Measuring Bonds and Understanding Resonance

Measurements test our drawings

Lewis structures are useful pictures, but a bond line is not a measurement. Experiments can reveal how far apart nuclei are, how much energy is needed to separate bonded atoms, and how the bonds are arranged. Comparing those measurements with the drawings tells us both what the model explains and where it needs improvement.

Bond length, atomic radius, and bond angle

The nuclei in a bonded pair have an equilibrium separation at the minimum-energy arrangement. This separation is called the bond length. Spectroscopy and diffraction methods can determine such distances. A bond length is a nuclear separation, rather than the distance from the outer edge of one electron cloud to the other.

For two identical covalently bonded atoms, half their nuclear separation is their covalent radius in that bonding situation. For unlike atoms, a bond length can often be estimated by adding the covalent radii. These radii are useful approximations, and their values depend on the bonding context.

A van der Waals radius describes an atom in a nonbonded contact. For two identical nonbonded atoms in neighbouring molecules, half the relevant contact distance gives this radius. It is generally larger than the covalent radius because bonded atoms are held closer together.

Bond angles describe spatial arrangement. A water molecule has an H–O–H angle of about 104.5°, so its atoms form a bent arrangement. Bond length and angle answer different questions: one is a distance, the other a direction difference.

The chapter’s covalent-radius reference table supports the same way of reading data: specify the element, its bonding situation, and the unit. Comparing H–F with H–I shows how a larger bonded atom can produce a longer bond. Comparing C–C, C=C, and C≡C shows the effect of multiplicity while keeping the element pair unchanged. These are different comparisons and should not be mixed.

Use single-bond radii unless a different order is specified. Carbon’s decreasing listed radius from single through triple bonding reflects the closer nuclear approach in higher-order bonds. The table also shows why “atomic radius” is not one unchanging number independent of bonding.

Bond enthalpy measures the energy cost of separation

Bond enthalpy is the energy needed to break one mole of a specified type of bond between gaseous species. Its unit is kilojoules per mole. Breaking a bond requires energy; the corresponding bond-forming process releases energy. A larger dissociation enthalpy indicates a stronger bond for the stated process.

The chapter gives about $498\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ for O₂ and $946\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ for N₂ dissociation. These high values help us recognise strong multiple bonds. In a polyatomic species, apparently similar bonds need not have identical successive dissociation energies because removing one atom changes the chemical environment of the remaining fragment.

Bond order links multiplicity with properties

In a simple Lewis drawing, bond order is the number of shared pairs between a particular pair of atoms. Thus a single bond has order one, a double bond order two, and a triple bond order three. For comparable bonds between the same element pair, increasing order generally shortens and strengthens the bond.

This trend works well for the C–C series in the table. It is not a rule that every triple bond in any species must be shorter than every double bond between unrelated elements. Atomic size, electron distribution, and molecular environment also matter. Molecular orbital theory later provides an electron-occupancy definition that can produce fractional orders. Particular isoelectronic species provide useful checks: F₂ and peroxide each have bond order one in the simple MO treatment, while N₂, CO, and NO⁺ each have order three. Isoelectronic means having the same total electron count. It is not a guarantee that all their measured properties are identical.

Resonance explains equivalent bonds

Ozone can be drawn with a double bond on either side of its central oxygen. Either drawing by itself predicts one long single bond and one short double bond. Experiment instead finds two equivalent O–O bonds of intermediate length. The molecule therefore needs a description that is not limited to one fixed Lewis drawing.

The alternative Lewis drawings are canonical structures. The real species is the resonance hybrid, with an electron distribution spread over the relevant bonded region. For ozone, the equivalent bonds are commonly described by an average order of 1.5. The hybrid has lower energy than either isolated canonical description would represent, so resonance contributes to stabilisation. The source compares a reference O–O single-bond length near 148 pm with an O=O length near 121 pm; ozone’s two equal bonds are about 128 pm. The measured intermediate value supports the shared, delocalised description.

Carbon dioxide also has contributing canonical forms in addition to its dominant neutral O=C=O drawing. Charge-separated forms can be drawn with a triple bond on one side and a single bond on the other. Their relative contributions are not necessarily equal: formal charge and energy help us judge the importance of a contributor. The physical molecule has equivalent C–O bonds. Comparisons of its measured distances with reference double- and triple-bond distances motivate these additional contributions. Reference lengths vary with chemical context, so they should not be treated as universal constants for every C–O bond.

Check your understanding

Use the measurement or model appropriate to the question. Distinguish a measured distance from a radius, an energy per mole from an electron count, and a resonance hybrid from its individual drawings.