Question

(a) Construct a Lewis structure for \(\mathrm{O}_{2}\) in which each atom achieves an octet of electrons. (b) Explain why it is necessary to form a double bond in the Lewis structure. (c) The bond in \(\mathrm{O}_{2}\) is shorter than the \(\mathrm{O}-\mathrm{O}\) bond in compounds that contain an \(\mathrm{O}-\mathrm{O}\) single bond. Explain this observation.

Short answer

The Lewis structure of \(\mathrm{O}_{2}\) consists of a double bond between the two oxygen atoms to fulfill the octet rule. The double bond is necessary because the initial single bond structure only provided 6 electrons to each oxygen atom's valence shell instead of the desired 8 electrons. The bond in \(\mathrm{O}_{2}\) is shorter than the \(\mathrm{O}-\mathrm{O}\) single bond in other compounds because the double bond involves stronger electron-electron interactions, resulting in a stronger and shorter bond.

Step-by-step solution

Determine the total number of valence electrons

Oxygen has 6 valence electrons. Since the \(\mathrm{O}_{2}\) molecule consists of two oxygen atoms, we have a total of 12 valence electrons.

Place the atoms and connect them with single bonds

Place the two oxygen atoms and connect them with a single bond. A single bond consists of 2 electrons, so we have used 2 electrons from the 12 available. It leaves us with 10 more electrons.

Distribute the remaining electrons

Now we can distribute the remaining electrons (10) around the oxygen atoms to fulfill the octet rule (8 electrons for each atom). Initially, each oxygen atom has 2 electrons from the single bond. Adding 6 electrons to each oxygen atom gives a total of 8 electrons for each atom. The Lewis structure now looks like this: \[\text{O} :::\text{O} ::: \]

Form a double bond

The structure created in Step 3 does not fulfill the octet rule. To achieve an octet of electrons for both atoms, we will form a double bond. Move two of the lone electrons from one oxygen atom to create a second bond with the other oxygen atom. Similarly, move two of the lone electrons from the other oxygen atom to create the other half of the double bond. This creates 4 shared electrons between the oxygen atoms in the molecule. The final Lewis structure of \(\mathrm{O}_{2}\) is: \[\text{O} ::= \text{O}\]

Explain the need for a double bond

It is necessary to form a double bond in the Lewis structure of \(\mathrm{O}_{2}\) to fulfill the octet rule for both oxygen atoms. In the initial single bond structure, both oxygen atoms only had 6 electrons in their valence shells. By forming a double bond, each oxygen atom now shares 4 electrons, achieving the desired octet.

Discuss the shorter bond in \(\mathrm{O}_{2}\)

The bond in \(\mathrm{O}_{2}\) is found to be shorter than the \(\mathrm{O}-\mathrm{O}\) single bond in compounds containing the \(\mathrm{O}-\mathrm{O}\) single bond. This is because a double bond involves sharing more electrons between the two atoms, resulting in stronger electron-electron interactions and ultimately a stronger and shorter bond.