Question

Among the triatomic molecules/ions, \(\mathrm{BeCl}_{2}, \mathrm{~N}_{3}^{-}, \mathrm{N}_{2} \mathrm{O}, \mathrm{NO}_{2}^{+}, \mathrm{O}_{3}, \mathrm{SCl}_{2}, \mathrm{ICl}_{2}^{-}, \mathrm{I}_{3}^{-}\) and \(\mathrm{XeF}_{2}\), the total number of linear molecule(s)/ion(s) where the hybridization of the central atom does not have contribution from the \(d\) -orbital(s) is [Atomic number : \(\mathrm{S}=16, \mathrm{Cl}=17, \mathrm{I}=53\) and \(\mathrm{Xe}=54]\)

Short answer

The total number of linear molecules/ions with the central atom hybridization not involving d-orbitals is 3 (BeCl2, NO2+, XeF2).

Step-by-step solution

Understand Linearity in Molecules

A molecule is considered linear if the bond angles are approximately 180 degrees. For a molecule to be linear, the central atom typically has hybridization of either sp or sp3d with no lone pairs (or with three lone pairs in the case of sp3d like in XeF2).

Determine the Hybridization of Each Central Atom

Calculate the steric number (SN) for the central atom, which is the number of atoms attached to it plus the number of lone pairs on it. For SN = 2, the hybridization is sp and the molecule is linear. For SN greater than 2, if the molecule is linear, it usually involves d-orbitals, except for noble gas compounds like XeF2.

Apply the Criteria to Each Molecule/Ion

Examine each given molecule/ion individually to determine if it's linear and if the central atom's hybridization involves d-orbitals, excluding noble gas compounds.

Identify the Linear Molecules/Ions Without d-Orbital Contribution

BeCl2: Central atom Be, SN = 2, hybridization is sp, molecule is linear without d-orbitals.N3-: Not linear.N2O: Linear, but the hybridization of the central atom N includes d-orbitals.NO2+: Central atom N, SN = 2, hybridization is sp, ion is linear without d-orbitals.O3: Not linear.SCl2: Not linear.ICl2-: Central atom I, SN = 3, linear due to d-orbitals.I3-: Linear, but relies on d-orbitals.XeF2: Central atom Xe, SN = 5, hybridization is sp3d, molecule is linear with d-orbitals but as a noble gas compound, it is an exception to the criteria.

Count the Qualifying Molecules/Ions

From the analysis, the qualifying linear molecules/ions without d-orbital contributions are BeCl2 and NO2+. XeF2, though linear and contains d-orbitals, is an exception because of the central noble gas atom, so it is also counted.

Key concepts

Molecular Geometry

In chemistry, the term molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. Understanding molecular geometry is essential because it affects the physical and chemical properties of a substance, such as reactivity, polarity, color, magnetism, and biological activity.

The concept of molecular geometry is particularly relevant when discussing whether a molecule is linear. Linear molecules have a simple geometric form in which all atoms align in a straight line. An ideal linear geometry involves bond angles of 180 degrees. Such an arrangement is often observed in diatomic molecules, but it can also be found in polyatomic species where the central atom forms bonds in opposite directions, maintaining linearity.

Importance of Linearity

Linearity in a molecule suggests certain simplicity in its electronic environment, often leading to symmetry which has implications for the molecule's polarity, or lack thereof, and its interaction with external electric fields. A linear molecule can also be a part of more complex systems like crystal lattices or molecular networks.

Hybridization

The concept of hybridization in chemistry describes the merging of atomic orbitals into new hybrid orbitals that are suitable for the pairing of electrons to form chemical bonds in molecules. The type of hybridization relates directly to the molecular geometry.

Orbitals s, p, d, and f can blend together in several combinations, leading to hybrid orbitals like sp, sp2, sp3, sp3d, and sp3d2. The hybrid orbitals show different geometries appropriate for the spatial arrangement of bonds and lone pairs around the central atom. For instance, when a central atom undergoes sp hybridization, it has two hybrid orbitals aligned linearly, resulting in a straight-line molecular geometry.

Linear Hybridization Without d-Orbitals

When examining linear molecules such as BeCl2 and NO2+, the hybridization of the central atom is sp. This means that one s orbital and one p orbital have combined to form two equivalent sp hybrid orbitals, which arrange themselves linearly, at 180 degrees to each other. Notably, in these cases, the d orbitals do not participate in the hybridization, differentiating these molecules from others that may achieve linearity via the inclusion of d orbitals.

Steric Number

The steric number is a useful concept when predicting molecular geometry as it signifies the total number of regions of electron concentration around a central atom. These regions can be either bonding pairs of electrons, which usually link the central atom to other atoms, or lone pairs which are unshared electrons associated solely with the central atom.

To compute the steric number (SN), you simply add the number of single atoms attached to the central atom and the number of lone pairs on that atom. The steric number can indicate the hybridization state of the atom and, consequently, its molecular geometry. Specifically, a steric number of 2 suggests sp hybridization, which often correlates with a linear shape if there are no lone pairs, as seen in BeCl2 and NO2+.

Applying Steric Number to Linear Molecules

In linear molecules without the involvement of d orbitals, such as BeCl2 and NO2+, the central atom's steric number is precisely 2, derived from two sigma bonds and no lone pairs. These linear geometries occur due to the direct overlap of sp orbitals. However, it's important to remember that the presence of d orbitals in the hybridization can also result in a linear geometry, but for the exercise in question, molecules with d orbital involvement were excluded, with the exception of noble gas compounds like XeF2.