Problem 110 - Chemistry The Central Science In Si Units

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 \(\mathrm{H}\) and \(\mathrm{F}\) 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 F interacting with a \(1 s\) 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.) \((\mathbf{e})\) Look at the Lewis structure for HF. Where are the nonbonding electrons?

Step-by-Step Solution

Answer

(a) 2 MOs; (b) 2 bonding, 6 nonbonding. (c) Only 2pz bonds; (d) MO diagram, bond order = 1; (e) 6 nonbonding electrons on F.

Step 1: Determine Valence Atomic Orbitals

The valence atomic orbitals for a hydrogen atom are the 1s orbital, while for a fluorine atom, the valence orbitals are the 2s and 2p orbitals.

Step 2: Identify Molecular Orbitals (MOs)

When the valence atomic orbitals combine to form molecular orbitals, each pair of atomic orbitals forms one bonding orbital and one antibonding orbital. However, we only consider the interaction between H's 1s and F's 2p in this case, as the interaction of 1s with 2s is negligible due to energy differences. Therefore, one bonding 1s-2p orbital and one antibonding 1s-2p* orbital are expected.

Step 3: Count Occupied Molecular Orbitals

Hydrogen has 1 valence electron, and fluorine has 7 valence electrons, totaling 8 valence electrons for HF. The bonding orbital from step 2 is filled by 2 electrons, leaving 6 electrons which fill three nonbonding fluorine 2p orbitals.

Step 4: Identify Bonding Orbital Interaction

The 1s orbital of hydrogen can only effectively overlap with the 2pz orbital of fluorine if the atoms lie along the z-axis, forming a sigma (F_1s-2p_z) bond.

Step 5: Draw Energy-Level Diagram

HF's energy-level diagram includes a lower energy bonding orbital 1s-2p_z), nonbonding orbitals (2s, and two 2p orbitals), and a higher energy antibonding 1s-2p_z)*. The bonding MO is occupied by 2 electrons, and the nonbonding orbitals are filled with 6 electrons.

Step 6: Calculate Bond Order

Bond order is calculated as:
7(number of electrons in bonding orbitals - number of electrons in antibonding orbitals)1s-2p_z) has 2 electrons and 1s-2p_z)* has 0, giving a bond order of 1.

Step 7: Identify Nonbonding Electrons in Lewis Structure

In HF's Lewis structure, fluorine has 3 lone pairs or 6 nonbonding electrons, while hydrogen has none.

Key Concepts

Valence Atomic Orbitals

Valence atomic orbitals are the orbitals that contain the outermost electrons of an atom; these electrons are involved in chemical bonding. For a hydrogen atom, the valence atomic orbital is the 1s orbital. In contrast, for a fluorine atom, the valence orbitals include the 2s and 2p orbitals.

• The 1s orbital of hydrogen contains one electron.
• Fluorine has its valence electrons distributed in the 2s () and 2p () orbitals.

These valence orbitals overlap to form molecular orbitals when atoms begin to interact and form molecules like hydrogen fluoride (HF).
Understanding the role of valence atomic orbitals is essential for predicting how different elements form bonds and how these bonds affect molecular structure and behavior.

Bonding and Antibonding Orbitals

When valence atomic orbitals combine, they form molecular orbitals, which can be classified into bonding and antibonding orbitals based on their relative energy and potential to stabilize the molecule. Bonding orbitals are formed when atomic orbitals overlap constructively, leading to an increase in electron density between the nuclei, thus holding them closer together and lowering the energy of the system.
On the other hand, antibonding orbitals result from destructive overlap, which creates a node between the nuclei where the probability of finding an electron is minimal, thus increasing the system's energy.

• In HF, hydrogen's 1s and fluorine's 2p orbitals primarily interact.
• This interaction produces one bonding (s-2p_z) orbital and one antibonding (s-2p_z)* orbital.

Understanding the difference between these orbitals explains why certain molecular arrangements are more stable than others.

Energy-Level Diagram

An energy-level diagram provides a visual representation of the relative energies of molecular orbitals compared to atomic orbitals. It helps explain how electrons are distributed in a molecule's orbitals and indicate its stability. In HF, the energy-level diagram illustrates:

• A lower energy bonding orbital s-2p_z).
• Nonbonding orbitals that maintain the energy of fluorine's 2s and two 2p orbitals.
• A higher-energy antibonding orbital, s-2p_z)*, which isn't occupied by electrons.

Electrons will fill the lowest energy orbitals first, starting with the 2 electrons in bonding s-2p_z) orbital, enhancing the stability of the molecule. Nonbonding orbitals, which are not involved in bonding, remain filled by valence electrons but do not affect the energy of bond formation.

Lewis Structure

A Lewis structure is a simplified way to show the valence electrons in a molecule. It helps predict the location of bonds and lone electron pairs. For HF, the Lewis structure demonstrates the single bond between hydrogen and fluorine. The fluorine atom has three lone pairs of electrons:

• These nonbonding pairs are represented as dots around fluorine.
• Lone pairs occupy space and affect molecular shape but don't contribute to bond order.

By drawing Lewis structures, one can visually account for all valence electrons in a molecule and gain insights into its potential shape and reactivity.

Bond Order

Bond order is a concept used to determine the stability of a chemical bond, calculated by the difference between the number of electrons in bonding and antibonding orbitals, divided by two.
For HF, the bond order is:\[ Bond\ Order = \frac{Number\ of\ electrons\ in\ bonding\ orbitals\ - \ Number\ of\ electrons\ in\ antibonding\ orbitals}{2} \]With 2 electrons in the bonding orbital and none in the antibonding orbital for HF, the bond order is 1, indicating a single, stable bond existing between hydrogen and fluorine.
A higher bond order generally means a more stable and shorter bond. Therefore, as the bond order increases, the energy and strength of the bond also increase. This concept is crucial for predicting the characteristics and reactivity of molecules.