Bond Parameters

Bond length is the equilibrium internuclear distance (measured in pm or Å). It shrinks as atomic size decreases and as bond order rises — a triple bond pulls two nuclei closer together than a single bond between the same atoms.

Bond angle is the angle between two adjacent bonds meeting at a common central atom; it encodes the molecule's shape, developed fully once VSEPR theory is introduced.

Bond enthalpy is the energy needed to break one mole of a particular bond in the gaseous state. For a molecule with several chemically equivalent bonds (like the four C–H bonds in methane), the successive bond-dissociation energies are not identical, so an average (mean) bond enthalpy is quoted instead.

Bond order, the number of electron pairs shared between two bonded atoms, is 1 for a single bond, 2 for a double bond, and 3 for a triple bond. In the valence-bond/molecular-orbital picture it is defined as:

where: $N_b$ is the number of electrons occupying bonding molecular orbitals and $N_a$ the number occupying antibonding molecular orbitals (the orbital picture itself belongs to molecular orbital theory, met later). The rule that matters here is directional: higher bond order means shorter bond length and greater bond enthalpy — the three parameters move together.

Resonance handles molecules a single Lewis structure cannot describe honestly, such as $\text{NO}_3^-$ or $\text{O}_3$. Chemists draw several valid Lewis structures — resonance structures — differing only in how electrons (not nuclei) are placed. None of them is the real molecule; the actual species is a single, unchanging resonance hybrid with properties intermediate between the contributing structures. Resonance structures are a notational device, not molecules flickering back and forth in time.

Polarity arises when two bonded atoms differ in electronegativity, leaving partial charges $\delta^+$ and $\delta^-$. It is quantified by the dipole moment:

where: $q$ is the magnitude of the separated charge and $d$ is the distance between the centres of positive and negative charge, with $\mu$ conventionally reported in debye (D). For a polyatomic molecule, the molecular dipole moment is the vector sum of all the individual bond dipoles — so a molecule built entirely of polar bonds can still be non-polar overall if those bond dipoles cancel by symmetry.

The dipole moment of $\text{CO}_2$ is measured to be zero even though each C=O bond is individually polar (oxygen, electronegativity $3.44$, is more electronegative than carbon, $2.55$). Explain this, and contrast it with $\text{H}_2\text{O}$, which has a non-zero dipole moment of about $1.85\ \text{D}$.

Step 1. Identify the bond polarity. In each C=O bond, the shared electrons sit closer to the more electronegative oxygen, giving oxygen a partial negative charge $\delta^-$ and carbon a partial positive charge $\delta^+$. Both C=O bonds in $\text{CO}_2$ are therefore genuinely polar, each with its own non-zero bond dipole.

Step 2. Fix the geometry. $\text{CO}_2$ is linear, $\text{O=C=O}$, with a bond angle of $180^\circ$ (the shape itself is explained fully in VSEPR theory; here it is simply given).

Step 3. Add the bond dipoles as vectors. The two C=O dipoles are equal in magnitude but point in exactly opposite directions along the same line, so their vector sum is zero:

$\text{CO}_2$ therefore has two polar bonds but is, overall, a non-polar molecule — $\mu = 0$.

Step 4. Contrast with $\text{H}_2\text{O}$. Water is bent, with a bond angle of about $104.5^\circ$, not $180^\circ$. The two O–H bond dipoles, equal in magnitude, no longer point in opposite directions, so their vector sum does not cancel. Answer: the resultant dipole moment of water is non-zero, about $\mu \approx 1.85\ \text{D}$, directed along the bisector of the H–O–H angle — the geometry, not the bond polarity, is what decides whether the molecule as a whole is polar.

Competitive stretch

The same reasoning rules on $\text{BF}_3$ (trigonal planar, $120^\circ$ angles, three equal B–F dipoles $120^\circ$ apart) and $\text{CCl}_4$ (tetrahedral, $109.5^\circ$ angles): in both cases the individual bond dipoles are polar, but full symmetry forces the vector sum to zero, so both molecules are non-polar overall — the same mechanism as $\text{CO}_2$, generalised to three and four bonds respectively.

• Assuming "polar bonds" automatically means "polar molecule" — geometry decides whether the bond dipoles cancel; $\text{CO}_2$ and $\text{H}_2\text{O}$ show the two possible outcomes.
• Treating resonance structures as if the molecule oscillates between them over time; they are alternate ways of drawing electrons on one fixed molecular skeleton, and the real molecule is a single, unchanging hybrid.
• Confusing bond enthalpy (always positive, energy needed to break a bond) with the enthalpy of formation of the whole molecule (which can be negative).
• Mixing up the direction of the length–order relationship: bond order and bond length are inversely related, while bond order and bond enthalpy are directly related.

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