Problem 36 - Chemistry: The Central Science

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.

Step-by-Step Solution

Answer

The Lewis structure of hydrogen peroxide (\(H_2O_2\)) is: O - O | | H H There are two bonding electrons between the two oxygen atoms in the single O-O bond. The O-O bond in \(H_2O_2\) is expected to be longer than the O-O bond in \(O_2\) due to the lower bond order (single bond) compared to the double bond present in \(O_2\). A higher bond order indicates a stronger and shorter bond.

Step 1: Determine the total number of valence electrons

We will start by counting the number of valence electrons available to be distributed in the Lewis structure. Hydrogen has 1 valence electron, and Oxygen has 6 valence electrons. Therefore, for hydrogen peroxide (\(H_2O_2\)), we have: Total valence electrons = 2 (number of Hydrogens) x 1 (valence electron per Hydrogen) + 2 (number of Oxygens) x 6 (valence electrons per Oxygen) = 2 + 12 = 14 valence electrons.

Step 2: Construct the Lewis structure

Start by connecting the two oxygen atoms with a single bond and placing hydrogens on each of the oxygen atoms with single bonds. Now, distribute the remaining valence electrons as lone pairs to complete the octet of electrons for each oxygen atom. Oxygen needs two more electrons to complete the octet (in addition to the single bonds to be hydrogen and the other oxygen atom). Thus, each oxygen atom will have 2 lone electron pairs, and the Lewis structure for hydrogen peroxide will be: O - O | | H H

Step 3: Determine the number of bonding electrons between oxygen atoms

Now let's determine the number of bonding electrons between the two oxygen atoms. In our Lewis structure, we can see that there is only one single bond between the oxygen atoms. It means that the O-O bond has two bonding electrons.

Step 4: Compare the O-O bond length in H2O2 and the O-O bond in O2

In order to determine whether the O-O bond in H2O2 is longer or shorter than the bond in O2, we need to consider the number of bonding electrons and the bond order. In the O2 molecule, there is a double bond between the two oxygen atoms. This double bond means that the bond order is equal to 2 (four bonding electrons total). In hydrogen peroxide, we determined that there is a single bond (bond order = 1) between the oxygen atoms. As a general rule, a higher bond order indicates a stronger and shorter bond. Since the bond order in O2 (2) is higher compared to the bond order in H2O2 (1), we would expect the O-O bond in H2O2 to be longer than the O-O bond in O2. The reason behind this is that a double bond between two atoms pulls them closer to each other compared to a single bond.

Key Concepts

Valence Electrons

Valence electrons play a vital role in understanding how atoms interact to form molecules. These are the outermost electrons in an atom and are involved in chemical bonding. For hydrogen peroxide (\(H_2O_2\)), we need to figure out the total number of valence electrons available.
When counting valence electrons:

• Hydrogen has 1 valence electron.
• Oxygen has 6 valence electrons.

So for \(H_2O_2\), we calculate:

• 2 Hydrogens x 1 valence electron = 2 electrons
• 2 Oxygens x 6 valence electrons = 12 electrons

This adds up to 14 valence electrons in total. Understanding this count is crucial, as it determines how many electrons we can use to form bonds and fill the octet around each atom. A stable Lewis structure requires placing these electrons correctly to satisfy the octet rule for each atom.

Bond Order

The concept of bond order helps us understand the strength and length of bonds between atoms. Bond order is the number of chemical bonds between a pair of atoms. Higher bond orders mean stronger, shorter bonds.
In hydrogen peroxide (\(H_2O_2\)), the two oxygen atoms are linked by a single bond:

• This corresponds to a bond order of 1.

In contrast, the oxygen molecule (\(O_2\)) is connected by a double bond:

• This has a bond order of 2.

Because the bond order in \(O_2\) is higher, its bond is stronger and shorter compared to \(H_2O_2\).
Generally, as bond order increases, atoms are pulled closer together, resulting in shorter bond lengths. This principle explains why the \(O-O\) bond in \(H_2O_2\) is longer than in \(O_2\).

Molecular Geometry

Molecular geometry provides insight into the shape and spatial arrangement of atoms within a molecule. Its understanding helps predict physical and chemical properties.
For hydrogen peroxide (\(H_2O_2\)), the molecule's geometry is influenced by the arrangement of bonded atoms and lone pairs around each oxygen atom.
Each oxygen in \(H_2O_2\) is bonded to one hydrogen and the other oxygen, forming a bent shape due to:

• Two lone pairs on each oxygen.
• Bonded pairs causing a repulsion effect.

This arrangement leads to the distinctive non-linear shape of the molecule. The angles between these bonds can significantly influence interactions with other molecules. Molecular geometry, governed by concepts like VSEPR theory (Valence Shell Electron Pair Repulsion), plays a crucial role in determining molecular behavior.