Problem 38 - General Chemistry: Principles and Modern Applications

Question

Use Lewis structures and other information to explain the observation that (a) the oxygen-to-oxygen bond lengths in \(\mathrm{O}_{2}, \mathrm{O}_{3}\) and \(\mathrm{H}_{2} \mathrm{O}_{2}\) are \(121,128,\) and \(148 \mathrm{pm},\) respectively. (b) the oxygen-to-oxygen bond length of \(\mathrm{O}_{2}\) is \(121 \mathrm{pm}\) and for \(\mathrm{O}_{2}^{+}\) is \(112 \mathrm{pm}\). Why is the bond length for \(\mathrm{O}_{2}^{+}\) so much shorter than for \(\mathrm{O}_{2} ?\)

Step-by-Step Solution

Answer

The bond lengths in \(\mathrm{O}_{2}, \(\mathrm{O}_{3}\) and \(\mathrm{H}_{2} \mathrm{O}_{2}\) are defined by the bond multiplicity, with double bonds being shorter than single bonds. The ionization of \(\mathrm{O}_{2}\) to \(\mathrm{O}_{2}^{+}\) results in an increase in the bond order and hence a decrease in bond length.

Step 1: Understanding Molecular Structures

Let's begin by understanding the molecular structures. \(\mathrm{O}_{2}\) is a diatomic molecule and its Lewis structure shows that it has a double bond. \(\mathrm{O}_{3}\) is a triatomic molecule and its Lewis structure shows that it has one double bond and one single bond, therefore has an average bond order of 1.5. \(\mathrm{H}_{2} \mathrm{O}_{2}\) on the other hand is a four atom molecule, and in its most stable conformation, it has a single bond between the two Oxygen atoms.

Step 2: Comparing Bond Lengths

Bond length is inversely proportional to bond strength and directly proportional to bond multiplicity. Double bonds are generally shorter and stronger than single bonds. Hence, in \(\mathrm{O}_{2}\) the bond length is shorter (121 pm) than in \(\mathrm{H}_{2} \mathrm{O}_{2}\) (148 pm) where there is a single bond between the Oxygen atoms. In \(\mathrm{O}_{3}\), with an average bond order of 1.5, the bond length (128 pm) is intermediate between the two extreme cases.

Step 3: Understanding Ionization

Now, let's analyze the effect of ionization on bond length. When a molecule is ionized, it loses an electron, often resulting in a higher bond order and thus a shorter bond length. This is the case for \(\mathrm{O}_{2}^{+}\). After losing an electron, \(\mathrm{O}_{2}^{+}\) will have a bond order slightly more than double bond, hence resulting in a shorter bond length (112 pm) as compared to \(\mathrm{O}_{2}\) (121 pm).

Key Concepts

Molecular Bonding

Molecular bonding refers to the way atoms connect and bind together to form molecules. These bonds can vary in type, such as single, double, or triple bonds. The type and number of bonds significantly affect the stability and properties of the molecule. For example, in molecular oxygen (\(\mathrm{O}_{2}\)), we see a double bond connecting the two oxygen atoms. A double bond indicates stronger attraction between the atoms, more electron sharing, and is generally shorter compared to a single bond.
However, in molecules like ozone (\(\mathrm{O}_{3}\)), the bonding is a bit different. Here, the structure is not simply two double bonded oxygens; instead, it consists of one double bond and one single bond, making the average bond order 1.5. This arrangement causes the bond to be longer than a typical double bond but shorter than a single bond.
The unique bonding situations among different molecules explain their varying behavior, such as bond lengths, stability, and reactivity:

• Single bonds are longer and usually found in molecules like hydrogen peroxide (\(\mathrm{H}_{2}\mathrm{O}_{2}\)), where oxygen atoms are bonded by a single bond.
• Double bonds are stronger, shorter, and exist in stable forms like in \(\mathrm{O}_{2}\).
• Resonance and intermediate bonds occur in \(\mathrm{O}_{3}\), where the structure suggests properties between a single and double bond.

Recognizing these bonding types helps predict molecular properties and interactions.

Bond Lengths

Bond lengths are an essential aspect of chemistry, determining how closely atoms are held together in a molecule. The length of a bond directly impacts the molecule's stability and strength. Shorter bonds, such as double bonds, mean a stronger attraction and more energy is required to break them.
When comparing bond lengths in molecules like \(\mathrm{O}_{2}\), \(\mathrm{O}_{3}\), and \(\mathrm{H}_{2}\mathrm{O}_{2}\), several patterns emerge:

• Double bonds are typically shorter due to stronger electron sharing, as observed in \(\mathrm{O}_{2}\) with a bond length of 121 pm.
• Single bonds are longer because they involve less electron sharing and thus a weaker connection, as seen in \(\mathrm{H}_{2}\mathrm{O}_{2}\) with a bond length of 148 pm.
• Intermediate bond lengths are found in molecules like \(\mathrm{O}_{3}\) that have resonance or partial bond characters, thus having an average length of 128 pm.

Furthermore, ionization can impact bond length. For instance, losing electrons in \(\mathrm{O}_{2}^{+}\) increases the bond order, leading to a shorter bond length of 112 pm. Understanding bond lengths is critical for predicting how a molecule might react with others and its performance in various conditions.

Oxygen Molecules

Oxygen, an essential element, forms a variety of molecules, each unique in its structure and properties. The type of molecular arrangements and bonds in these oxygen molecules influence their chemical behavior and physical characteristics.
Let's look at some common oxygen molecules:

• \(\mathrm{O}_{2}\) is a simple, stable diatomic molecule used extensively in respiration and combustion processes. It features a double bond resulting in a bond length of 121 pm.
• \(\mathrm{O}_{3}\), or ozone, plays a critical role in protecting Earth from UV radiation. Its structure of alternating single and double bonds gives an average bond length of 128 pm, illustrating its unique reactivity and transient nature.
• \(\mathrm{H}_{2}\mathrm{O}_{2}\), known as hydrogen peroxide, is used as a disinfectant with a significantly longer O-O single bond length of 148 pm, showing less bond strength than \(\mathrm{O}_{2}\).

Through ionization, oxygen molecules can become even more reactive. For example, \(\mathrm{O}_{2}^{+}\) is an ionized form where the loss of an electron increases its bond order, leading to a more tightly bound structure with a bond length of 112 pm. Understanding these variations allows us to predict and manipulate oxygen's role in chemical reactions and its application in everyday life.