Chemistry | The covalent model

The Covalent Model: Sharing the Load

Hello future Chemists! This chapter, The Covalent Model, is absolutely essential. While the ionic model explains how metals and non-metals transfer electrons, the covalent model explains how non-metals share them, forming the vast majority of compounds we encounter every day—from water to DNA.

Don't worry if bonding feels abstract; we will use simple rules and visual models (like Lewis diagrams and VSEPR theory) to predict the structure and properties of molecules. Mastering these models allows you to understand the world at the microscopic level!

1. Fundamentals of Covalent Bonding (SL & HL)

What is a Covalent Bond?

A covalent bond is the electrostatic attraction between a shared pair of electrons and the positively charged nuclei of the atoms involved. It primarily occurs between two non-metal atoms.

• The atoms share electrons in order to achieve a stable, full outer energy level, often satisfying the octet rule (8 valence electrons).
• Analogy: Think of a covalent bond as two friends sharing a textbook. Both need the textbook to succeed, so they agree to share it, keeping it centrally located where both can access it.

Bond Order, Length, and Strength

Atoms can share one, two, or three pairs of electrons, leading to different types of bonds. The bond order refers to the number of shared electron pairs between two specific atoms.

• Single Bond (Bond Order 1): Sharing one pair of electrons (e.g., in H–H).
• Double Bond (Bond Order 2): Sharing two pairs of electrons (e.g., in O=O).
• Triple Bond (Bond Order 3): Sharing three pairs of electrons (e.g., in N\(\equiv\)N).

There is a crucial relationship between these properties:

Bond Strength vs. Bond Length:

• As the bond order increases (Single \(\rightarrow\) Double \(\rightarrow\) Triple), the atoms are pulled closer together. Thus, bond length decreases.
• A shorter bond means the shared electrons are held more tightly between the nuclei. Thus, bond strength (energy) increases.

Key Takeaway: Triple bonds are the shortest and strongest; single bonds are the longest and weakest.

2. Representing Molecules: Lewis Structures (SL & HL)

Step-by-Step Guide to Drawing Lewis Structures

Lewis structures (or electron dot diagrams) are a simple way to visualize the valence electrons, bonding pairs, and lone pairs (non-bonding electrons) in a molecule.

Procedure:

1. Count Total Valence Electrons: Sum the valence electrons for all atoms. For ions, add one electron for each negative charge or subtract one for each positive charge.
2. Determine the Central Atom: This is usually the least electronegative atom (never Hydrogen). Place other atoms around it symmetrically.
3. Form Single Bonds: Draw a single line (representing two shared electrons) connecting the central atom to all surrounding atoms. Subtract these electrons from the total count.
4. Complete Octets (Outer Atoms First): Place remaining electrons as lone pairs on the outer atoms until they satisfy the octet rule (or duo rule for H).
5. Complete Octet (Central Atom): Place any leftover electrons on the central atom (as lone pairs).
6. Check and Adjust (Use Multiple Bonds): If the central atom still lacks an octet, move a lone pair from an outer atom to form a double or triple bond until the octet rule is satisfied for all atoms.

Exceptions to the Octet Rule (SL & HL)

While the octet rule is a useful guide, nature doesn't always follow it strictly. You must recognize these three main exceptions:

1. Incomplete Octet: Atoms like Beryllium (Be, 4 electrons) and Boron (B, 6 electrons) are stable with fewer than eight electrons. Example: \(BF_3\).
2. Expanded Octet (HL focus): Atoms in period 3 or below (P, S, Cl, etc.) can use their empty d orbitals to accommodate more than eight electrons, resulting in 10 or 12 valence electrons. Example: \(SF_6\) (12 electrons).
3. Odd-Electron Species (Radicals): Molecules with an odd number of total valence electrons cannot satisfy the octet rule for all atoms. These species are highly reactive. Example: Nitric Oxide (\(NO\)).

3. Predicting Shape: VSEPR Theory (SL & HL)

Once we have the Lewis structure, we need to know the molecule’s actual 3D shape, which dictates its properties. We use VSEPR Theory (Valence Shell Electron Pair Repulsion).

The VSEPR Principle

The core idea is simple: electron domains (regions of electron density) around a central atom repel each other and arrange themselves to be as far apart as possible to minimize this repulsion.

• A domain can be a single bond, a double bond, a triple bond, or a lone pair. (Crucial: Multiple bonds count as one domain).
• Lone Pair Repulsion: Lone pair - lone pair repulsion is stronger than lone pair - bonding pair repulsion, which is stronger than bonding pair - bonding pair repulsion. This difference causes bond angles to be slightly smaller than the ideal geometry angles. Example: Water (\(H_2O\)) has a bond angle of 104.5°, slightly less than the ideal 109.5° for a tetrahedron.

Electron Domain Geometry vs. Molecular Geometry

We differentiate between two types of shape:

1. Electron Domain Geometry: The arrangement of all electron domains (bonding and non-bonding).
2. Molecular Geometry: The arrangement of atoms only (determined by the position of the bonding domains).

The number of domains determines the basic geometry.

Total Domains	Domain Geometry	Lone Pairs	Molecular Geometry	Approximate Angle	Example
2	Linear	0	Linear	180°	\(CO_2\)
3	Trigonal Planar	0	Trigonal Planar	120°	\(BF_3\)
3	Trigonal Planar	1	Bent (V-shaped)	< 120°	\(SO_2\)
4	Tetrahedral	0	Tetrahedral	109.5°	\(CH_4\)
4	Tetrahedral	1	Trigonal Pyramidal	< 109.5°	\(NH_3\)
4	Tetrahedral	2	Bent (V-shaped)	<< 109.5°	\(H_2O\)

Note for HL Students: You must also know the geometries for 5 and 6 domains (Trigonal Bipyramidal and Octahedral, respectively). These generate shapes like Seesaw, T-shaped, Square Planar, and Square Pyramidal.

Key Takeaway: Lone pairs determine the molecular shape but are invisible to the eye; they push the bonding pairs closer together, reducing the bond angles.

4. Molecular Polarity (SL & HL)

Covalent bonds exist on a spectrum. While electrons are shared, they are not always shared equally. This leads us to polarity.

Step 1: Bond Polarity

Bond polarity is determined by the difference in electronegativity (\(\Delta EN\)) between the two atoms.

• Non-polar Covalent Bond: Electrons are shared equally (\(\Delta EN\) is very small, e.g., \(H_2\)).
• Polar Covalent Bond: Electrons are shared unequally. The more electronegative atom attracts the shared electrons more strongly, creating a dipole moment (partial positive charge, \(\delta+\), and partial negative charge, \(\delta-\)). Example: H-Cl.

Analogy: Bond polarity is like a tug-of-war. If the teams are equal (non-polar), the rope stays central. If one team is stronger (polar), the center of the rope shifts toward the stronger side.

Step 2: Molecular Polarity

Just because a molecule has polar bonds doesn't mean the molecule itself is polar. Molecular polarity depends on the vector sum of all individual bond dipoles. In simpler terms, it depends on symmetry.

• Non-Polar Molecule: The bond dipoles cancel each other out due to the symmetrical geometry. Example: \(CO_2\) (Linear) and \(CH_4\) (Tetrahedral).
• Polar Molecule: The bond dipoles do not cancel, resulting in a net dipole moment for the entire molecule. This happens when the molecule is asymmetrical or contains lone pairs (which strongly pull the electron density to one side). Example: \(H_2O\) (Bent) and \(NH_3\) (Trigonal Pyramidal).

The Symmetry Rule:

If the central atom is surrounded by identical atoms AND there are no lone pairs on the central atom, the molecule is generally non-polar. If either of these conditions fails, the molecule is likely polar.

5. HL Extension: Delocalization, Hybridization, and Orbitals

A. Resonance Structures and Formal Charge

Sometimes, a single Lewis structure cannot accurately represent the true bonding in a molecule.

• Resonance Structures: When two or more equivalent Lewis structures can be drawn for a molecule simply by moving electrons (double bonds), the true structure is an average (a resonance hybrid) of all possibilities. The electrons involved are delocalized over the entire structure, making the bonds identical in length and strength (e.g., the two C-O bonds in the carbonate ion, \({CO_3}^{2-}\)).

When multiple non-equivalent structures can be drawn, we use Formal Charge (FC) to determine which structure is the most stable (plausible).

Formal Charge Calculation:

\[FC = (\text{Valence electrons}) - (\text{Non-bonding electrons}) - \frac{1}{2} (\text{Bonding electrons})\]
Or using the standard IB notation: \(FC = V - N - B/2\)

Rules for Plausibility: The best structure is the one where:

1. The formal charges are closest to zero for all atoms.
2. Any negative formal charge resides on the most electronegative atom.

B. Hybridization: Explaining Molecular Shapes

VSEPR successfully predicts geometry, but standard atomic orbitals (s, p) do not explain how carbon can form four equivalent bonds in a tetrahedral shape (like in \(CH_4\)).

Hybridization is the mixing of atomic orbitals (s and p) to form new, identical hybrid orbitals suitable for bonding, resulting in the geometries predicted by VSEPR.

The relationship between Electron Domains and Hybridization is direct:

• 2 Domains: sp (Linear)
• 3 Domains: sp\(^2\) (Trigonal Planar)
• 4 Domains: sp\(^3\) (Tetrahedral)
• 5 Domains: sp\(^3\)d (Trigonal Bipyramidal)
• 6 Domains: sp\(^3\)d\(^2\) (Octahedral)

Memory Aid: Just count the domains! The superscript numbers in the hybridization (excluding the 'd' for HL structures) must add up to the number of domains (e.g., sp\(^3\) means 1 s orbital + 3 p orbitals = 4 domains).

C. Sigma (\(\sigma\)) and Pi (\(\pi\)) Bonds

Hybridization helps explain the two types of covalent bonds based on how the orbitals overlap:

1. Sigma (\(\sigma\)) Bonds: Formed by the head-on overlap of orbitals (either hybrid orbitals or unhybridized s orbitals). They allow for free rotation around the bond axis. All single bonds are \(\sigma\) bonds.
2. Pi (\(\pi\)) Bonds: Formed by the side-on overlap of unhybridized p orbitals. They restrict rotation.

Bond Type Breakdown:

• Single Bond: One \(\sigma\) bond
• Double Bond: One \(\sigma\) bond and one \(\pi\) bond
• Triple Bond: One \(\sigma\) bond and two \(\pi\) bonds

Did you know? The rotation restriction caused by \(\pi\) bonds is why double-bonded molecules (like those found in certain fats) can have distinct geometric isomers (cis/trans or E/Z).

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Chapter Summary: Key Takeaways

The Covalent Model provides the rules for building molecules. Remember the core sequence for analysis:

1. Lewis Structure: Count electrons and ensure octets (where applicable).
2. VSEPR: Count electron domains (lone pairs + bonds) to predict the 3D molecular geometry.
3. Polarity: Check bond polarity and molecular symmetry to determine the overall polarity.
4. (HL) Hybridization: Use the number of domains to assign the correct hybrid orbital model (sp, sp\(^2\), sp\(^3\), etc.).

By following these models systematically, you can accurately predict the chemical behavior and physical properties of a huge range of substances! Keep practicing your Lewis structures—they are the foundation for everything else!