Question

Predict the geometry of these molecules and ion using the VSEPR method: (a) \(\operatorname{HgBr}_{2}\), (b) \(\mathrm{N}_{2} \mathrm{O}\) (arrangement of atoms is NNO), (c) SCN \(^{-}\) (arrangement of atoms is SCN).

Short answer

The geometries of the molecules and ion are as follows based on the VSEPR method: (a) HgBr2 is linear, (b) N2O is bent, (c) SCN- is linear.

Step-by-step solution

Draw Lewis Structures

For each molecule, draw the Lewis structure. For \(HgBr_2\), Mercury (Hg) will be the central atom bonded to two Bromine (Br) atoms. For \(N_2O\), one Nitrogen (N) is bonded to the second Nitrogen (N), which is additionally bonded to an Oxygen (O). For \(SCN^-\), Sulfur (S) is bonded to Carbon (C), which is further bonded to Nitrogen (N).

Determine Number of Bond Pairs and Lone Pairs

For \(HgBr_2\), Mercury forms two bonds with no lone pair, therefore it's a linear shape. For \(N_2O\), the middle N has two bonding pairs and one lone pair which forms a bent shape. For \(SCN^-\), Carbon has 4 bond pairs and no lone pairs, so it forms a linear shape.

Match to VSEPR Geometries

The geometry of each molecule or ion corresponds to the shape that minimizes the repulsion between the valence electron pairs. Thus, \(HgBr_2\) and \(SCN^-\) are linear, and \(N_2O\) is bent based on the principles of VSEPR theory.

Key concepts

Lewis Structures

Understanding the Lewis structure of a molecule is the foundation for predicting its geometry. Lewis structures are diagrams that show how the valence electrons are distributed among the atoms in a molecule.

When we draw a Lewis structure, we start by arranging the atoms so that every atom, except hydrogen, follows the octet rule – meaning it is surrounded by eight valence electrons. We represent shared pairs of electrons — bonds between atoms — with lines, and lone pairs of electrons with dots.

For instance, in the molecule HgBr₂, we illustrate it with Mercury having a single bond with each of the two Bromine atoms. No lone pairs of electrons are on the Mercury, and each Bromine has three lone pairs. Similarly, the Lewis structure of N₂O as per the given arrangement (NNO) will show the first Nitrogen with a triple bond to the second Nitrogen, and the second Nitrogen having a double bond with Oxygen and a single lone pair of electrons. The ion SCN^- will have Sulfur single-bonded to Carbon, which is triple-bonded to Nitrogen; Carbon also has a negative charge, indicating an additional electron.

These structures are crucial in predicting molecular shapes using VSEPR theory because they reveal the number and type of electron pairs surrounding the central atom – both of which strongly affect molecular geometry.

Molecular Geometry

The molecular geometry, or the shape of a molecule, can greatly influence the properties and behavior of a substance. After constructing the Lewis structures, we can predict the molecular geometry of molecules using the Valence Shell Electron Pair Repulsion (VSEPR) method.

This method is based on the concept that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsive interactions. Bonding pairs of electrons and lone pairs of electrons both contribute to the final shape.

In the case of HgBr₂, the molecule has no lone pairs and two bonding pairs on the central Mercury atom, resulting in a linear shape. For N₂O, the central Nitrogen has one lone pair and two bonding pairs, giving us a bent shape—as lone pairs repel more strongly and occupy more space. Lastly, in SCN^-, with Carbon as the central atom and no lone pairs but four bonding pairs, the molecular geometry is also linear.

It is essential to consider formal charges and resonance structures, which might be part of more advanced exercises, to understand the complete picture for molecular shapes.

Valence Electron Pair Repulsion Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is the backbone of understanding molecular geometry. It is a set of rules used for predicting the shape of individual molecules based on the extent of electron-pair electrostatic repulsion.

According to VSEPR theory, electron pairs in the valence shell of an atom will take a configuration that minimizes repulsion between them, dictating the geometry of the molecule.

Here's how the theory applies to our examples:

• In HgBr₂, two bond pairs are on the Mercury atom. They arrange themselves in opposite directions resulting in a linear shape.
• For N₂O, the lone pair on the central Nitrogen pushes the bonding pairs away, forming a bent shape.
• With SCN^-, Carbon has four bond pairs that maximize their distance in a linear fashion, as there are no lone pairs to cause additional repulsion.

While the VSEPR theory is an excellent predictor of molecular shapes, it sometimes requires adjustments to account for differences in repulsion strength between lone pairs and bonding pairs, and for the presence of double or triple bonds which can also influence molecular shape.