Question

(a) Using only the valence atomic orbitals of a hydrogen atom and a fluorine atom, and following the model of Figure 9.46, how many MOs would you expect for the HF molecule? (b) How many of the MOs from part (a) would be occupied by electrons? (c) It turns out that the difference in energies between the valence atomic orbitals of H and F are sufficiently different that we can neglect the interaction of the 1 s orbital of hydrogen with the 2\(s\) orbital of fluorine. The 1 s orbital of hydrogen will mix only with one 2\(p\) orbital of fluorine. Draw pictures showing the proper orientation of all three 2\(p\) orbitals on Finteracting with a 15 orbital on \(\mathrm{H} .\) Which of the 2\(p\) orbitals can actually make a bond with a 1\(s\) orbital, assuming that the atoms lie on the z-axis? (d) In the most accepted picture of HF, all the other atomic orbitals on fluorine move over at the same energy into the molecular orbital energy-level diagram for HF. These are called "nonbonding orbitals." Sketch the energy-level diagram for HF using this information and calculate the bond order. (Nonbonding electrons do not contribute to bond order.) (e) Look at the Lewis structure for HF. Where are the nonbonding electrons?

Short answer

In summary, the HF molecule is expected to have 2 molecular orbitals (1 bonding and 1 antibonding) formed by the interaction of hydrogen's 1\(s\) orbital and fluorine's 2\(p_z\) orbital. Only the bonding orbital is occupied by electrons. The fluorine atom has three nonbonding orbitals: 2\(s\), \(2p_x\), and \(2p_y\), which result in 3 lone pairs of electrons in the Lewis structure. The bond order is calculated as 1, indicating a single bond between hydrogen and fluorine.

Step-by-step solution

Identify atomic orbitals involved in bond formation for HF

Hydrogen has only one electron in its 1\(s\) orbital, and fluorine has 7 electrons – 2 in the 2\(s\) orbital and 5 in the 2\(p\) orbitals (1 electron in each 2\(p_x\), 2\(p_y\), and 2\(p_z\) orbital).

Determine the number of molecular orbitals

Molecular orbitals are created when atomic orbitals combine. Based on the atomic orbitals of H and F, and that the hydrogen 1\(s\) orbital will mix with one of the 2\(p\) orbitals of fluorine, we can expect a total of 2 molecular orbitals: a bonding orbital and an antibonding orbital.

Determine the number of occupied molecular orbitals

Both H and F each contribute one electron to the bond formation. Hence, out of the 2 molecular orbitals formed, only the bonding orbital will be occupied by electrons.

Identify 2\(p\) orbitals making bond with 1\(s\) orbital

As the atoms lie on the z-axis, only the 2\(p_z\) orbital of fluorine can make a bond with the 1\(s\) orbital of hydrogen. The other two 2\(p\) orbitals (\(2p_x\) and \(2p_y\)) will not interact with the hydrogen 1\(s\) orbital.

Draw energy-level diagrams and calculate bond order

With the information that all other atomic orbitals on fluorine move over at the same energy into the MO energy-level diagram for HF and are called "nonbonding orbitals," we can draw the following energy-level diagram: - The 1\(s\) orbital of H and 2\(p_z\) orbital of F combine to form a bonding molecular orbital and an antibonding molecular orbital. - The 2\(s\), \(2p_x\), and \(2p_y\) orbitals of fluorine move as nonbonding orbitals. Bond order = (number of electrons in bonding orbitals - number of electrons in antibonding orbitals) / 2 = (2 - 0) / 2 = 1

Identify nonbonding electrons in Lewis structure

The nonbonding orbitals are the 2\(s\), \(2p_x\), and \(2p_y\) orbitals of fluorine. In the Lewis structure of HF, the nonbonding electrons are represented by lone pairs on the fluorine atom. There will be three lone pairs of electrons on the fluorine atom.

Key concepts

Valence Atomic Orbitals

Valence atomic orbitals are the outermost orbitals of an atom that are involved in chemical bonding. Each atom has a unique set of valence atomic orbitals where its electrons reside. For example, in hydrogen (H), the electron is in the 1s orbital, which is spherical. In fluorine (F), with a more complex electron configuration, there are 2s and 2p orbitals. These orbitals define how atoms connect and form molecules.

When two atoms approach each other, their valence atomic orbitals can overlap, resulting in bonds. The type of bond formed depends on how the orbitals interact. If the overlap is constructive, a bonding orbital is formed; if the overlap is destructive, it leads to an antibonding orbital. Understanding the specific orientations and energies of these atomic orbitals is essential for predicting the electron configuration in the resulting molecule.

Molecular Orbitals

Molecular orbitals (MOs) form when atoms combine in a molecule and their atomic orbitals overlap. According to the molecular orbital theory, electrons are not assigned to individual bonds between atoms, but are considered to be spread over orbitals that can cover the entire molecule. The formation of MOs from atomic orbitals can lead to two types: bonding orbitals, which are lower in energy because they are stabilized by the attraction between the nuclei and the electrons; and antibonding orbitals, which are higher in energy due to the repulsion involving similar electron clouds.

As we've seen in the HF molecule example, when an H atom comes close to an F atom, their orbitals mix to create molecular orbitals. These include a bonding orbital from the overlap of H's 1s and F's 2pz orbitals, as well as corresponding antibonding orbitals. However, 2s, 2px, and 2py orbitals of fluorine remain nonbonding since they do not significantly overlap with hydrogen's 1s orbital.

Bond Order Calculation

Bond order is a way to determine the number of chemical bonds between a pair of atoms. It's calculated as the difference between the number of electrons in bonding orbitals and antibonding orbitals, divided by two. In mathematical terms, bond order can be expressed as\[ \text{Bond Order} = \frac{(\text{number of electrons in bonding MOs}) - (\text{number of electrons in antibonding MOs})}{2} \].

A higher bond order indicates a stronger bond. For HF, there are two electrons in the bonding molecular orbital and none in the antibonding orbital, leading to a bond order of 1. This represents a single bond between H and F. In contrast, if the bond order is zero, it implies that there is no net bonding – the molecule is either highly unstable or doesn't exist under normal conditions. The bond order not only reflects the strength and stability of a bond but can also help predict the bond length and the magnetic properties of molecules.