Question

Use valence bond theory to explain the bonding in \(\mathrm{Cl}_{2}\) and \(\mathrm{HCl}\). Show how the atomic orbitals overlap when a bond is formed

Short answer

In Cl2, a covalent bond forms through the overlap of the half-filled 3p atomic orbitals of each Cl atom, which allows two unpaired electrons to pair up. In HCl, the bond forms when the half-filled 1s orbital of H overlaps with the half-filled 3p orbital of Cl, and their single electrons pair up.

Step-by-step solution

Understanding Valence Bond Theory

Valence Bond Theory (VBT) essentially posits that a covalent bond is formed between two atoms through the overlap of half-filled atomic orbitals. Each of these half-filled orbitals contains one unpaired electron. When overlapped, these two unpaired electrons can pair up and create a bond.

Bonding in Cl2

Chlorine (Cl) has 7 electrons in its outermost shell. For Cl2, two Cl atoms form a bond by overlapping their half-filled 3p atomic orbitals. This overlap allows the two unpaired electrons (one from each Cl) to pair up and form a covalent bond. This results in the Cl2 molecule being stable.

Bonding in HCl

In the case of HCl, Hydrogen (H) has one electron in its K shell, and Chlorine (Cl) has 7 electrons in its outermost shell, with one unpaired electron in the 3p orbital. The bond between H and Cl forms when the half-filled 1s orbital of H overlaps with the half-filled 3p orbital of Cl. The single electron from H and the unpaired electron from Cl then pair up within this overlapped region, forming a covalent bond.

Graphical Representation

To visually understand this, it can help to draw the atomic orbitals for each atom before the bond forms and then after the overlap occurs. For Cl2, two 3p orbitals (each with an unpaired electron) will overlap, while for HCl, the 1s orbital of H (with 1 electron) will overlap with the 3p orbital of Cl (with an unpaired electron).

Key concepts

Covalent Bonding

Covalent bonding is essential when understanding molecular structures. It occurs when two atoms share electrons to achieve more stable electron configurations.
In essence, this type of bonding lets atoms complete their outer electron shells, often achieving the electron configuration of a noble gas.

Here's what you should know about covalent bonds:

• They are usually formed between non-metal atoms.
• Electrons are shared between the two atoms, rather than transferred as in ionic bonds.
• The resulting molecule often has a lower energy state, making it more stable than the individual atoms.

In the molecule \(\mathrm{Cl}_{2}\), two chlorine atoms come together to share their unpaired electrons through their 3p orbitals. By sharing electrons, each chlorine atom effectively has access to eight outer electrons, satisfying what's known as the octet rule. Similarly, in \(\mathrm{HCl}\), hydrogen shares its lone electron with chlorine, allowing both atoms to approach stability through shared electrons.

Atomic Orbitals

Atomic orbitals are the regions around an atom's nucleus where electrons are likely to be found. Different orbitals have various shapes and energy levels. Understanding these shapes is crucial for grasping how bonds form.
When covalent bonds are discussed, the focus is usually on the s and p orbitals, as these are the outermost orbitals involved in bonding.

Key characteristics of atomic orbitals include:

• 's' orbitals, which are spherical in shape.
• 'p' orbitals, which have a dumbbell-like shape and are oriented along specific axes (x, y, z).
• The number of orbitals available increases with each energy level. For instance, the second energy level has one 2s and three 2p orbitals.

In \(\mathrm{Cl}_{2}\), the vital interaction involves the 3p \(\text{orbital}\). Each chlorine atom contributes one electron from this orbital, leading to a sharing of electrons. For \(\mathrm{HCl}\), hydrogen's lone electron in the 1s orbital is shared with chlorine's unpaired electron in the 3p orbital, demonstrating how these atomic orbitals are crucial for covalent bond formation.

Orbital Overlap

Orbital overlap is the mechanism through which covalent bonds form according to Valence Bond Theory. When two atomic orbitals overlap, an area known as a 'bonding region' is created where the electrons can be shared.
This overlap is crucial for the stabilization of bonded atoms, allowing them to share electrons more effectively.

To delve deeper:

• Strong overlap of orbitals usually results in a stronger covalent bond.
• The nature of this overlap affects the bond's directionality and strength.
• For a sigma bond, orbitals overlap head-on, while for a pi bond, they overlap laterally.

In \(\mathrm{Cl}_2\), the overlap occurs between the 3p orbitals of the two chlorine atoms, creating a stable covalent bond. With \(\mathrm{HCl}\), the 1s orbital of hydrogen and the 3p orbital of chlorine overlap. This interaction forms a sigma bond, which is the most straightforward form of covalent bond, representing a direct overlap where electrons are shared freely between the bonded atoms.