Problem 40 - General Chemistry: Principles and Modern Applications

Question

Construct the molecular orbital diagram for CaF. Would you expect the bond length of \(\mathrm{CaF}^{+}\) to be longer or shorter than that of CaF?

Step-by-Step Solution

Answer

The molecular orbital diagram for CaF includes 9 valence electrons filling up σ2s, σ*2s, σ2pz, π2px, and π2py orbitals sequentially. The bond order is 1.5. The bond length of CaF+ would be longer than that of CaF as the removal of an electron decreases bond order, hence increasing bond length.

Step 1: Identify the valence electrons

Start by identifying the valence electrons in both atoms. Calcium (Ca) is in group 2, hence it has 2 valence electrons. Fluorine (F) is in group 17, hence it has 7 valence electrons. Thus, the total number of valence electrons in CaF is 2 + 7 = 9 electrons.

Step 2: Construct the molecular orbital diagram

Start by drawing the energy levels of atomic orbitals of the individual atoms on the sides, then fill up the molecular orbitals in the center sequentially with the total number of valence electrons identified in step 1. There are 3 types of molecular orbitals formed: sigma, pi and sigma*. Fill up in the sequence σ2s, σ*2s, σ2pz, π2px=π2py, π*2px=π*2py, σ*2pz. Since we have 9 valence electrons, they fill up σ2s(2), σ*2s(2), σ2pz(2), π2px(2), and the remaining 1 electron goes to π2py.

Step 3: Deduce the bond order

First calculate the bond order which is defined as half the difference between number of electrons in bonding and antibonding orbitals. Bond Order = 0.5*(Number of electrons in bonding orbitals - number of electrons in antibonding orbitals) = 0.5*(6-3)=1.5.

Step 4: Compare Bond lengths

When one more electron is removed to form CaF+, it's being removed from a bonding orbital, thus reducing the overall bond order. When bond order decreases, bond length increases. Hence, the bond length of CaF+ will be longer than that of CaF.

Key Concepts

Valence Electrons

Understanding valence electrons is crucial in molecular orbital theory. These are the electrons available for bonding, located in the outermost shell of an atom. In the case of calcium (Ca) and fluorine (F), we consider their positions on the periodic table. Calcium is in group 2, which means it has 2 valence electrons because it has two electrons in its outer shell. On the other hand, fluorine is found in group 17, indicating it has 7 valence electrons.
Together, in a compound like CaF, we would calculate the total valence electrons by simply adding them up: 2 from calcium and 7 from fluorine, making 9 in total. These 9 electrons are the ones used to fill the molecular orbitals when constructing a molecular orbital diagram.
Being familiar with the concept of valence electrons helps immensely as it is the starting point for building molecular structures and understanding the nature of chemical bonds.

Bond Order

The bond order is a valuable measure in molecular orbital theory to assess the stability of a bond between two atoms. It is calculated using the formula:\[\text{Bond Order} = \frac{1}{2} \left( \text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals} \right)\]Calculating bond order involves examining the molecular orbital diagram and counting the electrons in bonding and antibonding orbitals. In molecular systems like CaF, the bond order indicates how many bonds effectively hold the atoms together.
A higher bond order suggests a stronger, more stable bond, usually leading to a shorter bond length, as the atoms are pulled closer together. For CaF, with a bond order of 1.5, it means there is a partial double bond character, making the bond moderately strong but not quite a double bond.
This concept helps predict how changes in electron configuration, such as the removal or addition of electrons, can impact the bond's stability and length, as seen with changes between CaF and its ion CaF+.

Molecular Orbital Diagram

Constructing a molecular orbital (MO) diagram is an excellent method for visualizing how atomic orbitals combine to form molecular orbitals, which influence molecule stability. An MO diagram displays the relative energy levels of the orbitals and the sequence in which they fill as electrons are added.
For CaF, the MO diagram starts by placing individual atomic orbitals of Ca and F on opposite sides, then builds the central molecular orbitals. Fill these orbitals according to energy levels:

• Sigma (\(\sigma\)) orbitals come first, representing strong head-on overlaps.
• Pi (\(\pi\)) orbitals are next, indicating lateral overlaps, adding extra stability.
• Sigma-star (\(\sigma^*\)) orbitals are higher in energy, and filling these can destabilize a bond.

With 9 valence electrons available, they fill the orbitals starting from the lowest energy level up to π2py, considering both bonding and antibonding characteristics.
MO diagrams not only assist in understanding the electron configuration but also in determining properties like magnetism and the bond order of a molecule. As electrons settle into these orbitals, they shape how a molecule like CaF will behave, offering a clear picture of the electronic influence on molecular structure.