Question

a. What determines bond length? b. In general, how are bond energies and bond lengths related?

Short answer

Bond length is determined by atomic sizes and bond order. Generally, shorter bond lengths correlate with higher bond energies.

Step-by-step solution

- Understanding Bond Length

Bond length is the average distance between the nuclei of two bonded atoms. It depends on the sizes of the atoms (atomic radii) and the bond order. In general, smaller atoms and higher bond orders (single, double, triple bonds) result in shorter bond lengths.

- Relation Between Bond Length and Bond Energy

Bond energy is the energy required to break a bond between two atoms. Generally, shorter bond lengths correspond to stronger bonds and higher bond energies, because the atoms are held together more tightly. Thus, there is an inverse relationship between bond length and bond energy.

Key concepts

atomic radii

Atomic radii refer to the size of an atom, which is a critical factor in determining bond length. The atomic radius is the distance from the nucleus of an atom to the outermost electrons. Smaller atoms have shorter radii, leading to shorter bond lengths when they form bonds. This is because the nuclei of smaller atoms can come closer together. For example, a hydrogen atom has a smaller atomic radius compared to a chlorine atom, resulting in shorter bond lengths when hydrogen forms bonds.
In summary, the smaller the atomic radius, the shorter the bond length, while larger atomic radii result in longer bond lengths.

bond order

Bond order represents the number of chemical bonds between a pair of atoms. Higher bond orders indicate stronger bonds and shorter bond lengths. For example:

• A single bond (bond order of 1) is longer than a double bond (bond order of 2).
• A double bond is longer than a triple bond (bond order of 3).

This is because multiple bonds bring atoms closer together, reducing the distance between their nuclei. So, as the bond order increases, bond length decreases because more bonding electron pairs draw the nuclei together. Additionally, higher bond order results in higher bond energy, since more energy is required to break multiple bonds.

inverse relationship

An inverse relationship exists between bond length and bond energy. When bond length decreases, bond energy increases. This means that as two atoms come closer together, the bond becomes stronger, requiring more energy to break it. Consequently, when the bond length is short, atoms are tightly bound together which leads to high bond energy.

• Short bond lengths correspond to high bond energies.
• Long bond lengths correspond to low bond energies.

For example, a triple bond, which is shorter and stronger than a single bond, has a higher bond energy than a single bond due to the greater overlap of electron orbitals. This principle helps us understand that atoms forming shorter bonds are held together more strongly, making the bonds harder to break.