Problem 104 - Chemistry: The Central Science in SI Units, Global Edition

Question

Potassium peroxide is composed of \(70.96 \% \mathrm{~K}\) and \(29.04 \% \mathrm{O}\). Each peroxide ion has a net charge of \(2^{-}\). (a) Given the molecular weight of the compound is 110.19 , determine the chemical formula of potassium peroxide. \((\mathbf{b})\) What is the number of valance electron pairs in the peroxide ion? (c) Draw the Lewis structure of the peroxide ion. (d) Compare the \(\mathrm{O}-\mathrm{O}\) bond distance in oxygen molecule and potassium peroxide.

Step-by-Step Solution

Answer

The chemical formula of potassium peroxide is \(K_2O_2\). The peroxide ion has 6 valence electron pairs. The Lewis structure of the peroxide ion is O-O with a '-' sign on both O. The O=O bond in an oxygen molecule is shorter and stronger than the O-O bond in potassium peroxide due to the double bond in the oxygen molecule.

Step 1: 1. Calculate the moles of K and O in the compound

Since we know the percentage composition of potassium (K) and oxygen (O) in potassium peroxide, we can assume we have 100 grams of the compound. With this assumption, we can calculate the moles of K and O present in 100 grams of potassium peroxide: Moles of \(K = \dfrac{70.96 g}{39.1 g/mol} = 1.815\text{ moles}\) (using the molar mass of K = 39.1 g/mol) Moles of \(O = \dfrac{29.04 g}{16.0 g/mol} = 1.815\text{ moles}\) (using the molar mass of O = 16.0 g/mol)

Step 2: 2. Determine the chemical formula

Using the moles of K and O calculated in step 1, the chemical formula of the compound can be determined by dividing the moles of each element by the lowest moles value and then multiplying the ratios by the net charge of the peroxide ion (2^-): Moles ratio of K : O = 1.815 moles : 1.815 moles = 1 : 1 Thus, the chemical formula of potassium peroxide is \(K_2O_2\).

Step 3: 3. Count the valance electron pairs in the peroxide ion

In the peroxide ion, the two oxygen atoms are bonded together. Since oxygen has 6 valence electrons, and there are two oxygen atoms, there are a total of 12 valence electrons for the peroxide ion. As each bond requires 2 electrons, there are a total of 6 valence electron pairs in the peroxide ion.

Step 4: 4. Draw the Lewis structure of the peroxide ion

To draw the Lewis structure of the peroxide ion (O2^2-), follow these steps: i. Arrange the O atoms to form an O-O bond ii. Allocate the remaining valence electrons to form O=O with 4 valence electrons already used iii. Add the extra 2 electrons to fulfill the octet rule iv. Add the charge specification as 2^- The resulting Lewis structure is shown below: O-O with a '-' sign on both O.

Step 5: 5. Compare the O-O bond distance in oxygen molecule and potassium peroxide

The O=O bond in an oxygen molecule is shorter and stronger than the O-O bond in potassium peroxide because the oxygen molecule has a double bond (O=O) while the potassium peroxide has a single bond (O-O). The double bond in the oxygen molecule requires more overlap of atomic orbitals, which brings the O atoms closer together and results in a shorter bond distance.

Key Concepts

Chemical Formula of Potassium Peroxide

The chemical formula of potassium peroxide is determined by its molar composition. Potassium peroxide consists of 70.96% potassium (K) and 29.04% oxygen (O). To find the chemical formula, we need to convert these percentages into moles. Assuming we have 100 grams of potassium peroxide, we calculate the moles of potassium as \(\frac{70.96}{39.1} = 1.815\text{ moles}\), and for oxygen, \(\frac{29.04}{16.0} = 1.815\text{ moles}\). Since the moles of K and O are the same, the ratio is 1:1. However, due to the peroxide ion's charge of \(2^-\), the actual formula becomes \(K_2O_2\), reflecting two potassium ions for every peroxide di-anion.

Lewis Structure of Peroxide Ion

The Lewis structure is essential for visualizing the bonding of atoms within a molecule. For the peroxide ion \((O_2^{2-})\), it involves two oxygen atoms sharing a bond. Each oxygen atom begins with 6 valence electrons, giving us a total of 12 valence electrons to arrange. Initially, we form a single O-O bond using 2 electrons.
To satisfy the octet rule, we then distribute the remaining 10 electrons around the oxygen atoms. This fulfills their octets and the structure shows additional lone pairs on each oxygen atom, with the entire structure carrying a \(2^-\) charge to reflect the extra electrons added.
The Lewis structure not only shows bonds but also highlights the charge and distribution of electrons, helping in understanding the molecule's reactivity and interactions.

Valence Electrons in Peroxide Ion

Valence electrons play a crucial role in determining how atoms bond in a molecule. In the peroxide ion, each oxygen atom has 6 valence electrons, resulting in a total of 12 valence electrons for the peroxide ion \((O_2^{2-})\).
When oxygen atoms bond in this di-anion, two of the electrons form a bond between the oxygen atoms, creating a single bond. The remaining 10 electrons are present as lone pairs on the oxygen atoms, contributing to a total of 6 electron pairs including the bonding pair.
This electron arrangement demonstrates that the peroxide ion is more reactive due to the presence of excess electrons that can participate easily in chemical reactions, increasing the potential for interactions with other chemical species.

Oxygen Bond Distance in Peroxide Ion

The bond distance in molecules is determined by the type of bond between atoms. In the case of the peroxide ion \((O_2^{2-})\), the O-O bond is a single bond. Single bonds result in greater distances between the bonded atoms compared to double bonds.
In contrast, in an oxygen molecule \((O_2)\), the bond is a double bond \((O=O)\), which is shorter and stronger as a result of greater atomic orbital overlap. This increased overlap draws the oxygen atoms closer together, creating a shorter bond distance.
Thus, the bond distance in a potassium peroxide is longer than that in an oxygen molecule, indicating weaker interaction, which makes the peroxide ion more susceptible to breaking and reacting, reflecting its chances for participating in redox reactions.