Bond parameters, resonance and polarity

Bond length

The bond length is the distance between the nuclei of two bonded atoms. It is measured by X-ray or spectroscopic methods. For carbon to carbon bonds, in pm:

• $\text{C-C}$ in ethane: $154$
• $\text{C=C}$ in ethene: $134$
• $\text{C}\equiv\text{C}$ in ethyne: $120$

More shared pairs pull the atoms closer. Half the length of a bond between two like atoms is the covalent radius of the atom.

Bond angle

The bond angle is the angle between two bonds that meet at one atom. In water the angle between the two O-H bonds is $104.5^\circ$. Bond angles give the shape of a molecule. The next course explains them with VSEPR theory.

Bond enthalpy

The bond enthalpy is the energy needed to break one mole of a bond in the gas phase. A larger value means a stronger bond. In kJ/mol:

• $\text{H-H}$: $435.8$
• $\text{O=O}$: $498$
• $\text{N}\equiv\text{N}$: $946$

In a molecule with several bonds of the same kind, each break costs a different amount. Water loses its first hydrogen for $502$ kJ/mol and its second for $427$ kJ/mol. So we use the average bond enthalpy: $\dfrac{502 + 427}{2} = 464.5$ kJ/mol.

Bond order

The bond order is the number of bonds between two atoms in a Lewis structure. In $\text{H}_2$ it is 1, in $\text{O}_2$ it is 2, and in $\text{N}_2$ it is 3.

Molecules and ions with the same number of electrons are isoelectronic, and they often have the same bond order. $\text{N}_2$, CO and $\text{NO}^+$ all have 14 electrons and a bond order of 3. A higher bond order means a shorter bond and a larger bond enthalpy.

Resonance

Ozone has two Lewis structures of equal energy: $\text{O=O-O}$ and $\text{O-O=O}$. If either were true, ozone would have one short and one long bond. In fact both bonds measure $128$ pm. That lies between a single O-O bond, $148$ pm, and a double one, $121$ pm.

The real molecule is a single structure between the two. We call it a resonance hybrid, and the Lewis structures are its canonical forms.

• The canonical forms are not real. The molecule does not flip between them.
• The hybrid has lower energy than any canonical form, which makes it more stable.

The carbonate ion has three canonical forms. Each places the double bond on a different oxygen. So every carbon to oxygen bond is the same, with a bond order of $\tfrac{4}{3}$.

Polarity and dipole moment

In $\text{H}_2$ or $\text{F}_2$ the two atoms share the pair equally. The bond is non-polar. In HF, fluorine is more electronegative, so it pulls the shared pair closer. Fluorine gets a partial negative charge $\delta-$, and hydrogen a partial positive charge $\delta+$. The bond is polar.

The dipole moment measures the polarity:

Here $q$ is the partial charge and $d$ the distance between the charges. Its unit is the debye, D, with $1\ \text{D} = 3.33564 \times 10^{-30}$ C m. It is drawn as an arrow from the positive end to the negative end.

Hydrogen fluoride is set: a charge of $0.41e$ across $92$ pm. Make the charge 1. That is the dipole of a fully ionic bond, and real bonds always fall short of it.

Dipoles in polyatomic molecules

A molecule's dipole moment is the vector sum of its bond dipoles.

• Carbon dioxide is straight. Its two C=O dipoles are equal and opposite, so $\mu = 0$.
• Water is bent. Its two O-H dipoles add, so $\mu = 1.85$ D.
• Ammonia, $1.47$ D, and nitrogen trifluoride, $0.23$ D, have the same shape. In ammonia the lone pair adds to the bond dipoles. In $\text{NF}_3$ it works against them.

So a molecule can have polar bonds and still be non-polar overall.

Covalent character in ionic bonds

No bond is purely ionic. A small, highly charged cation pulls the electron cloud of a large anion towards itself. This polarisation gives the bond some covalent character. Fajans' rules sum it up. The covalent character is larger when:

• the cation is small;
• the anion is large;
• the charges are high;
• the cation has an outer shell like $\text{Cu}^+$, with 18 electrons, rather than a noble gas shell like $\text{Na}^+$.

So aluminium chloride is much more covalent than sodium chloride.

Practise with new numbers

Try it in Python

The program compares each hydrogen halide's measured dipole moment with the dipole a fully ionic bond would give. The ratio is the percent ionic character.

Common mistakes

• Thinking a double bond is twice as strong as a single bond. $\text{C=C}$ is strong, but less than twice $\text{C-C}$.
• Picturing resonance as switching. The hybrid is one structure all the time.
• Calling a molecule polar because its bonds are polar. $\text{CO}_2$ and $\text{BF}_3$ have polar bonds but zero dipole moment.
• Forgetting the lone pair when comparing $\text{NH}_3$ and $\text{NF}_3$.

Remember these

• Bond length falls and bond enthalpy rises as the bond order goes up.
• Average bond enthalpy: the mean of the steps that break the same kind of bond.
• Resonance: the real molecule is a hybrid of its canonical forms, with lower energy than any of them.
• $\mu = q \times d$, in debye. A molecule's dipole is the vector sum of its bond dipoles.
• Fajans: small, highly charged cations and large anions give more covalent character.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Put the carbon to carbon bonds of ethane, ethene and ethyne in order of increasing length.

2. What is the bond order of $\text{NO}^+$, and which molecule is it isoelectronic with?

3. Why are both bonds in ozone the same length?

4. Why is the dipole moment of $\text{BF}_3$ zero, though each B-F bond is polar?

5. Which is more covalent, LiCl or KCl, and why?