Question

(a) An AB \(_{2}\) molecule is linear. How many non bonding electron pairs are around the A atom from this information? (b) How many non bonding electrons surround the Xe in \(\mathrm{XeF}_{2} ?(\mathbf{c})\) Is XeF \(_{2}\) linear?

Short answer

(a) In a linear AB2 molecule, there are 0 non-bonding electron pairs around the A atom. (b) In XeF2, there are 6 non-bonding electrons surrounding the Xe atom. (c) The XeF2 molecule is linear.

Step-by-step solution

(a) Determine Electron Number and Geometry around A in AB2

Let's consider an AB2 molecule. According to VSEPR theory, the electronic geometry around atom A depends on the total number of electron pairs, both bonding and non-bonding. To determine the number of non-bonding electron pairs around A, we should first determine the total number of electron pairs around A and the number of bonding electron pairs. Since it's an AB2 molecule, there are two B atoms bonded to the A atom. This means that the A atom has two bonding electron pairs. The question states that the molecule is linear, meaning that there are no lone pairs around the A atom because otherwise the angle would have been less than 180 degrees due to lone pair-lone pair, lone pair-bonding pair and bonding pair-bonding pair repulsions. Consequently: The number of non-bonding electron pairs around the A atom = total electron pairs - bonding electron pairs = 2 - 2 = 0.

(b) Determine Electron Number and Geometry around Xe in XeF2

Let's consider the XeF2 molecule. Xenon (Xe) has 8 valence electrons in its outermost shell. In XeF2, Xe is bonded to 2 Fluorine (F) atoms, each using 1 electron from Xe, leaving 6 non-bonding electrons around Xe. Since there are three electron pairs (2 bonding pairs with F atoms and 3 non-bonding pairs), the VSEPR theory predicts a geometry with 5 electron pair domains. This geometry is called trigonal bipyramidal. The number of non-bonding electrons surrounding the Xe in XeF2 is 6.

(c) Determine the Linearity of XeF2

In the XeF2 molecule, the central Xe atom is surrounded by 5 electron pair domains (2 bonding pairs with F atoms and 3 non-bonding pairs), forming a trigonal bipyramidal geometry. The non-bonding pairs should always be placed at an equatorial position to minimize the repulsion between them. Thus, in XeF2, the non-bonding pairs are in equatorial positions, and the two F atoms bond with Xe at the axial positions forming a straight line. Therefore, the XeF2 molecule is linear.

Key concepts

Molecular Geometry

Understanding the concept of molecular geometry is fundamental when studying the shapes that molecules form. Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule.

The Valence Shell Electron Pair Repulsion (VSEPR) theory is the cornerstone model used to predict the geometric configuration of atoms. It is based upon the simple premise that electron pairs around a central atom will adopt an arrangement as far apart as possible to minimize the repulsion between their negative charges. This theory takes into account both the bonding pairs of electrons, which are shared between atoms to form chemical bonds, and the non-bonding pairs of electrons, also known as lone pairs.

The configuration is determined by the number of electron pairs in the valence shell of the central atom. Fewer repulsions are experienced when electron pairs are located at the maximum distance from one another, leading to a stable molecular structure.

Non-bonding Electron Pairs

The concept of non-bonding electron pairs, or lone pairs, is crucial in molecular geometry. These pairs are located on the central atom and are not shared with other atoms in a molecule. Non-bonding electron pairs exert a greater repulsive force on adjacent electron pairs than bonding pairs. This is due to their greater electron-electron repulsion, as they are held more closely to the nucleus.

As a result of these interactions, non-bonding electron pairs often dictate the shape of a molecule as they require more space than bonding pairs. In scenarios where non-bonding electron pairs are present, the VSEPR theory helps us understand how they modify the angles between the bonding electron pairs and thereby the overall geometry of the molecule. For instance, in a water molecule (H2O), the two non-bonding pairs on the oxygen atom push the hydrogen atoms closer together, resulting in a bent rather than linear shape.

Linear Molecular Shape

When it comes to linear molecular shape, the arrangement of atoms and electron pairs is crucial. A molecule is classified as linear if all its atoms are arranged in a straight line. This arrangement means that the molecule has a 180-degree bond angle.

For a molecule to have a linear shape, the central atom must have a total of two regions of electron density—these regions can include both bonds and lone pairs. Importantly, if there are any non-bonding electron pairs on the central atom, the geometry could not be linear as these pairs would repel the bonding electron pairs, causing the angle to be less than 180 degrees.

For example, in carbon dioxide (CO2), the central carbon atom has no non-bonding electron pairs and is double-bonded to two oxygen atoms. Because of this arrangement, CO2 is linear. Likewise, in diatomic molecules like hydrogen gas (H2) or oxygen gas (O2), the lack of lone pairs and the presence of a single bond between the atoms establish a linear shape.