Problem 33 - Chemistry: The Central Science

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.

Step-by-Step Solution

Answer

The Lewis structure for O2 is constructed with a double bond (O=O) between the oxygen atoms, satisfying the octet rule by providing 8 electrons for each oxygen atom. The double bond is necessary for stable octet formation, as a single bond would provide only 7 electrons for each oxygen atom. The O-O bond in O2 is shorter than the O-O single bond in other compounds due to the stronger electron-electron repulsion in the double bond, pulling the atoms closer together.

Step 1: Determine the total number of valence electrons

Oxygen has 6 valence electrons. In the oxygen molecule (O2), there are 2 oxygen atoms. Therefore, the total number of valence electrons is 2 × 6 = 12.

Step 2: Construct the Lewis structure

Place both oxygen atoms side-by-side and share 4 electrons (2 pairs) between them. This forms a double bond (O=O). After forming the double bond, each oxygen atom will have 8 electrons (an octet) around it, including the shared electrons. The Lewis structure for O2 is: ``` O = O ``` Each oxygen atom will have two unshared electron pairs (lone pairs) on it. The full Lewis structure is: ``` O : : O ``` Now let's answer the following questions according to the given data.

Step 3: Explain why it is necessary to form a double bond

Since oxygen has 6 valence electrons, it needs 2 more electrons to achieve a stable octet for each oxygen atom. Forming a single bond (sharing one electron pair) provides 7 electrons for each oxygen atom, which is not enough to satisfy the octet rule. Forming a double bond (sharing two electron pairs), however, provides 8 electrons for each oxygen atom, meeting the octet rule. Thus, forming a double bond is necessary to achieve a stable octet for each oxygen atom in the O2 molecule.

Step 4: Explain why the O-O bond in O2 is shorter than the O-O single bond

In a double bond, there are two shared pairs of electrons between the bonded atoms (in this case, oxygen atoms). These shared pairs create stronger electron-electron repulsion, causing the atoms to be pulled closer together. This results in a shorter bond length compared to a single bond, which only has one shared pair of electrons. Consequently, the O-O bond in O2 is shorter than the O-O single bond in other compounds, since there is more electron-electron repulsion in the double bond.