Problem 8 - Chemistry An Atoms First Approach

Question

What are the relationships among bond order, bond energy, and bond length? Which of these quantities can be measured?

Step-by-Step Solution

Answer

The relationships among bond order, bond energy, and bond length are as follows: as bond order increases, bond energy also increases (positive correlation), while bond length decreases (negative correlation); and as bond energy increases, bond length decreases (negative correlation). Both bond energy and bond length can be measured experimentally using various techniques, while bond order is a theoretical concept and cannot be directly measured.

Step 1: Define bond order

Bond order refers to the number of chemical bonds between a pair of atoms. It represents the stability of the bond; higher bond order indicates a more stable bond. In molecular orbital theory, bond order can be calculated using the following formula: \(\frac{1}{2}(n_\mathrm{bonding} - n_\mathrm{antibonding})\), where \(n_\mathrm{bonding}\) is the number of electrons in bonding orbitals, and \(n_\mathrm{antibonding}\) is the number of electrons in antibonding orbitals.

Step 2: Define bond energy

Bond energy, also known as bond dissociation energy, is the amount of energy required to break one mole of a bond in a diatomic molecule or a polyatomic molecule, averaged across a range of compounds. It is an indicator of the stability of a bond; a higher bond energy means a more stable bond because more energy is required to break it.

Step 3: Define bond length

Bond length is the equilibrium distance between the nuclei of two bonded atoms in a molecule. It is a measure of the size of the bond. Shorter bond lengths usually indicate stronger bonds, while longer bond lengths indicate weaker bonds.

Step 4: Describe the relationship between bond order, bond energy, and bond length

As the bond order increases, the bond energy also increases, and the bond length decreases. This means that a higher bond order results in a more stable bond with higher bond energy and shorter bond length. Conversely, a lower bond order results in a less stable bond with lower bond energy and longer bond length. The relationship can be summarized as follows: 1. Bond order and bond energy: Positive correlation (as bond order increases, bond energy increases). 2. Bond order and bond length: Negative correlation (as bond order increases, bond length decreases). 3. Bond energy and bond length: Negative correlation (as bond energy increases, bond length decreases).

Step 5: Identify which quantities can be measured

Both bond energy and bond length can be measured experimentally. Bond energy measurements are obtained through various techniques, such as spectroscopy, calorimetry, or photoelectron spectroscopy. Bond length measurements can be determined through methods such as X-ray diffraction and electron microscopy. Bond order, on the other hand, is a theoretical concept used to describe the stability of a bond and can be deduced from the molecular orbital diagram or other bonding theories (such as Lewis structures, VSEPR theory, or valence bond theory). It cannot be directly measured experimentally.