Bond Length & Strength

If you tie two friends together with one rope, they can stand fairly far apart and the connection is easy to cut. Tie them with two ropes, and they are pulled closer together, harder to separate. Tie them with three ropes, and they are practically glued to each other - very close, very hard to break free.

That is the relationship between bond order, bond length, and bond strength in a single image. More bonds between two atoms means a shorter distance between them and more energy required to break them apart. This three-way relationship is one of the most predictable trends in organic chemistry, and the MCAT tests it regularly.

Bond Order

Bond order is the number of chemical bonds between two atoms. For simple covalent bonds:

• Single bond: Bond order = 1
• Double bond: Bond order = 2
• Triple bond: Bond order = 3

For molecules described by resonance, bond order can be a non-integer. In the carbonate ion (CO3 2-), each C-O bond has a bond order of $\frac{4}{3}$ (four bonds distributed over three positions). In benzene, each C-C bond has a bond order of 1.5 (three double bonds shared over six positions).

From MO theory, bond order = (bonding electrons - antibonding electrons) / 2. This formula handles diatomic molecules and gives the same results as simple bond counting for organic molecules.

Bond Length

Bond length is the equilibrium distance between two bonded nuclei. It depends on three main factors:

1. Bond order. Higher bond order means shorter bond length. More bonds pull the nuclei closer together.

2. Atomic size. Bonds involving larger atoms are longer. A C-I bond (214 pm) is much longer than a C-F bond (135 pm) because iodine is much larger than fluorine.

3. Hybridization. Orbitals with more s character are held closer to the nucleus, creating shorter bonds. An sp-sp sigma bond is shorter than an sp3-sp3 sigma bond.

Bond Strength (Bond Dissociation Energy)

Bond dissociation energy (BDE) is the energy required to homolytically break one mole of bonds in the gas phase. Higher BDE means a stronger, harder-to-break bond.

Notice that a C=C double bond (614 kJ/mol) is not exactly twice the energy of a C-C single bond (347 kJ/mol). The sigma component contributes about 347 kJ/mol, and the pi component contributes about 267 kJ/mol. The pi bond is weaker because side-by-side overlap is less effective than head-on overlap.

The Bond Order Trend Summary

Resonance and Bond Order

When a molecule has resonance structures, the actual bond order is the average across all contributors. This affects both length and strength.

Benzene has alternating single and double bonds in any single resonance structure, but the true bond order of each C-C bond is 1.5. Accordingly, benzene’s C-C bond length (140 pm) falls between a single bond (154 pm) and a double bond (134 pm), and its bond energy is between the two as well.

Carboxylate ion (RCOO-): Two equivalent resonance structures share a double bond between two C-O positions. Each C-O bond has a bond order of 1.5, and both bonds are the same length - longer than a typical C=O but shorter than a C-O single bond.

Comparing Bonds Between Different Atoms

The trends above apply cleanly when comparing bonds between the same two elements (e.g., C-C vs. C=C). When comparing bonds between different elements, atomic size also matters:

• C-F (135 pm) is shorter than C-Cl (177 pm) because fluorine is smaller
• C=O (123 pm) is shorter than C=C (134 pm) because oxygen is smaller and more electronegative, pulling the bond tighter
• C-H (109 pm) is shorter than C-C (154 pm) because hydrogen is very small

When the MCAT asks you to rank bond lengths, first check bond order (higher order = shorter), then check atomic size (smaller atoms = shorter bonds).