Question

(a) Construct a Lewis structure for hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), in which each atom achieves an octet of electrons. (b) Do you expect the \(\mathrm{O}-\mathrm{O}\) bond in \(\mathrm{H}_{2} \mathrm{O}_{2}\) to be longer or shorter than the \(\mathrm{O}-\mathrm{O}\) bond in \(\mathrm{O}_{2} ?\)

Short answer

The Lewis structure for hydrogen peroxide (H2O2) is H - O - O - H, with each oxygen atom having 2 lone pairs. The O-O bond in H2O2 is a single bond, while in O2, it is a double bond. As bond order increases, bond length decreases, so the O-O bond in H2O2 will be longer than the O-O bond in O2.

Step-by-step solution

Determine the total number of valence electrons in H2O2

The key to constructing a Lewis structure is determining the number of valence electrons for each element. Hydrogen has 1 valence electron, and Oxygen has 6 valence electrons. For H2O2, we have: - Two hydrogen atoms, each with 1 valence electron, giving us a total of 2 valence electrons. - Two oxygen atoms, each with 6 valence electrons, giving us a total of 12 valence electrons. Adding these together, we have 14 valence electrons in H2O2.

Arrange the atoms and form bonds

We will arrange the atoms in such a way that each atom satisfies the octet rule (2 electrons for hydrogen, and 8 electrons for oxygen). Since there is only one type of bond (O-O) in the molecule besides the hydrogen atoms, we will start by placing the oxygen atoms in the center. The structure will look like this: H-O-O-H. Now, we will form single bonds between: 1) Each hydrogen atom and the adjoining oxygen atom. 2) The two central oxygen atoms. Each single bond consists of 2 electrons, and since we have three single bonds, 6 out of the 14 valence electrons would be used up in bonding.

Place the remaining electrons around the oxygen atoms

We have 8 valence electrons remaining. We will place them around the central oxygen atoms to complete their octet. Both of the oxygen atoms already have 4 electrons (from the single bonds with the other oxygen atom and the hydrogen atom). Each oxygen atom will need 4 more electrons. We will place these additional electrons as lone pairs on each of the oxygen atoms: two lone pairs per oxygen atom.

Construct the final Lewis structure for H2O2

With all the valence electrons assigned, the final Lewis structure for hydrogen peroxide (H2O2) is as follows: H - O - O - H : : Each oxygen atom has 2 lone pairs, and each hydrogen atom has a single bond to an oxygen atom, while both oxygen atoms have a single bond with the other.

Compare the O-O bond length in H2O2 with that in O2

In H2O2, the O-O bond is a single bond. In an O2 molecule, the O-O bond is a double bond. In general, as bond order increases, bond length decreases. Therefore, the O-O bond in H2O2 (single bond) will be longer than the O-O bond in O2 (double bond).

Key concepts

Valence Electrons

Each element in the periodic table contains valence electrons, which are the electrons present in the outermost shell of an atom. These electrons play a pivotal role in chemical bonding, as they are the electrons involved in forming bonds with other atoms. In the case of hydrogen peroxide, represented as \(\text{H}_2\text{O}_2\), we need to determine the total number of valence electrons to construct its Lewis structure.

For hydrogen, each atom contains 1 valence electron. Since there are two hydrogen atoms in \(\text{H}_2\text{O}_2\), this contributes 2 valence electrons to the molecule. Oxygen, on the other hand, has 6 valence electrons. With two oxygen atoms in the molecule, they contribute a total of 12 valence electrons. When we sum these contributions, the total number of valence electrons in \(\text{H}_2\text{O}_2\) is 14.

By knowing the number of valence electrons, we can arrange atoms appropriately while forming the necessary bonds.

Octet Rule

The octet rule is a guideline in chemistry that asserts atoms tend to form connections and bonds in such a manner that each atom, aside from hydrogen, ends up with eight electrons in its valence shell. This gives a more stable electronic arrangement, similar to noble gases. While creating the Lewis structure for hydrogen peroxide (\(\text{H}_2\text{O}_2\)), the octet rule is fundamental.

In our case, each hydrogen connects to an oxygen atom through a single bond since hydrogen aims to have only 2 electrons in its shell. Meanwhile, each oxygen must achieve an octet. Initially, the oxygen atoms share two electrons due to the O-O single bond. Each oxygen is also bonded to a hydrogen atom, sharing two more electrons.

• Each oxygen atom gets its required octet by acquiring and sharing electron pairs as lone pairs and through the bonds they form.
• The remaining electrons, in the form of lone pairs, complete each oxygen's octet.

By achieving the octet where applicable, hydrogen peroxide ensures stability in its electron configuration.

Bond Length Comparison

Bond length is the distance between the nuclei of two bonded atoms. It varies depending on factors like bond order, which refers to the number of bonds between a pair of atoms. Typically, the higher the bond order, the shorter the bond length.

In \(\text{H}_2\text{O}_2\), the oxygen-oxygen bond is a single bond, resulting in a larger bond length compared to the double bond found in \(\text{O}_2\). This is an important principle: as bond order increases, such as in a transition from a single to a double bond, bond length tends to decrease. The atoms are pulled closer together due to the additional bonding, requiring a contraction of the bond length.

• In \(\text{H}_2\text{O}_2\), the O-O single bond takes up more space compared to the O-O double bond in \(\text{O}_2\).
• Higher bond orders mean more shared electron pairs, leading to stronger attraction between atoms and reduced bond length.

This concept is crucial when examining different molecules and their structures, as it helps predict physical properties like molecular geometry and reactivity.