Unit 5: Chemical Bonding and Shapes of Molecules

1. Valence Shell, Valence Electron, and Octet Theory

The reactivity and bonding behavior of an atom are primarily determined by its outermost electrons. Understanding these concepts is crucial for predicting how atoms will interact.

Valence Shell

The valence shell is defined as the outermost electron shell of an atom. These are the electrons that are farthest from the nucleus and are therefore involved in chemical reactions.

Valence Electrons

Valence electrons are the electrons residing in the valence shell. They are the key players in chemical bonding, as they are either gained, lost, or shared between atoms to achieve a stable electron configuration.

Example:

Sodium (Na), with atomic number 11, has an electron configuration of 2, 8, 1. Its valence shell is the third shell, and it has 1 valence electron.
Chlorine (Cl), with atomic number 17, has an electron configuration of 2, 8, 7. Its valence shell is the third shell, and it has 7 valence electrons.

Octet Rule

The Octet Rule states that atoms tend to gain, lose, or share electrons in order to achieve eight electrons in their valence shell. This configuration is exceptionally stable, mirroring the electron configuration of noble gases (except helium), which are known for their chemical inertness. Achieving an octet provides maximum stability for most elements.

Example:

Oxygen (O) has 6 valence electrons. It tends to gain 2 electrons to achieve an octet (8 valence electrons).
Carbon (C) has 4 valence electrons. It tends to share 4 electrons to achieve an octet.

Duplet Rule

For very small atoms, specifically Hydrogen (H), Helium (He), and Lithium (Li), the Octet Rule does not apply. Instead, these atoms tend to achieve a stable configuration with two electrons in their valence shell, resembling the electron configuration of Helium. This is known as the Duplet Rule.

Example:

Hydrogen (H) has 1 valence electron. It will share or gain 1 electron to achieve a duplet.
Lithium (Li) has 1 valence electron. It will lose 1 electron to achieve a duplet (by having its first shell, which contains 2 electrons, as its new outermost shell).

2. Ionic Bond

An ionic bond is a strong electrostatic attraction between oppositely charged ions, formed by the complete transfer of electrons.

Formation

An ionic bond is formed by the complete transfer of one or more electrons from a metal atom to a non-metal atom. Metal atoms, typically having low ionization energies, tend to lose valence electrons to form positively charged ions called cations. Non-metal atoms, typically having high electron affinities, tend to gain these electrons to form negatively charged ions called anions. The resulting electrostatic attraction between these oppositely charged ions constitutes the ionic bond.

Diagrammatic representation: Imagine a sodium atom (Na) with one valence electron and a chlorine atom (Cl) with seven valence electrons. The sodium atom transfers its single valence electron to the chlorine atom. Sodium becomes Na⁺ (electron configuration like Neon), and chlorine becomes Cl^- (electron configuration like Argon). These oppositely charged ions then attract each other strongly.

Properties of Ionic Compounds

High Melting and Boiling Points: Due to the strong electrostatic forces holding the ions together in a crystal lattice, a large amount of energy is required to overcome these forces.
Brittle: Ionic compounds are typically brittle. When a stress is applied, layers of ions can shift, bringing like-charged ions next to each other, leading to strong repulsion and shattering of the crystal.
Conduct Electricity in Molten or Aqueous State: In the solid state, ions are fixed in the lattice and cannot move, so they do not conduct electricity. However, when melted or dissolved in water, the ions become mobile and can carry an electric current.
Soluble in Polar Solvents: Ionic compounds tend to dissolve well in polar solvents like water. The polar water molecules can surround and stabilize the individual ions, separating them from the crystal lattice.

Examples

Sodium Chloride (NaCl): Na transfers an electron to Cl.
Magnesium Oxide (MgO): Mg transfers two electrons to O.
Calcium Chloride (CaCl₂): Ca transfers one electron to each of two Cl atoms.
Sodium Oxide (Na₂O): Two Na atoms each transfer one electron to an O atom.

Lattice Energy

Lattice energy is defined as the energy released when one mole of an ionic solid is formed from its constituent gaseous ions. It is a measure of the strength of the ionic bond within the crystal lattice. A higher lattice energy indicates stronger ionic bonds and a more stable ionic compound.

Formula: While complex to calculate directly, it's related to Coulomb's Law: E = k * (q1 * q2) / r, where q1 and q2 are the charges of the ions, and r is the distance between their centers. Lattice energy is directly proportional to the product of the charges and inversely proportional to the distance between the ions.

3. Covalent Bond

A covalent bond is formed by the mutual sharing of electron pairs between atoms, typically between two non-metal atoms.

Formation

A covalent bond is formed when two non-metal atoms share one or more pairs of electrons. This sharing allows both atoms to achieve a stable electron configuration, typically an octet (or a duplet for hydrogen). The shared electron pair is attracted by the nuclei of both atoms, holding them together.

Diagrammatic representation: Imagine two hydrogen atoms, each with one valence electron. They come together and share their single electrons, forming a shared pair. This shared pair counts towards the duplet of both hydrogen atoms, forming an H-H bond.

Types of Covalent Bonds

Single Bond: Involves the sharing of one pair of electrons between two atoms.
Examples:
- Hydrogen molecule (H-H): Each H shares 1 electron.
- Chlorine molecule (Cl-Cl): Each Cl shares 1 electron.
Double Bond: Involves the sharing of two pairs of electrons (four electrons) between two atoms.
Examples:
- Oxygen molecule (O=O): Each O shares 2 electrons.
- Ethylene (C=C): The two carbon atoms share 2 pairs of electrons.
Triple Bond: Involves the sharing of three pairs of electrons (six electrons) between two atoms.
Examples:
- Nitrogen molecule (N≡N): Each N shares 3 electrons.
- Acetylene (C≡C): The two carbon atoms share 3 pairs of electrons.

4. Coordinate Covalent Bond (Dative Bond)

A special type of covalent bond where one atom donates both electrons to the shared pair.

Formation

A coordinate covalent bond, also known as a dative bond, is a type of covalent bond where both electrons in the shared pair are donated by only one of the two participating atoms. The atom donating the electron pair is called the donor, and the atom accepting the electron pair is called the acceptor. Once formed, a coordinate covalent bond is indistinguishable from a regular covalent bond in terms of its properties within the molecule.

Diagrammatic representation: An arrow is typically used to represent a coordinate covalent bond, pointing from the donor atom to the acceptor atom (e.g., A → B). The donor usually has a lone pair of electrons, and the acceptor has an empty orbital.

Examples

Ammonium ion (NH₄⁺): Ammonia (NH₃) has a lone pair on the nitrogen atom. A hydrogen ion (H⁺), which has an empty 1s orbital, accepts this lone pair from nitrogen to form the NH₄⁺ ion.
Hydronium ion (H₃O⁺): Water (H₂O) has two lone pairs on the oxygen atom. An H⁺ ion accepts one of these lone pairs to form the H₃O⁺ ion.
Carbon Monoxide (CO): In CO, there is a triple bond. Two of these are regular covalent bonds, and one is a coordinate covalent bond where oxygen donates a lone pair to carbon to achieve an octet for both atoms.

5. Properties of Covalent Compounds

Covalent compounds, also known as molecular compounds, exhibit distinct physical properties compared to ionic compounds, primarily due to the nature of their intermolecular forces.

Low Melting and Boiling Points: Unlike ionic compounds, covalent compounds are held together by relatively weak intermolecular forces (Van der Waals forces, hydrogen bonding). Less energy is required to overcome these forces, leading to lower melting and boiling points.
Soft: Molecular solids are generally soft because the intermolecular forces are weak, allowing molecules to be easily separated or moved relative to each other.
Poor Conductors of Electricity: Covalent compounds do not have free-moving ions or delocalized electrons. Therefore, they do not conduct electricity in solid, molten, or aqueous states (unless they react with water to form ions, like HCl).
Soluble in Non-polar Solvents: Covalent compounds tend to dissolve in non-polar solvents (e.g., oil in petrol) due to the "like dissolves like" principle, where similar intermolecular forces facilitate dissolution.

6. Lewis Dot Structures

Lewis dot structures are simplified representations of molecules that show the valence electrons and how they are arranged in bonds and lone pairs.

Concept

Lewis Dot Structures (also known as Lewis structures or electron-dot structures) are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule. They represent valence electrons as dots around the element symbols. A pair of dots between two atoms represents a shared electron pair (a covalent bond), and dots on a single atom represent lone pairs.

Steps for drawing Lewis structures:

Count the total number of valence electrons for all atoms in the molecule/ion. Add electrons for negative charge, subtract for positive charge.
Determine the central atom (usually the least electronegative, never H or F).
Draw single bonds between the central atom and terminal atoms. Subtract these electrons from the total.
Distribute remaining electrons as lone pairs to terminal atoms to satisfy their octets (or duplets for H).
Place any leftover electrons on the central atom as lone pairs.
If the central atom does not have an octet, convert lone pairs from terminal atoms into double or triple bonds with the central atom.

Examples

H₂: H-H (each H has 2 dots, shared)
O₂: O=O (each O has 4 shared dots and 4 lone pair dots)
N₂: N≡N (each N has 6 shared dots and 2 lone pair dots)
CH₄: Central C bonded to four H atoms, each single bond.
H₂O: Central O bonded to two H atoms, two lone pairs on O.
NH₃: Central N bonded to three H atoms, one lone pair on N.
CO₂: Central C double-bonded to two O atoms, two lone pairs on each O.
HCl: H-Cl, three lone pairs on Cl.
CCl₄: Central C bonded to four Cl atoms, three lone pairs on each Cl.

7. Resonance

Resonance describes situations where a single Lewis structure cannot accurately represent the actual bonding in a molecule or ion.

Concept

Resonance occurs when a molecule or ion cannot be adequately described by a single Lewis structure. In such cases, the actual bonding is an average or "hybrid" of several contributing Lewis structures, known as resonance structures. These structures differ only in the placement of electrons (especially pi electrons and lone pairs), not in the arrangement of atoms. The actual structure, the resonance hybrid, is more stable than any single contributing resonance structure and has delocalized electrons.

Diagrammatic representation: Resonance structures are typically drawn with a double-headed arrow (↔) between them to indicate that they are contributing forms, not in equilibrium. The resonance hybrid is often represented by dotted lines to show partial double bond character.

Examples

Ozone (O₃): Ozone has two resonance structures, where the double bond shifts between the central oxygen and each of the terminal oxygens. The actual structure has two equivalent O-O bonds, each with partial double bond character.
Carbonate ion (CO₃^2-): The carbonate ion has three resonance structures, with the double bond shifting among the three C-O bonds. All three C-O bonds in the actual ion are equivalent and have partial double bond character.
Benzene (C₆H₆): Benzene is a classic example, having two Kekulé resonance structures with alternating single and double bonds in the ring. The actual benzene molecule has delocalized pi electrons across the entire ring, making all C-C bonds equivalent and intermediate between single and double bonds.
Nitrate ion (NO₃^-): Similar to carbonate, the nitrate ion has three resonance structures.
Sulfur Dioxide (SO₂): SO₂ has two resonance structures, with the double bond shifting between the central sulfur and each oxygen atom.

8. VSEPR Theory and Shapes

VSEPR theory helps predict the three-dimensional geometry of molecules based on the repulsion between electron pairs.

Valence Shell Electron Pair Repulsion (VSEPR) Theory

The VSEPR Theory postulates that electron pairs (both bonding pairs and lone pairs) in the valence shell of a central atom repel each other. To minimize this repulsion and achieve maximum stability, these electron pairs arrange themselves as far apart as possible around the central atom. The molecular geometry is then determined by the positions of the atomic nuclei, influenced by these electron pair arrangements.

Key principles:

Lone pair-lone pair repulsion > lone pair-bonding pair repulsion > bonding pair-bonding pair repulsion.
Multiple bonds (double or triple) are treated as a single "super" electron domain for determining geometry, though they exert greater repulsion than single bonds.

Shapes of Molecules

The following table summarizes common molecular shapes predicted by VSEPR theory, based on the number of bonding pairs (BP) and lone pairs (LP) around the central atom:

Molecule/Ion	Bonding Pairs (BP)	Lone Pairs (LP)	Electron Geometry	Molecular Shape	Ideal Bond Angle	Description / Example
BeF₂	2	0	Linear	Linear	180°	Central atom with two bonds, no lone pairs. Atoms arranged in a straight line.
BF₃	3	0	Trigonal Planar	Trigonal Planar	120°	Central atom with three bonds, no lone pairs. All atoms lie in one plane.
CH₄	4	0	Tetrahedral	Tetrahedral	109.5°	Central atom with four bonds, no lone pairs. Symmetrical 3D arrangement.
CH₃Cl	4	0	Tetrahedral	Distorted Tetrahedral	~109.5°	Still tetrahedral electron geometry, but different bond lengths/angles due to different attached atoms.
PCl₅	5	0	Trigonal Bipyramidal	Trigonal Bipyramidal	90°, 120°	Central atom with five bonds, no lone pairs. Three bonds in equatorial plane, two axial.
SF₆	6	0	Octahedral	Octahedral	90°	Central atom with six bonds, no lone pairs. Symmetrical 3D arrangement.
H₂O	2	2	Tetrahedral	Bent/Angular	104.5°	Central O with two bonds and two lone pairs. Lone pairs compress bond angle from ideal tetrahedral.
NH₃	3	1	Tetrahedral	Trigonal Pyramidal	107°	Central N with three bonds and one lone pair. Lone pair compresses bond angle from ideal tetrahedral.
CO₂	2	0	Linear	Linear	180°	Central C with two double bonds, no lone pairs. Double bonds treated as single domains.
H₂S	2	2	Tetrahedral	Bent	92°	Similar to water, but larger central atom (S) leads to even smaller bond angle due to less effective lone pair repulsion relative to bond pair repulsion.
PH₃	3	1	Tetrahedral	Trigonal Pyramidal	93°	Similar to ammonia, but larger central atom (P) leads to even smaller bond angle.

9. Valence Bond Theory (Elementary)

Valence Bond Theory (VBT) explains the formation of covalent bonds through the overlap of atomic orbitals.

Concept

The Valence Bond Theory (VBT) states that a covalent bond is formed when two half-filled atomic orbitals (each containing one electron) from different atoms overlap. The electrons in the overlapping region are then shared between the two atoms, leading to a region of increased electron density between the nuclei. The strength of the bond is proportional to the extent of overlap.

Types of Overlap and Bonds

Sigma (σ) Bond:
A sigma bond is formed by the head-on (or axial) overlap of atomic orbitals. This overlap occurs directly along the internuclear axis. Sigma bonds are generally stronger than pi bonds because of the greater extent of overlap.

Examples:
- H₂: Formed by the head-on overlap of two 1s atomic orbitals (s-s overlap).
- HF: Formed by the head-on overlap of the 1s orbital of hydrogen and a 2p orbital of fluorine (s-p overlap).
- Cl₂: Formed by the head-on overlap of two 3p atomic orbitals (p-p overlap).
- All single bonds are sigma bonds. In multiple bonds, one is a sigma bond.
Pi (π) Bond:
A pi bond is formed by the sideways (or lateral) overlap of unhybridized parallel p orbitals. This overlap occurs above and below the internuclear axis. Pi bonds are generally weaker than sigma bonds due to the lesser extent of overlap.

Examples:
- In a double bond (e.g., C=C in ethene), there is one sigma bond and one pi bond.
- In a triple bond (e.g., C≡C in ethyne), there is one sigma bond and two pi bonds.

10. Hybridization (s and p orbitals)

Hybridization is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds.

Concept

Hybridization is the process of intermixing atomic orbitals of slightly different energies (e.g., s and p orbitals) on the same atom to form a new set of equivalent orbitals known as hybrid orbitals. These hybrid orbitals are degenerate (have the same energy) and are oriented in specific directions, leading to predictable molecular geometries and stronger bonds.

The number of hybrid orbitals formed is equal to the number of atomic orbitals that combine. The type of hybridization determines the electron geometry around the central atom.

Types of Hybridization (involving s and p orbitals)

sp Hybridization:
Formed by the mixing of one s orbital and one p orbital, resulting in two equivalent sp hybrid orbitals. These orbitals are oriented 180° apart.

Geometry: Linear

Examples:
- BeCl₂: Central Be atom is sp hybridized.
- CO₂: Central C atom is sp hybridized.
- C₂H₂ (Ethyne/Acetylene): Each C atom is sp hybridized.
sp² Hybridization:
Formed by the mixing of one s orbital and two p orbitals, resulting in three equivalent sp² hybrid orbitals. These orbitals are oriented 120° apart in a plane.

Geometry: Trigonal Planar

Examples:
- BF₃: Central B atom is sp² hybridized.
- C₂H₄ (Ethene): Each C atom is sp² hybridized.
- Benzene (C₆H₆): Each C atom is sp² hybridized.
sp³ Hybridization:
Formed by the mixing of one s orbital and three p orbitals, resulting in four equivalent sp³ hybrid orbitals. These orbitals are oriented 109.5° apart in a tetrahedral arrangement.

Geometry: Tetrahedral

Examples:
- CH₄ (Methane): Central C atom is sp³ hybridized.
- NH₃ (Ammonia): Central N atom is sp³ hybridized (one hybrid orbital contains a lone pair).
- H₂O (Water): Central O atom is sp³ hybridized (two hybrid orbitals contain lone pairs).
- C₂H₆ (Ethane): Both C atoms are sp³ hybridized.

11. Bond Characteristics

Chemical bonds can be characterized by various properties that define their nature and strength.

Bond Length

Bond length is defined as the average equilibrium distance between the nuclei of two bonded atoms in a molecule. It is typically measured in picometers (pm) or angstroms (Å). Bond length is influenced by factors such as atomic size (larger atoms lead to longer bonds), bond order (multiple bonds are shorter than single bonds), and electronegativity.

Formula (approximation for covalent bonds): The bond length between two atoms A and B is approximately the sum of their covalent radii: d(A-B) ≈ r(A) + r(B).

Ionic Character

The ionic character of a covalent bond describes the degree to which electrons are unequally shared between two bonded atoms. It is primarily determined by the difference in electronegativity between the two atoms. A larger electronegativity difference leads to a more polar bond and thus greater ionic character. If the difference is very large, the bond becomes predominantly ionic (electron transfer).

Electronegativity difference scale (approximate):

0 - 0.4: Pure covalent / Nonpolar covalent
0.4 - 1.7: Polar covalent
> 1.7: Ionic

Dipole Moment

The dipole moment (μ) is a quantitative measure of the polarity of a chemical bond or a molecule. It arises when there is a separation of positive and negative charges. For a bond, it's caused by the difference in electronegativity, creating partial positive (δ+) and partial negative (δ-) charges.

Formula: μ = q × d, where q is the magnitude of the separated charge (in coulombs) and d is the distance between the charges (in meters). The unit for dipole moment is typically Debye (D).

Molecules with a non-zero dipole moment are considered polar molecules. This occurs when individual bond dipoles do not cancel each other out due to the molecule's geometry (e.g., H₂O, NH₃). Molecules where bond dipoles cancel out (e.g., CO₂, CCl₄) are nonpolar despite having polar bonds.

12. Intermolecular Forces

Intermolecular forces (IMFs) are attractive forces that exist between molecules, influencing the physical properties of substances.

Van der Waals Forces

Van der Waals forces are a general term for weak intermolecular forces that arise from temporary or permanent dipoles in molecules. They are significantly weaker than covalent or ionic bonds.

Dipole-Dipole Forces: Occur between polar molecules that have permanent dipoles. The positive end of one molecule is attracted to the negative end of an adjacent molecule.
London Dispersion Forces (LDFs) / Induced Dipole-Induced Dipole Forces: Present in all molecules (polar and nonpolar). They arise from temporary, instantaneous dipoles created by the random movement of electrons. These instantaneous dipoles can induce dipoles in neighboring molecules, leading to weak attractions. LDFs increase with increasing molecular size and surface area.

Molecular Solids

Molecular solids are solids composed of discrete molecules held together by weak intermolecular forces (Van der Waals forces or hydrogen bonding).

Properties:

Generally have low melting points and boiling points.
Are soft and easily deformable.
Are poor conductors of electricity.

Examples: Ice (solid H₂O), Dry ice (solid CO₂), Iodine (I₂).

Hydrogen Bonding

Hydrogen bonding is a special, strong type of dipole-dipole interaction that occurs when a hydrogen atom covalently bonded to a highly electronegative atom (Fluorine (F), Oxygen (O), or Nitrogen (N)) is attracted to a lone pair of electrons on another highly electronegative atom in an adjacent molecule. This creates a particularly strong intermolecular attraction.

Types:

Intermolecular Hydrogen Bonding: Occurs between different molecules (e.g., between water molecules, between ammonia molecules).
Intramolecular Hydrogen Bonding: Occurs within the same molecule (e.g., in some organic compounds like salicylic acid).

Applications and Significance:

High Boiling Point of Water: Water's unusually high boiling point (compared to H₂S, H₂Se, H₂Te) is due to extensive intermolecular hydrogen bonding, requiring significant energy to break.
Ice Less Dense than Water: In ice, water molecules form an open, cage-like structure stabilized by hydrogen bonds, leading to a lower density than liquid water at 0°C.
Protein Structure: Hydrogen bonds play a crucial role in maintaining the secondary (alpha-helices, beta-sheets) and tertiary structures of proteins.
DNA Base Pairing: Hydrogen bonds are responsible for holding together the two strands of the DNA double helix, specifically between complementary base pairs (A-T and G-C).

Metallic Bonding

Metallic bonding is a type of chemical bonding found in metals, characterized by a "sea" of delocalized valence electrons shared among a lattice of positively charged metal ions (cations).

Formation: Metal atoms readily lose their valence electrons, which then become delocalized and move freely throughout the entire metallic structure. The positive metal ions remain in fixed positions, surrounded by this mobile electron sea. The electrostatic attraction between the positive metal ions and the delocalized electrons constitutes the metallic bond.

Properties of Metallic Solids:

High Electrical Conductivity: The presence of highly mobile, delocalized electrons allows metals to conduct electricity efficiently.
High Thermal Conductivity: Delocalized electrons can rapidly transfer kinetic energy, making metals good conductors of heat.
Malleability: Metals can be hammered into thin sheets without breaking. The delocalized electron sea allows metal ions to slide past each other without disrupting the overall metallic bond.
Ductility: Metals can be drawn into thin wires. Similar to malleability, the electron sea accommodates the movement of metal ions.
Luster: The delocalized electrons can absorb and re-emit photons of light, giving metals their characteristic shiny appearance.