Problem 88 - General Chemistry: Principles and Modern Applications

Question

In your own words, define the following terms or symbols: (a) \(s p^{2} ;\) (b) \(\sigma_{2 p}^{*} ;\) (c) bond order; (d) \(\pi\) bond.

Step-by-Step Solution

Answer

(a) \(s p^{2}\) hybridization is the mixing of one \(s\) and two \(p\) orbitals to form three identical hybrid orbitals in a molecule with a trigonal planar arrangement. (b) \(\sigma_{2 p}^{*} \) orbital is an anti-bonding molecular orbital formed by the out-of-phase overlap of \(2 p\) atomic orbitals. (c) Bond order indicates the number of chemical bonds between a pair of atoms. (d) A \(\pi\) bond is a type of covalent bond that exists between atoms, formed by the side-on overlap of atomic orbitals and is present in addition to a \( \sigma\) bond in molecules where double or triple bonds exist.

Step 1: Define the \(s p^{2} \) Hybridization

\(s p^{2} \) hybridization refers to the mixing of one \(s\) and two \( p\) orbitals, resulting in three identical hybrid orbitals in a molecule. This type of hybridization is found in atoms with a 'trigonal planar' arrangement of atoms such as \( BCl_3 \), \( CO_3^{2-} \).

Step 2: Define the \(\sigma_{2 p}^{*} \) Orbital

The \(\sigma_{2 p}^{*} \) orbital refers to the anti-bonding molecular orbital formed by the out-of-phase overlap of \(2 p\) atomic orbitals. 'Anti-bonding' means the electrons in this orbital do not help in the formation of a bond; instead, they can weaken or even break a bond.

Step 3: Define Bond Order

The 'Bond order' indicates the number of chemical bonds between a pair of atoms. It can be calculated as: (Number of electrons in bonding orbitals - Number of electrons in anti-bonding orbitals) / 2. A higher bond order generally means a stronger bond.

Step 4: Define the \(\pi\) Bond

A \(\pi\) bond is a type of covalent bond that exists between atoms where the electrons are on top and bottom of the axis connecting the nuclei of the atoms. It's formed by the side-on overlap of atomic orbitals, typically \( p\) orbitals, and is present in addition to a \( \sigma\) bond in molecules where double or triple bonds exist.

Key Concepts

sp2 hybridization

Understanding the concept of sp2 hybridization can be quite useful when studying how atoms form bonds. Specifically, sp2 hybridization occurs when one s orbital and two p orbitals mix to form three equivalent hybrid orbitals. This kind of hybridization prepares the atom for bonding in a trigonal planar shape.

For example, in a molecule like boron trifluoride (BF3), each boron atom forms three bonds in a flat plane. The mixing of these orbitals allows atoms to achieve an optimal structure for strong chemical bonding. You'll find sp2 hybridization in molecules where you need to maintain a planar geometry, like ethene (C2H4) or carbon dioxide (CO3^{2-}) molecules.

sigma and pi bonds

Sigma (\(\sigma\) ) and pi (\(\pi\) ) bonds are two distinct types of covalent bonds. They are important for understanding how molecules are structured.

• A sigma bond is the first bond formed between two atoms. It's characterized by a head-on overlap of orbitals, usually s or hybrid orbitals. Sigma bonds allow atoms to rotate freely around the bond axis.
• On the other hand, a pi bond forms when the side-by-side overlapping of p orbitals occurs. Pi bonds are typically found in double and triple bonds, complementing the sigma bond that already exists.

The combination of these bonds provides strength and rigidity to a molecule's structure, influencing physical properties such as boiling and melting points.

bond order

Bond order is a crucial concept that gives insight into a molecule's chemical stability and bond strength. It defines the number of chemical bonds between a pair of atoms in a molecule. You can calculate the bond order using the formula:\[ \text{Bond Order} = \frac{(\text{Number of electrons in bonding orbitals} - \text{Number of electrons in anti-bonding orbitals})}{2}.\] A higher bond order typically signifies a stronger bond. For instance, a bond order of 1, as seen in single bonds, indicates one bonding interaction. A bond order of 2, seen in double bonds, means there are two bonding interactions. It effectively predicts the likelihood of molecules staying together under various conditions.

molecular orbital theory

Molecular orbital (MO) theory is a method used to describe the electronic structure of molecules. Instead of viewing electrons as residing in distinct atomic orbitals, it places them in molecular orbitals that extend over the entire molecule.

• MOs are formed through the linear combination of atomic orbitals, which can either be bonding or anti-bonding.
• A bonding orbital, like the \(\sigma\_{2p}\), is lower in energy and helps hold the molecule together.
• An anti-bonding orbital, such as \(\sigma\_{2p}^*\), is higher in energy and can weaken bonds or promote breaking if occupied by electrons.

By applying MO theory, chemists gain predictive insights into whether a molecule will form or how existing bonds will behave.