extit{Hexaaquairon(III) ion}, exttt{[Fe(H$_2$O)$_6$]$^{3+}$}

These complexes can exhibit interesting magnetic and electronic properties, depending on the nature of the ligands and the specific metal center involved.

Ligands

Ligands are the atoms, ions, or molecules that donate one or more pairs of electrons to a central metal ion, forming a complex. They play a pivotal role in defining the properties of a coordination complex, including its stability, color, and reactivity. Ligands can vary widely, and they have several classifications based on different criteria:

Types of Ligands

• Monodentate ligands attach to the central metal atom through a single atom. Typical examples include water (H$_2$O) and ammonia (NH$_3$).
• Bidentate and polydentate ligands: These ligands attach through two or more atoms, like ethylenediamine (en) or ethylenediaminetetraacetate (EDTA).

Role in Complex Formation

• Ligands determine the coordination number of a complex by the number of places they can attach to the metal.
• They influence the geometry of the complex by the orientation and number of bonds they form.
• The nature of ligands affects the electronic configuration of the metal center, influencing properties like color and magnetism.

Overall, understanding ligands is essential to grasp the behavior and characteristics of coordination compounds.