Question

Consider the series \(\mathrm{Cl}_{2}, \mathrm{Br}_{2}, \mathrm{I}_{2}\). a) What is the bond order for each \(\mathrm{X}-\mathrm{X}\) bond? b) What trend is observed in bond energy? c) Considering the relative size of \(\mathrm{Cl}, \mathrm{Br}\), and \(\mathrm{I}\), what trend would you predict in \(\mathrm{X}-\mathrm{X}\) bond length?

Short answer

a) The bond order for each X-X bond in Cl2, Br2, and I2 is 1. b) The trend in bond energy is Cl-Cl > Br-Br > I-I. c) The projected trend in X-X bond length is Cl-Cl < Br-Br < I-I.

Step-by-step solution

Determine Bond Order

The bond order represents the number of bonds between two atoms in a molecule. For halogens like Cl, Br, and I, they exist in diatomic form in their elemental states, hence the bond order will be 1 for each, meaning there is a single bond between the atoms. So, the bond order for each X-X (Cl-Cl, Br-Br, I-I) is 1.

Determine Bond Energy

The bond energy is the amount of energy required to break a bond between two covalently bonded atoms. Generally, the bond energy decreases down the group in the periodic table because the size of the atoms increases, which results in a longer bond length and a weaker bond. Therefore, the trend in bond energy is Cl-Cl > Br-Br > I-I.

Predict Bond Length

The bond length is the distance between the centers of two chemically bonded atoms, which is directly related to the size of the atoms. As you move down the periodic table, atomic radius increases because additional electron shells are added. This means that the bond length will increase down the group. Therefore, the trend in the bond length would be Cl-Cl < Br-Br < I-I.

Key concepts

Bond Energy

Bond energy refers to the energy required to break a bond between two atoms in a molecule. In the series of diatomic halogens like

• \( \text{Cl}_2 \),
• \( \text{Br}_2 \), and
• \( \text{I}_2 \)

We observe a trend in bond energy when we move down the periodic table. The bond energy trend reflects the change in atomic size and bond length within these molecules. As we move down from chlorine to iodine, the atomic size increases. Larger atoms form longer and generally weaker bonds. Therefore, a longer bond will require less energy to break. For these halogens, the bond energy decreases in the order:

• Cl-Cl (highest bond energy)
• Br-Br
• I-I (lowest bond energy).

Understanding bond energy helps explain how stable a molecule is, as stronger bonds usually mean a more stable molecule.

Bond Length

Bond length is crucial to understanding the physical properties of molecules. It refers to the distance between the centers of two bonded atoms. In diatomic molecules such as

• \( \text{Cl}_2 \),
• \( \text{Br}_2 \), and
• \( \text{I}_2 \)

the bond length is influenced by the size of the atoms involved. Larger atoms (e.g., iodine) will naturally have longer bond lengths because they possess more electron shells, which increase the distance between the bonded atoms' centers. When we compare the bond lengths among these halogens:

• Cl-Cl has the shortest bond length because chlorine has a smaller atomic radius.
• Br-Br bond length is moderate as bromine is larger than chlorine but smaller than iodine.
• I-I exhibits the longest bond length due to the largest atomic size among the three.

Bond length provides insight into molecular geometry and potential reactivity.

Periodic Trends

Periodic trends are patterns within the periodic table that help predict various chemical properties. These trends are tied to the arrangement of electrons within atoms as we move across periods or down groups.For the halogen series \(\text{Cl}_2\), \(\text{Br}_2\), and \(\text{I}_2\), periodic trends greatly influence both bond energy and bond length.

• Atomic Size: As we move down the group from chlorine to iodine, the atomic size increases due to the addition of electron shells.
• Bond Energy: Increased atomic size typically results in decreased bond energy. Larger atoms form longer and weaker bonds because the electrons are more distant from the nucleus.
• Bond Length: Simultaneously, bond length increases down the group. The greater distance between atomic centers is because of the larger atomic radii.

Understanding periodic trends gives insight into predicting the behavior and characteristics of elements and their compounds, aiding in the study of chemical reactions and bonding interactions.