2.7.A.2 Predicting Properties of Molecules and Ions Using Lewis Diagrams and VSEPR Theory:

1. Molecular Geometry:

2. Bond Angles:

i. General Influence of Electron Pair Repulsion on Bond Angles:

a. Bonding Pairs vs Lone Pairs:

• Bonding pairs: Electrons shared between atoms form bonds and tend to push away other electron pairs, but they do so less strongly than lone pairs.
• Lone pairs: Electrons not shared between atoms tend to repel more strongly than bonding pairs because lone pairs are localized on the central atom, closer to the nucleus, which creates a stronger repulsion force.

b. Repulsion Order (Most to Least Repulsive):

• • Lone pair–lone pair (strongest repulsion)
  • Lone pair–bonding pair
  • Bonding pair–bonding pair (weakest repulsion)

ii. Effects of Electron Pair Repulsion on Specific Molecular Geometries:

iii. Key Points on Bond Angle Distortion:

a. Lone pairs cause more repulsion than bonding pairs

• Lone pairs are localized closer to the nucleus, leading to stronger repulsion. This results in smaller bond angles as lone pairs push bonding pairs closer together.

b. Multiple bonds (double and triple bonds)

• Double and triple bonds have more electron density than single bonds, which increases repulsion. This can distort bond angles, typically making them slightly smaller compared to single bonds.

c. Electron pairs in equatorial positions

• In trigonal bipyramidal or octahedral geometries, electron pairs in the equatorial positions are farther apart than those in axial positions. This reduces repulsion, resulting in larger bond angles in the equatorial plane.

3.  Bond Energies and Bond Order:

Bond Energy and Bond Order are important concepts in chemistry that help explain the stability of molecules and the strength of chemical bonds. Here’s how they are related:

i. Bond Order:

a. Bond order refers to the number of chemical bonds between a pair of atoms in a molecule.

b. It can be calculated as:

$$\text{Bond Order} = \frac{1}{2} \left( \text{Number of bonding electrons} – \text{Number of anti-bonding electrons} \right)$$

In simpler terms, bond order is the difference between the number of electrons in bonding and anti-bonding orbitals divided by two.

c. Bond order also helps predict the type of bond:

• • Single bond = Bond order = 1
  • Double bond = Bond order = 2
  • Triple bond = Bond order = 3
  • A bond order of zero indicates that no stable bond exists between the atoms (e.g., in a dissociated molecule).

ii. Bond Energy:

a. Bond energy (also called bond dissociation energy) is the amount of energy required to break one mole of a particular bond in a molecule in the gas phase, separating the atoms into individual gaseous atoms.

b. Higher bond energy corresponds to stronger bonds, while lower bond energy indicates weaker bonds.

c. Bond energy typically increases with bond order, but it is also influenced by other factors such as atomic size and electronegativity.

iii. Relationship Between Bond Order and Bond Energy:

a. Higher Bond Order = Higher Bond Energy:

1. • As bond order increases, the strength of the bond increases. For example:
     • Single bonds (bond order = 1) are generally weaker and have lower bond energies compared to double bonds (bond order = 2) or triple bonds (bond order = 3).
     • A triple bond has the highest bond energy because it involves more electron sharing, making the bond stronger.

b. Explanation of the Relationship:

1. • • • Increased electron density in a bond (as bond order increases) leads to a stronger attractive force between the bonded atoms. This stronger attraction results in higher bond energy.
       • Multiple bonds (double and triple bonds) involve more electron pairs between atoms, leading to greater bond strength and higher bond energy compared to single bonds.

c. Bond Order and Stability:

• • A higher bond order implies greater stability for the molecule because the atoms are held together more strongly.
  • For example, O₂ has a bond order of 2 (double bond) and is more stable than N₂ with a bond order of 3 (triple bond), as the bond order in nitrogen is higher and thus stronger.

4. Bond Length:

The length of a bond between two atoms in a molecule is influenced by several factors, with bond order and atomic radius being two key contributors. Here’s an overview of how each factor impacts bond length:

i. Bond Order:

• Bond Order refers to the number of bonding electron pairs between two atoms. For example, in a single bond (bond order = 1), two atoms share one pair of electrons; in a double bond (bond order = 2), they share two pairs of electrons; and in a triple bond (bond order = 3), they share three pairs of electrons.
• Impact on Bond Length: Generally, as bond order increases, bond length decreases. This happens because a higher bond order means a stronger attraction between the atoms, pulling them closer together. For example:
  • A single bond (like in H₂) has a longer bond length compared to a double bond (like in O₂), and a triple bond (like in N₂) has the shortest bond length.

ii. Atomic Radius:

• Atomic Radius refers to the size of an atom, typically measured from the nucleus to the outermost electron shell. Larger atoms have a greater atomic radius.
• Impact on Bond Length: Larger atoms have larger atomic radii, which results in longer bond lengths when they form bonds with other atoms. Conversely, smaller atoms tend to form shorter bonds because their atomic radii are smaller. For example:
  • A carbon-carbon bond (C-C) in ethane (C₂H₆) will be longer than a nitrogen-nitrogen bond (N-N) in hydrazine (N₂H₄), because carbon atoms are smaller than nitrogen atoms.

iii. Multiple Bonds and Atomic Radius:

• When a multiple bond (such as a double or triple bond) is formed between atoms, the bond length decreases due to the increased electron density between the atoms, which strengthens the attraction and pulls them closer together.
• The atomic radius of the atoms involved also plays a role. If the atoms in the multiple bond are smaller (e.g., C=C or N≡N), the bond will be shorter compared to multiple bonds formed between larger atoms (e.g., S=S or P=P).

iv. Example:

• In the case of carbon compounds:
  • A C-H bond (between carbon and hydrogen) is shorter than a C-C bond because hydrogen has a much smaller atomic radius than carbon.
  • A C≡C bond (triple bond) in acetylene (C₂H₂) is shorter than a C=C bond (double bond) in ethene (C₂H₄) because the triple bond has a higher bond order, which pulls the atoms closer together.

5. Dipole moment:

Q. How Molecular Geometry and Electronegativity Determine Dipole Moment:

i. Electronegativity:

1. • Electronegativity is the tendency of an atom to attract bonding electrons. If two atoms in a bond have different electronegativities, the electron density will be unevenly distributed.
   • The more electronegative atom will pull the electrons closer to itself, creating a partial negative charge (δ-) on that atom and a partial positive charge (δ+) on the less electronegative atom.
   • Dipole Moment: The greater the difference in electronegativity, the larger the dipole moment. For example, in a H-F bond, fluorine is much more electronegative than hydrogen, resulting in a strong dipole moment.

ii. Molecular Geometry:

• • • Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. Even if a molecule has polar bonds (due to electronegativity differences), the overall dipole moment depends on the shape of the molecule.
    • Symmetry: If the molecule is symmetrical (like carbon dioxide, CO₂), the dipoles of individual bonds can cancel out, resulting in no net dipole moment.
    • Asymmetry: In molecules with an asymmetrical shape (like water, H₂O), the dipoles do not cancel out and result in a net dipole moment.

iii. Example:

• Water (H₂O):

  • The oxygen atom is more electronegative than the hydrogen atoms, so each O-H bond is polar.
  • The bent molecular geometry (not linear) means that the individual dipoles do not cancel, and the molecule has a net dipole moment, making it polar.

• Carbon Dioxide (CO₂):

  • The C=O bonds are polar because oxygen is more electronegative than carbon. However, CO₂ has a linear geometry, and the two O=C bonds are opposite each other, so the dipoles cancel out, resulting in no net dipole moment. Thus, CO₂ is nonpolar.

6. Hybridization of Valence Orbitals:

Hybridization is a concept in chemistry that explains how atomic orbitals combine to form new, hybrid orbitals during chemical bonding. These hybrid orbitals have different shapes and energy levels compared to the original atomic orbitals and are used to form covalent bonds in molecules. The hybridization process allows for the bonding that leads to specific molecular shapes and angles.

i. Concept of Orbital Hybridization:

a. Atomic Orbitals: Atoms have orbitals (such as s, p, d, and f) that hold electrons. The s orbitals are spherical, while the p orbitals are dumbbell-shaped, and d orbitals are more complex in shape.

b. Hybridization occurs when atomic orbitals of different energies (like s and p) mix to form new orbitals, called hybrid orbitals, which are used to bond with other atoms. The number of hybrid orbitals formed is equal to the number of atomic orbitals mixed.

c. The newly formed hybrid orbitals have different shapes, energy levels, and orientations to allow for maximum overlap with orbitals from other atoms, leading to stronger covalent bonds.

ii. Types of Hybridization:

a. sp Hybridization (Linear geometry):

1. • When one s orbital and one p orbital mix, two sp hybrid orbitals are formed. These hybrid orbitals are arranged in a linear configuration (180° bond angle).
   • Example: BeCl₂ (Beryllium chloride) — Beryllium uses sp hybridization to form two bonds with chlorine atoms in a straight line

b. sp² Hybridization (Trigonal planar geometry):

1. • • When one s orbital and two p orbitals mix, three sp² hybrid orbitals are formed. These orbitals are arranged in a trigonal planar shape (120° bond angles).
     • Example: C₂H₄ (Ethene) — The carbon atoms use sp² hybridization to form a trigonal planar structure, with one unhybridized p orbital involved in a π bond for the double bond.

c. sp³ Hybridization (Tetrahedral geometry):

1. • When one s orbital and three p orbitals mix, four sp³ hybrid orbitals are formed. These orbitals are arranged in a tetrahedral shape (109.5° bond angles).
   • Example: CH₄ (Methane) — The carbon atom undergoes sp³ hybridization to form four bonds with hydrogen atoms in a tetrahedral structure.

d. sp³d Hybridization (Trigonal bipyramidal geometry):

1. • When one s orbital, three p orbitals, and one d orbital mix, five sp³d hybrid orbitals are formed. These orbitals arrange themselves in a trigonal bipyramidal geometry (90° and 120° bond angles).
   • Example: PF₅ (Phosphorus pentafluoride) — Phosphorus undergoes sp³d hybridization to form five bonds with fluorine atoms.

e. sp³d² Hybridization (Octahedral geometry):

• • When one s orbital, three p orbitals, and two d orbitals mix, six sp³d² hybrid orbitals are formed. These orbitals arrange themselves in an octahedral geometry (90° bond angles).
  • Example: SF₆ (Sulfur hexafluoride) — Sulfur uses sp³d² hybridization to form six bonds with fluorine atoms.

iii. Role of Hybridization in Molecular Structure: