For each of the following, (i) give the systematic name of the compound and specify the oxidation state of the transition metal, (ii) draw a crystal field energy-level diagram and assign the d electrons to orbitals, (iii) indicate whether the complex is high-spin or low-spin (for d⁴ - d⁷ complexes), and (iv) specify the number of unpaired electrons.
(a) (NH₄)[Cr(H₂O)₆](SO₄)₂

Verified step by step guidance

1. **Step 1:** Determine the systematic name of the compound. The compound is a coordination complex with the formula (NH4)[Cr(H2O)6](SO4)2. The central metal is chromium (Cr), and the ligands are water molecules (H2O). The ammonium ion (NH4) and sulfate ions (SO4) are counterions. The systematic name is ammonium hexaaquachromium(III) sulfate.
2. **Step 2:** Determine the oxidation state of the transition metal. The overall charge of the complex ion [Cr(H2O)6] is balanced by the charges of the counterions. Since sulfate (SO4) has a charge of -2 and there are two sulfate ions, the total negative charge is -4. The ammonium ion (NH4) has a charge of +1. Therefore, the charge of the complex ion must be +3 to balance the charges. Thus, the oxidation state of chromium is +3.
3. **Step 3:** Draw a crystal field energy-level diagram for the complex. Chromium in the +3 oxidation state has a d^3 electron configuration. In an octahedral field, the d orbitals split into two sets: t2g (lower energy) and eg (higher energy). Place the three d electrons in the t2g orbitals, as they are lower in energy.
4. **Step 4:** Determine if the complex is high-spin or low-spin. For d^3 complexes, there is no distinction between high-spin and low-spin because all three electrons will occupy the t2g orbitals, resulting in the same electron configuration regardless of the ligand field strength.
5. **Step 5:** Specify the number of unpaired electrons. Since all three d electrons are in separate t2g orbitals, there are three unpaired electrons in the complex.

Key Concepts

Coordination Compounds

Coordination compounds consist of a central metal atom or ion bonded to surrounding molecules or ions called ligands. The nature of these ligands and their arrangement around the metal ion significantly influence the properties of the complex, including its color, magnetic behavior, and stability. Understanding the coordination number and geometry is essential for analyzing the compound's structure and reactivity.

Crystal Field Theory

Crystal Field Theory (CFT) explains the electronic structure of transition metal complexes by considering the effect of ligands on the d orbitals of the metal ion. According to CFT, the presence of ligands causes the degenerate d orbitals to split into different energy levels, which affects the distribution of electrons among these orbitals. This theory is crucial for determining the oxidation state of the metal and predicting whether a complex is high-spin or low-spin.

Spin States and Unpaired Electrons

The spin state of a transition metal complex refers to the arrangement of electrons in the d orbitals, which can be either high-spin or low-spin. High-spin complexes have more unpaired electrons due to a weaker field strength of the ligands, while low-spin complexes have fewer unpaired electrons as a result of stronger field ligands causing greater splitting of the d orbitals. The number of unpaired electrons is critical for understanding the magnetic properties of the complex.