Problem 74 - General Chemistry: Principles and Modern Applications

Question

The number of unpaired electrons in the complex ion \(\left[\operatorname{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) is (a) \(5 ;(\mathrm{b}) 4 ;(\mathrm{c}) 3 ;(\mathrm{d}) 2 ;(\mathrm{e}) 1\).

Step-by-Step Solution

Answer

The correct answer is (b) 4. The metal atom Chromium (Cr) in the complex ion \(\left[\operatorname{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) has 4 unpaired electrons.

Step 1: Identify the Metal

The complex ion in this problem is \(\left[\operatorname{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\). The metal atom in this complex ion, upon which its properties depend, is Chromium (Cr).

Step 2: Determine the Electron Configuration

To solve this problem, knowledge of the electron configuration of Chromium is necessary. The electron configuration of Cr is \([Ar] 3d^5 4s^1\) in its ground state. However, when it loses 2 electrons to form \(\operatorname{Cr}^{2+}\), it loses 1 electron from the 4s orbital and one from the 3d orbital, making the configuration \([Ar] 3d^4\). Therefore, Chromium (Cr) in this complex ion has 4 unpaired electrons.

Step 3: Match Answer Choice

According to the options provided, the number of unpaired electrons in the complex ion is either a) 5, b) 4, c) 3, d) 2, or e) 1. Thus, after determining that the number of unpaired electrons in Chromium in the complex ion is 4, we can see that the correct answer is (b) 4.

Key Concepts

Metal Electron Configuration

Understanding metal electron configuration is essential, especially when dealing with transition metals like Chromium. Electron configurations tell us how electrons are distributed in an atom's orbitals, which influences the atom's reactivity and interactions. For transition metals, their electron configurations involve filling of the

• d orbitals
• s orbitals

These two orbital types play a significant role in their chemical behavior.
Chromium (Cr) is a transition metal with an unusual electron configuration:

• In its ground state, it is written as \[ \text{[Ar]} \ 3d^5 \ 4s^1 \]
• This differs from the expected \[ \text{[Ar]} \ 3d^4 \ 4s^2 \] configuration due to electron stability considerations and the exchange energy that arises when orbitals are half-filled.

Additionally, when Chromium forms an ion like \[ \operatorname{Cr}^{2+} \], it involves losing electrons. Typically, electrons are lost from the s orbital first, followed by the d orbitals. Thus, the \[ \operatorname{Cr}^{2+} \] ion has the configuration \[ \text{[Ar]} \ 3d^4 \]. Each unpaired electron in this configuration contributes to the magnetic properties and reactivity of the complex.

Transition Metal Chemistry

Transition metal chemistry is fascinating due to its rich interplay of properties stemming from d electron configurations. Transition metals like Chromium have partially filled d orbitals, which have several important implications:

• Variable Oxidation States: Transition metals can exhibit multiple oxidation states, making them incredibly versatile in forming compounds. For example, Chromium can exist in several oxidation states like +2, +3, and +6.
• Magnetism: The presence of unpaired electrons gives many transition metals magnetic properties. Unpaired 3d electrons in \[ \operatorname{Cr}^{2+} \] contribute to its paramagnetism.
• Color: Transition metals often form colorful compounds, which occur due to d-d electronic transitions. These colors are influenced by the specific ligands surrounding the metal ion.

Complexes like \[ \left[\operatorname{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} \] exemplify how transition metals interact with ligands, becoming integral parts of coordination compounds.

Coordination Chemistry

Coordination chemistry involves the study of compounds formed between metal ions and ligands, which are ions or molecules that donate electron pairs to the metal. In the coordination complex \[ \left[\operatorname{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} \], ammonia (\( \mathrm{NH}_{3} \)) acts as the ligand, donating its lone pair of electrons to the central Chromium ion.

Several key principles govern coordination chemistry:

• Coordination Number: This refers to the number of ligand atoms directly bonded to the central metal ion. For \[ \left[\operatorname{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} \], the coordination number is 6.
• Ligand Geometry: The arrangement of ligands around a central metal ion determines the geometry of the complex. A coordination number of 6 typically results in an octahedral geometry.
• Electron Pair Donation: Ligands provide electron pairs to fill the metal’s coordination sphere, affecting its electronic structure and stability.

Understanding coordination chemistry is crucial for explaining the physical and chemical properties of metal complexes, such as solubility, reactivity, and color.