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) How many bonding electrons are between the two oxygen atoms? (c) 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 \(\mathrm{O}_{2} ?\) Explain.

Short answer

The Lewis structure of \(\mathrm{H}_{2}\mathrm{O}_{2}\) has a single bond between the two oxygen atoms. There are 2 bonding electrons between these oxygen atoms. The O-O bond in H2O2 is expected to be longer than the O-O bond in O2 because single bonds are generally longer than double bonds, and O2 has a double bond between its oxygen atoms.

Step-by-step solution

Determine the total number of valence electrons

First, we need to find out how many valence electrons are present in one molecule of \(\mathrm{H}_{2}\mathrm{O}_{2}\). Hydrogen has 1 valence electron, and oxygen has 6 valence electrons. So the total number of valence electrons for \(\mathrm{H}_{2}\mathrm{O}_{2}\) is: \[(2\times 1) + (2\times 6) = 14\]

Arrange the atoms and create a skeleton structure

Next, we will arrange the atoms in a way that makes sense for forming bonds. Since hydrogen can only form one bond, we will place one hydrogen atom next to each oxygen atom, since the oxygen atoms need to bond as well. So, our skeleton structure will be H-O-O-H.

Distribute the remaining electrons

Now, we need to distribute the remaining electrons to satisfy the octet rule for each atom (except hydrogen, which can only have two electrons). We already have 4 electrons in the H-O-O-H skeleton. So, we can distribute the remaining 10 electrons amongst the oxygen atoms. Each oxygen atom will have 3 lone pairs, meaning they now have a total of 8 electrons (including the shared pair). Finally, the Lewis structure of \(\mathrm{H}_{2}\mathrm{O}_{2}\) looks like this: O / \ H O - H \ O

Answer part (b) - Number of bonding electrons

From the Lewis structure above, we can see that there is a single bond between the two oxygen atoms. A single bond consists of two electrons, so there are 2 bonding electrons between the two oxygen atoms in H2O2.

Answer part (c) - Comparing O-O bond length in H2O2 and O2

In molecular oxygen (\(\mathrm{O}_{2}\)), there is a double bond between the two oxygen atoms. On the other hand, in hydrogen peroxide (H2O2), there is a single bond between the oxygen atoms. Generally, single bonds are longer than double bonds, because the increased electron density in a double bond causes the atoms to be closer together. Therefore, we expect the O-O bond in H2O2 to be longer than the O-O bond in O2.

Key concepts

Valence Electrons

Valence electrons play a pivotal role in understanding the chemical bonding of elements. These are the electrons that reside in the outermost shell of an atom and are instrumental in forming bonds with other atoms. To construct a Lewis structure, which is a visual representation of molecule showing all the valence electrons, the first step is to calculate the total number of valence electrons available in the molecule.

For hydrogen peroxide (H_{2}O_{2}), we begin by determining the valence electrons for each constituent atom. Hydrogen, by nature, has one valence electron, while oxygen has six. It's important for students to remember that the total count of valence electrons is crucial as it dictates how atoms can bond together to achieve stable electron configurations, often leading toward the satisfaction of the octet rule.

The process involves adding up the valence electrons from all the atoms in the molecule. In the case of H_{2}O_{2}, two hydrogen atoms contribute two electrons (1 electron each), and two oxygen atoms contribute twelve electrons (6 electrons each), totaling fourteen valence electrons that need to be distributed in the molecule's Lewis structure.

Understanding how these electrons pair up to form bonds or remain as lone pairs is a fundamental aspect of chemistry that governs the behavior and properties of molecules.

Octet Rule

The octet rule is a chemical rule of thumb that reflects a pattern of stability seen in most molecules. According to this rule, atoms seek to have eight electrons in their valence shell, which corresponds to a full outer shell and resembles the electron configuration of the noble gases, known for their chemical inertness.

In the case of hydrogen peroxide, each oxygen atom strives to fulfill this rule by sharing electrons via bonds and maintaining lone pairs. Hydrogen is an exception to the octet rule; it is content with two electrons in its valence shell, which makes it stable and similar to the configuration of helium.

Distributing the valence electrons to satisfy the octet rule for the oxygen atoms while considering the capacities of the hydrogen atoms is a nuanced process. Remember, each bond formed between atoms involves two shared valence electrons, contributing to the octet or duet (for hydrogen) completion. The Lewis structure we construct based on these principles gives us a clear visual of how the atoms in H_{2}O_{2} are bonded and how the remaining valence electrons form lone pairs over the oxygen atoms. These lone pairs affect the shape and angle of the molecule, which is further explored in VSEPR theory.

Bond Length

Bond length, the distance between the nuclei of two bonded atoms, is influenced by the type of chemical bond and the size of the atoms involved. Generally, single bonds are longer than double bonds because they have fewer shared electrons. The reduced electron density between the atoms in a single bond allows them to reside further apart.

Using our understanding of bond length, we can analyze the structure of hydrogen peroxide (H_{2}O_{2}) and compare it to that of molecular oxygen (O_{2}). In O_{2}, two oxygen atoms are connected by a double bond, containing four shared electrons, pulling the atoms closer together and leading to a shorter bond length. Conversely, in H_{2}O_{2}, a single bond connects the two oxygen atoms, resulting in a longer bond since only two electrons are shared.

Recognizing the different bond lengths is important for predicting the physical and chemical properties of a substance. In relation to the exercise, it is an analytical conclusion based on chemical understanding that the O-O bond in H_{2}O_{2} is expected to be longer than in O_{2} due to the single versus double bonding. Discussing bond length assists students in connecting the concepts of electron sharing, bond types, and molecular geometry.