Apply The Covalent Model — Apply Structure 2.2—The covalent model in problem-solving and explanations - IB Chemistry

SECTION 1

Historical Context & Motivation

For centuries, scientists struggled to explain why certain atoms stick together so stubbornly while others barely interact. Early alchemists knew that water and carbon dioxide were stable substances, but they lacked any framework for understanding why hydrogen and oxygen would combine at all. The breakthrough came when researchers began to realize that electrons — the tiny, negatively charged particles orbiting each nucleus — hold the key to chemical bonding.

The covalent model of bonding proposes that atoms can form stable connections by sharing pairs of electrons rather than completely transferring them. This idea transformed chemistry from a descriptive science into a predictive one, letting us explain molecular shapes, polarities, and reactivities from first principles.

1897 • Discovery of the Electron

J.J. Thomson identifies electrons as subatomic particles using cathode ray experiments, opening the door to understanding chemical bonding at the atomic level.

1916 • Lewis's Electron-Pair Model

Gilbert N. Lewis proposes that atoms bond by sharing electron pairs to achieve a stable octet configuration. His dot diagrams become the universal language of covalent bonding.

1927 • Quantum Mechanical Bonding Theory

Heitler and London apply quantum mechanics to the hydrogen molecule, showing mathematically how electron sharing lowers energy and stabilizes the bond.

1957 • VSEPR Theory Formalized

Ronald Gillespie and Ronald Nyholm publish their Valence Shell Electron Pair Repulsion model, allowing chemists to predict three-dimensional molecular shapes from Lewis structures.

The central question this lesson addresses is: How can we apply the covalent bonding model to predict molecular structures, explain physical properties, and solve real chemical problems? Understanding the "why" behind the model is essential, but the IB course demands that you use it as a tool — drawing Lewis structures, predicting shapes, and reasoning about polarity.

SECTION 2

Core Principles of the Covalent Model

The covalent model rests on a set of interconnected ideas that let you move from an element's position on the periodic table all the way to a prediction of its molecular behavior. Each principle builds on the one before, creating a powerful chain of reasoning that the IB expects you to use fluently in both Paper 1 and Paper 2 responses.

Electron Sharing

Atoms form covalent bonds by sharing one or more pairs of valence electrons. Each shared pair constitutes one bond: a single bond (one pair), double bond (two pairs), or triple bond (three pairs).

The Octet Rule

Most atoms bond until they are surrounded by eight valence electrons (or two for hydrogen), mimicking the electron configuration of a noble gas. This guideline helps you determine how many bonds an atom will form.

Lewis Structures

A Lewis structure is a diagram showing all valence electrons in a molecule as bonding pairs (lines) and lone pairs (dots). It is the starting point for every shape and polarity prediction.

VSEPR & Molecular Geometry

Electron domains (bonding pairs and lone pairs) around a central atom repel each other and arrange themselves as far apart as possible. This VSEPR principle determines the three-dimensional shape of the molecule.

Bond Polarity & Molecular Polarity

When atoms of different electronegativity share electrons, the bond is polar. Whether the overall molecule is polar depends on its geometry — symmetrical arrangements can cancel individual bond dipoles.

✦

KEY TAKEAWAY

Think of covalent bonding like two people sharing a textbook between them. If both pull equally, the book stays centered (a nonpolar bond). If one person is stronger, the book drifts toward them (a polar bond). The shape of the molecule is like seating people around a table — everyone wants maximum personal space, which dictates the arrangement.

SECTION 3

Visualizing Lewis Structures & VSEPR Shapes

A Lewis structure is your roadmap for predicting molecular geometry. The diagram below walks through the process of building a Lewis structure step by step, using water (H₂O) as an example. Notice how counting valence electrons, placing them as bonding and lone pairs, and then applying VSEPR leads directly to the molecule's bent shape.

The four-step process for building a Lewis structure of water. Step 1 counts valence electrons (8 total). Steps 2–3 arrange bonding pairs. Step 4 distributes remaining electrons as lone pairs. VSEPR then predicts the bent molecular geometry with a bond angle of approximately 104.5°.

In the diagram, notice that the oxygen atom has four electron domains — two bonding pairs (shown as lines to each hydrogen) and two lone pairs (shown as dots above the oxygen). VSEPR tells us these four domains adopt a tetrahedral arrangement in space. However, because we describe molecular shape by the positions of atoms only (not lone pairs), the resulting shape is called bent. The lone pairs compress the H–O–H angle from the ideal tetrahedral 109.5° down to about 104.5°, since lone pairs occupy more space than bonding pairs.

SECTION 4

Quantitative Tools: Formal Charge & Electronegativity

While much of covalent bonding is qualitative, two quantitative tools are essential for the IB. Formal charge helps you choose the best Lewis structure when more than one option is possible. Electronegativity difference tells you how polar a bond is and whether a molecule is likely to be polar overall.

FORMAL CHARGE

FC = V − L − ½B

Where V = number of valence electrons in the free atom, L = number of lone-pair electrons on the atom, and B = number of bonding electrons around the atom. The best Lewis structure minimizes formal charges on all atoms.

BOND POLARITY GUIDELINE

Δχ = |χ_A − χ_B|

Where Δχ is the electronegativity difference between atoms A and B. If Δχ < 0.4, the bond is essentially nonpolar covalent. If 0.4 ≤ Δχ < 1.7, the bond is polar covalent. If Δχ ≥ 1.7, the bond is generally considered ionic (though exceptions exist).

VALENCE ELECTRON COUNT

Total valence e⁻ = Σ(group number of each atom) ± charge

For neutral molecules, add the group numbers (main group) of each atom. For polyatomic anions, add electrons equal to the charge. For cations, subtract electrons equal to the charge. For example, NO₃⁻ has 5 + 3(6) + 1 = 24 valence electrons.

💡

IB Exam Tip

On Paper 2, you may be asked to draw Lewis structures for molecules with expanded octets (like PCl₅ or SF₆). Elements in Period 3 and beyond can accommodate more than eight electrons because they have accessible d orbitals. Always check if the central atom is in Period 3 or higher before assuming the octet rule applies.

SECTION 5

VSEPR Shapes and Molecular Polarity

One of the most powerful applications of the covalent model is predicting molecular geometry and, from that, whether a molecule is polar or nonpolar. The table below summarizes the key VSEPR shapes that the IB requires you to know, along with their bond angles and examples. After the table, a detailed diagram illustrates how the same number of electron domains can produce different molecular shapes depending on how many are lone pairs.

Electron Domains	Bonding Pairs	Lone Pairs	Molecular Shape	Bond Angle	Example
2	2	0	Linear	180°	CO₂
3	3	0	Trigonal planar	120°	BF₃
3	2	1	Bent (V-shape)	≈117°	SO₂
4	4	0	Tetrahedral	109.5°	CH₄
4	3	1	Trigonal pyramidal	≈107°	NH₃
4	2	2	Bent	≈104.5°	H₂O

Key VSEPR molecular geometries required for IB Chemistry

All three molecules have four electron domains and start from a tetrahedral arrangement. As lone pairs replace bonding pairs, the bond angle decreases (109.5° → 107° → 104.5°) and the molecular shape changes from tetrahedral to trigonal pyramidal to bent. More lone pairs also make the molecule more polar because the distribution of charge becomes more asymmetric.

The key insight from this diagram is that electron-domain geometry and molecular geometry are not always the same thing. The electron-domain geometry describes the arrangement of all electron pairs (bonding and lone). The molecular geometry describes only where the atoms sit. This distinction is critical for IB questions that ask you to explain polarity: a molecule like CH₄ is nonpolar because its symmetrical tetrahedral shape cancels all bond dipoles, while NH₃ is polar because the lone pair creates an asymmetric distribution.

SECTION 6

Worked Example: Predicting the Shape and Polarity of SCl₂

Let's apply the full covalent model workflow to sulfur dichloride (SCl₂). This is a typical IB question: given a molecular formula, draw the Lewis structure, predict the shape, and determine whether the molecule is polar.

Predicting the Shape and Polarity of SCl₂

1
Step 1 — Count Valence Electrons

Sulfur is in Group 16, so it has 6 valence electrons. Each chlorine is also in Group 17, with 7 valence electrons. Total = 6 + 2(7) = 20 valence electrons.

20 valence electrons
2
Step 2 — Identify the Central Atom and Draw Single Bonds

Sulfur is the central atom because it is the least electronegative of the three (hydrogen is not present, so we compare S and Cl). Draw a single bond from S to each Cl. Two single bonds use 2 × 2 = 4 electrons. This leaves 20 − 4 = 16 electrons to distribute.

16 electrons remaining
3
Step 3 — Distribute Lone Pairs to Outer Atoms First

Each chlorine needs three lone pairs (6 electrons) to complete its octet. That uses 2 × 6 = 12 electrons. Remaining: 16 − 12 = 4 electrons, which go on sulfur as two lone pairs.

S has 2 lone pairs; each Cl has 3 lone pairs
4
Step 4 — Apply VSEPR to Determine Shape

Sulfur has 4 electron domains (2 bonding pairs + 2 lone pairs). The electron-domain geometry is tetrahedral. The molecular geometry, determined by the positions of atoms only, is bent (V-shaped). The bond angle is approximately 103°, slightly less than the ideal 109.5° because the two lone pairs compress the bonding pairs.

Bent shape, ≈103° bond angle
5
Step 5 — Determine Polarity

Each S–Cl bond is polar because chlorine (χ = 3.16) is more electronegative than sulfur (χ = 2.58), giving Δχ ≈ 0.58 (polar covalent). Because the molecule is bent rather than linear, the two bond dipoles do not cancel. The lone pairs reinforce the asymmetry. Therefore, SCl₂ is a polar molecule with a net dipole moment.

SCl₂ is polar (bent shape, Δχ ≈ 0.58)

⚠

Common Mistake

Students sometimes confuse SCl₂ with CO₂, thinking both are linear because they have two bonds. The key difference: CO₂ has no lone pairs on carbon (only two double bonds), giving it two electron domains and a linear shape. SCl₂ has four electron domains on sulfur. Always count all electron domains, not just bonds.

SECTION 7

Strengths and Limitations of the Covalent Model

The Lewis/VSEPR covalent model is remarkably useful, but like all scientific models, it has boundaries. Understanding where it works well and where it breaks down is itself an IB assessment objective — you're expected to evaluate the strengths and limitations of models you use.

Strengths	Limitations
Accurately predicts shapes for most simple molecules (up to 6 electron domains)	Cannot explain why O₂ is paramagnetic (has unpaired electrons); molecular orbital theory is needed
Correctly identifies polar vs. nonpolar molecules using symmetry and electronegativity	Does not account for delocalized electrons well; resonance is a workaround, not a true picture
Simple to apply — requires only a periodic table and electron counting	Fails for metallic bonding and some transition metal complexes
Predicts bond order and relative bond strength (single < double < triple)	Bond angles are approximate; real molecules may deviate due to steric effects or multiple bonding
Useful for explaining trends in boiling/melting points via intermolecular forces	Cannot predict exact bond energies or bond lengths without additional data

Comparing the strengths and limitations of the Lewis/VSEPR covalent model

✦

KEY TAKEAWAY

Think of the Lewis/VSEPR model like a road map. A road map accurately shows you the route between cities and the general layout of highways, but it can't tell you the exact traffic conditions or the elevation of every hill. Similarly, the covalent model gives you a reliable framework for predicting shapes and polarities, but for deeper details like exact energies or magnetic properties, you'll eventually need more advanced models like molecular orbital theory.

SECTION 8

Connection to Advanced Theory

While the covalent model you've learned in Structure 2.2 is the foundation, IB Chemistry at HL and beyond introduces more sophisticated theories. Understanding how the Lewis/VSEPR approach connects to these advanced models helps you appreciate why it works so well for most molecules and where the next level of detail comes from.

Feature	Lewis / VSEPR (This Lesson)	Hybridization / MO Theory (HL)
Bond description	Shared electron pairs as lines	Overlapping orbitals (σ and π bonds)
Shape prediction	Electron-domain repulsion (VSEPR)	Hybridization explains why certain geometries arise (sp³ → tetrahedral)
Delocalization	Resonance structures (multiple Lewis diagrams)	Molecular orbitals spread over entire molecule
Magnetism	Cannot predict	MO diagrams show unpaired electrons
Math required	Electron counting only	Energy-level calculations

Lewis/VSEPR versus advanced bonding theories

If you continue to IB Chemistry HL, you will learn about hybridization — the idea that atomic orbitals mix to form new hybrid orbitals that match the shapes predicted by VSEPR. For example, a carbon atom in methane forms four sp³ hybrid orbitals pointing toward the corners of a tetrahedron. This doesn't contradict Lewis structures — it explains why they work. For now, master the Lewis/VSEPR approach; it's the essential toolkit that everything else builds upon.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

Explain why carbon dioxide (CO₂) is a nonpolar molecule even though each C=O bond is polar.

Show answer

CO₂ is linear because the central carbon has two electron domains (two double bonds) and no lone pairs. The two C=O bond dipoles point in exactly opposite directions (180° apart). Since they are equal in magnitude and opposite in direction, they cancel each other out, resulting in no net dipole moment. The key principle is that molecular polarity depends on both bond polarity and molecular geometry — symmetry can cancel individual bond dipoles.

Question 2: BASIC CALCULATION

Draw the Lewis structure for phosphorus trichloride (PCl₃). How many valence electrons are there in total? State the molecular geometry and the approximate bond angle.

Show answer

Phosphorus is in Group 15 (5 valence electrons) and each chlorine is in Group 17 (7 valence electrons each). Total valence electrons = 5 + 3(7) = 26. Phosphorus is the central atom with three single bonds to Cl and one lone pair (26 − 6 = 20 remaining after bonds; 18 go to three lone pairs on each Cl, and 2 form one lone pair on P). This gives four electron domains around P. The electron-domain geometry is tetrahedral, but the molecular geometry is trigonal pyramidal with a bond angle of approximately 107°. PCl₃ is polar because the asymmetric shape (one lone pair) prevents the bond dipoles from cancelling.

Question 3: INTERMEDIATE

The molecule XeF₂ exists even though xenon is a noble gas. Draw its Lewis structure, determine the number of electron domains, and predict the molecular geometry. Is XeF₂ polar or nonpolar? Explain.

Show answer

Xenon has 8 valence electrons and each fluorine has 7, giving a total of 8 + 2(7) = 22 valence electrons. XeF₂ has two single bonds (using 4 electrons) and each F gets three lone pairs (using 12 electrons). The remaining 6 electrons go on Xe as three lone pairs. Xenon therefore has 5 electron domains (2 bonding + 3 lone pairs), giving a trigonal bipyramidal electron-domain geometry. The two bonding pairs occupy the axial positions (180° apart) to minimize lone-pair–lone-pair repulsion, resulting in a linear molecular shape. Because the molecule is linear and symmetric, the two Xe–F bond dipoles cancel, making XeF₂ nonpolar. This is an example of an expanded octet, possible because Xe is in Period 5.

Question 4: APPLIED

Methanol (CH₃OH) is miscible with water, but methane (CH₄) is nearly insoluble. Using the covalent model and your knowledge of molecular polarity and intermolecular forces, explain this difference.

Show answer

Methane is a tetrahedral, nonpolar molecule (all four C–H bonds are nearly nonpolar, and the symmetric shape cancels any small dipoles). It can only form weak London dispersion forces with water molecules, which is insufficient to overcome the strong hydrogen bonds between water molecules. Methanol, in contrast, has an O–H group with two lone pairs on the oxygen. The large electronegativity difference between O and H creates a strongly polar bond, and the lone pairs on oxygen allow methanol to form hydrogen bonds directly with water. Because "like dissolves like," the polar, hydrogen-bonding methanol mixes readily with polar water, while nonpolar methane does not. This problem illustrates how Lewis structures and VSEPR lead to polarity predictions, which in turn explain macroscopic physical properties like solubility.

Question 5: CRITICAL THINKING

Ozone (O₃) has two equivalent O–O bonds with a bond length of 128 pm, which is intermediate between a typical O–O single bond (148 pm) and a typical O=O double bond (121 pm). Draw two resonance structures for ozone, calculate the formal charges on each atom, and explain how the concept of resonance accounts for the observed bond length. What does this tell you about a limitation of using a single Lewis structure?

Show answer

Ozone has 18 valence electrons (3 × 6). Two resonance structures can be drawn: in one, the left O=O is a double bond and the right O–O is a single bond (with a lone pair on the terminal O), and in the other, the positions are switched. In each structure, the central O has FC = 6 − 2 − ½(6) = +1, the double-bonded terminal O has FC = 6 − 4 − ½(4) = 0, and the single-bonded terminal O has FC = 6 − 6 − ½(2) = −1. The real molecule is a hybrid of both resonance structures, so each O–O bond is effectively a 1.5 bond — neither purely single nor purely double. This explains why the bond length (128 pm) falls between single and double bond values. The limitation revealed is that no single Lewis structure can accurately represent ozone; the true electron distribution is delocalized across the molecule. Resonance is the Lewis model's workaround for delocalization, but it requires drawing multiple structures, and the real molecule doesn't "flip" between them — it exists simultaneously as the average of all resonance contributors.

SUMMARY

Lesson Summary

Summary

The covalent model explains bonding as the sharing of electron pairs between atoms. Using Lewis structures, you count valence electrons, place bonding and lone pairs, and apply the octet rule to draw molecular diagrams. The VSEPR model then predicts three-dimensional shapes — linear, trigonal planar, tetrahedral, trigonal pyramidal, bent, and others — based on the principle that electron domains repel each other and spread as far apart as possible.

Once you know the shape, you can determine molecular polarity by combining electronegativity differences (which create polar bonds) with molecular symmetry (which can cancel or reinforce those dipoles). Formal charge helps choose the best Lewis structure, and resonance structures handle delocalized electrons. While the model has limitations — it cannot explain magnetism or give exact energies — it is the essential starting tool for predicting and explaining molecular behavior in IB Chemistry.