What hybrid orbitals are used by the metal ion and how many unpaired electrons are present the complex ion [VCl₄]^- with tetrahedral geometry?
(a) sp³; 2 unpaired electrons
(b) sp³; 3 unpaired electrons
(c) sp³d²; 3 unpaired electrons
(d) sp³d²; 4 unpaired electrons

Verified step by step guidance

1. Identify the central metal ion in the complex. Here, it is vanadium (V).
2. Determine the oxidation state of vanadium in the complex [VCl_4]^-. Chlorine (Cl) has a -1 charge, and there are four Cl^- ions, so the total charge from Cl is -4. The complex has an overall charge of -1, so the oxidation state of V is +3.
3. Write the electron configuration for the V^3+ ion. Vanadium (V) has an atomic number of 23, so its electron configuration is [Ar] 3d^3 4s^2. For V^3+, remove three electrons, resulting in [Ar] 3d^2.
4. Determine the hybridization of the metal ion. Since the complex has a tetrahedral geometry, the hybridization is sp^3.
5. Count the number of unpaired electrons in the 3d orbitals of V^3+. With the electron configuration [Ar] 3d^2, there are 2 unpaired electrons.

Key Concepts

Hybridization

Hybridization is the concept of mixing atomic orbitals to form new hybrid orbitals that can accommodate bonding in molecules. In the case of transition metals, the hybridization can involve s, p, and d orbitals, depending on the coordination number and geometry of the complex. For tetrahedral complexes, the common hybridization is sp³, which involves one s and three p orbitals.

Tetrahedral Geometry

Tetrahedral geometry occurs when a central atom is surrounded by four substituents arranged at the corners of a tetrahedron. This geometry is characterized by bond angles of approximately 109.5 degrees. In coordination complexes, tetrahedral geometry typically arises when a metal ion is bonded to four ligands, influencing the hybridization of the metal's orbitals.

Unpaired Electrons

Unpaired electrons are electrons in an atom or ion that are not paired with another electron in an orbital. The presence of unpaired electrons is crucial for determining the magnetic properties of a substance and can influence the color and reactivity of coordination complexes. In transition metal complexes, the number of unpaired electrons can be determined by the electron configuration of the metal ion and its hybridization state.