Covalent Bonding and the Shared Pair
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You should be comfortable with the basic structure of atoms, specifically the arrangement of electrons in shells and subshells, and have a general understanding of electrostatic attraction between opposite charges.
Why this matters
Covalent bonding explains why non-metals combine to form stable molecules rather than ions.
While ionic bonding involves the complete transfer of electrons to create charged species, covalent bonding relies on the sharing of electron pairs between atoms. This mechanism allows atoms to achieve a stable electronic configuration, typically resembling that of a noble gas, without the high energy cost of full ionisation. Understanding the shared pair model is fundamental to predicting molecular geometry, reactivity, and the physical properties of organic and inorganic compounds.
The Shared Pair Concept
Imagine two hydrogen atoms approaching each other. Each has one electron in its 1s orbital. Separately, each atom is higher in energy than the bonded pair. If one electron were transferred to the other, we would form H+ and H-, but hydrogen has a very high ionisation energy, making this energetically unfavourable. Instead, the atoms share their electrons. The electron pair now resides in the region between the two nuclei. This shared pair is attracted to both positive nuclei simultaneously. The result is a stable arrangement where both nuclei are surrounded by two electrons, satisfying the duet rule. This mutual attraction is the covalent bond. It is not a physical chain, but a region of high electron density that holds the nuclei together against their mutual repulsion.
Electrostatic Balance and Bond Length
A covalent bond is a dynamic equilibrium of forces. The attractive forces are between the shared electron pair and each nucleus. The repulsive forces are between the two nuclei and between the two electron pairs (if multiple bonds are present). As two atoms approach, the attractive forces initially dominate, lowering the potential energy of the system. However, as the nuclei get too close, the nucleus-nucleus repulsion increases sharply. The bond length is the internuclear distance at which the total potential energy is minimised. At this distance, the net force is zero, and the molecule is stable. If the atoms are forced closer, the repulsion dominates and the energy rises steeply; if they are pulled apart, the attraction weakens and the bond dissociates.
Bond Energy and Strength
The strength of a covalent bond is quantified by the bond dissociation energy, \( D \). This is the energy required to break one mole of bonds in the gaseous state. The bond energy depends on the size of the atoms and the number of shared pairs. Smaller atoms form shorter bonds, which are generally stronger because the electron density is closer to the nuclei, increasing the electrostatic attraction. For example, the H–H bond energy is approximately \( 436\ \mathrm{kJ\,mol^{-1}} \). In contrast, the F–F bond is weaker, at approximately \( 159\ \mathrm{kJ\,mol^{-1}} \), despite fluorine being small, due to lone pair repulsions between the non-bonding electrons on the fluorine atoms. Multiple bonds (double and triple) are stronger and shorter than single bonds because more electron pairs are shared, increasing the attractive force between the nuclei.
Polarity in Covalent Bonds
Not all covalent bonds are equal. If the two atoms sharing electrons have different electronegativities, the shared pair will be pulled closer to the more electronegative atom. This creates a dipole, with a partial negative charge (\( \delta^- \)) on the more electronegative atom and a partial positive charge (\( \delta^+ \)) on the other. The degree of polarity is determined by the difference in electronegativity, \( \Delta \chi \). If \( \Delta \chi \) is small (e.g., C–H), the bond is considered non-polar covalent. If \( \Delta \chi \) is large (e.g., O–H), the bond is polar covalent. When \( \Delta \chi \) exceeds a certain threshold (typically around 1.7), the bond is often classified as ionic, although the boundary is gradual. This polarity influences boiling points, solubility, and chemical reactivity.
A common misconception is that a covalent bond is a physical "glue" holding atoms together. In reality, it is a quantum mechanical phenomenon where the electron wavefunction is delocalised over both nuclei. The "sharing" is a description of probability density, not a literal back-and-forth movement of electrons. Furthermore, bond energy values are averages; the energy required to break a specific bond in a complex molecule may differ from the tabulated average value due to the local chemical environment. C
Worked example
Problem. Calculate the energy change when 2.0 moles of H2 molecules are formed from hydrogen atoms in the gas phase. Assume the bond dissociation energy of H–H is \( 436\ \mathrm{kJ\,mol^{-1}} \).
- Identify the process: Formation of bonds releases energy. The reaction is \( 2\mathrm{H}(g) \rightarrow \mathrm{H_2}(g) \).
- Determine the energy released per mole of H2 formed: This is equal to the bond dissociation energy, \( 436\ \mathrm{kJ\,mol^{-1}} \).
- Calculate the total energy for 2.0 moles: Multiply the molar energy by the number of moles.
- Apply the sign convention: Energy release is negative in thermodynamic terms (exothermic).
Units check. Moles cancel, leaving kilojoules, which is the correct unit for energy.
Three quick tests
- Why is the F–F bond weaker than expected based on atomic size alone?
Answer
Repulsion between lone pairs of electrons on the fluorine atoms weakens the bond. - Which has a shorter bond length: C–C or C=C?
Answer
C=C, because multiple bonds pull nuclei closer together. - Is the H–Cl bond polar or non-polar?
Answer
Polar, because chlorine is more electronegative than hydrogen.
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Every lecture and every result in this unit, with prerequisites and threads.
Lecture notes drafted with a local model and checked line by line by the editor; every number in the worked example was recomputed.