Question

In which of the following molecules would you expect the oxygen-to-oxygen bond to be the shortest: (a) \(\mathrm{H}_{2} \mathrm{O}_{2},\) (b) \(\mathrm{O}_{2},\) (c) \(\mathrm{O}_{3} ?\) Explain.

Short answer

The shortest oxygen-to-oxygen bond should be in \(\mathrm{O}_{2}\) because it has the highest bond order (2), which means it has the strongest bond and thus the shortest bond length.

Step-by-step solution

Understand the Molecules

First, we need to understand the structure of the given molecules. Hydrogen peroxide (\(\mathrm{H}_{2} \mathrm{O}_{2}\)) is a simple molecule where each oxygen is single-bonded to another oxygen and two hydrogen atoms. Dioxygen (\(\mathrm{O}_{2}\)) is a molecule in which two oxygen atoms are double-bonded to each other. Ozone (\(\mathrm{O}_{3}\)) is a polyatomic molecule in which one oxygen atom is double-bonded to a second oxygen atom, which is in turn single-bonded to a third oxygen atom.

Determine Bond Order

Now we need to determine the bond order of the oxygen-to-oxygen bonds in each molecule. In hydrogen peroxide, there is a single bond between the oxygen atoms, so the bond order is 1. In dioxygen, there is a double bond, so the bond order is 2. In ozone, there are 1.5 bonds on average between each pair of oxygen atoms (one double bond and one single bond shared among three atoms), so the bond order is 1.5.

Determine Bond Length

We know that bond length decreases as bond order increases. Therefore, we should expect the shortest oxygen-oxygen bond to occur in the molecule with the highest oxygen-oxygen bond order. This is dioxygen (\(\mathrm{O}_{2}\)) with the bond order of 2, so the bond in \(\mathrm{O}_{2}\) would be expected to be the shortest.

Key concepts

molecular structure

Every molecule has a unique molecular structure, which determines its physical and chemical properties. The molecular structure refers to the arrangement of atoms within a molecule. Knowing how atoms are bonded—whether by single, double, or triple bonds—helps us understand the molecule's behavior.

Taking hydrogen peroxide (\(\mathrm{H}_{2} \mathrm{O}_{2}\)) as an example, it consists of two oxygen atoms connected by a single bond, with each oxygen also bonded to a hydrogen atom. This forms a bent structure due to the repulsion between electron pairs.

• The bonding results in weak \(\mathrm{O}-\mathrm{O}\) bonds, giving the molecule its particular properties.

Dioxygen (\(\mathrm{O}_{2}\)), on the other hand, showcases a different structure, as it features a double bond between two oxygen atoms. This double bond results in a linear shape, providing it with unique characteristics.

• A double bond stems from sharing two pairs of electrons, making this type of bond stronger and shorter.

For ozone (\(\mathrm{O}_{3}\)), the structure is more complex. It includes a resonance structure featuring one double bond and one single bond, shared variably among three oxygen atoms. This resonates, meaning the structure is not fixed and can be depicted as an average of multiple arrangements.

Understanding molecular structures helps inform how molecules will interact, react, and what properties they will exhibit.

bond order

Bond order is a concept used to understand the stability and strength of bonds within a molecule. When determining bond order, one counts the number of chemical bonds between a pair of atoms.

A higher bond order generally means a stronger and shorter bond. For example, in dioxygen (\(\mathrm{O}_{2}\)), the bond order is 2 because there is a double bond between the oxygen atoms. This indicates a strong and short bond compared to a single bond, which has a bond order of 1.

In hydrogen peroxide (\(\mathrm{H}_{2} \mathrm{O}_{2}\)), the bond order is lower, at 1. This weaker bond reflects a longer bond distance between the oxygen atoms.

• Bond order corresponds directly with bond length and bond stability.

Ozone (\(\mathrm{O}_{3}\)) poses a unique situation. Here, due to its resonance, the bond order averages to 1.5. This intermediate bond order suggests bonds stronger than in \(\mathrm{H}_{2} \mathrm{O}_{2}\) but not as strong as in \(\mathrm{O}_{2}\). The concept of bond order is essential as it directly affects molecule interactions and properties.

oxygen molecules

Oxygen molecules appear in different forms within various chemical contexts, and each form possesses unique properties.

Dioxygen (\(\mathrm{O}_{2}\)) is the most common form of oxygen, vital to life on Earth. The double bond in \(\mathrm{O}_{2}\) signifies a strong connection between the two oxygen atoms, making it a stable and essential component of the atmosphere.

• It is crucial for cellular respiration processes in living organisms.
• \(\mathrm{O}_{2}\)'s double bond differs significantly from the weaker single bond seen in \(\mathrm{H}_{2} \mathrm{O}_{2}\)

Hydrogen peroxide (\(\mathrm{H}_{2} \mathrm{O}_{2}\)) represents a more reactive form of oxygen, often used as a disinfectant due to its ability to break down into water and oxygen.

Ozone (\(\mathrm{O}_{3}\)) is another interesting form, forming a layer in the Earth's stratosphere that absorbs ultraviolet radiation, protecting life on our planet. Its bond order of 1.5 reflects a delicate balance, ensuring sufficient reactivity to function effectively as an atmospheric shield.

• Ozone's resonance and bond arrangements lead it to have selective and crucial environmental roles.

These variations of oxygen molecules demonstrate the chemical diversity and importance of oxygen in different environmental and biological contexts.