Question

The diatomic molecule OH exists in the gas phase. The bond length and bond energy have been measured to be \(97.06 \mathrm{pm}\) and \(424.7 \mathrm{~kJ} / \mathrm{mol}\), respectively. Assume that the OH molecule is analogous to the HF molecule discussed in the chapter and that molecular orbitals result from the overlap of a lower-energy \(p_{z}\) orbital from oxygen with the higher- energy \(1 s\) orbital of hydrogen (the \(\mathrm{O}-\mathrm{H}\) bond lies along the \(z\) -axis). a. Which of the two molecular orbitals will have the greater hydrogen \(1 s\) character? b. Can the \(2 p_{x}\) orbital of oxygen form molecular orbitals with the \(1 s\) orbital of hydrogen? Explain. c. Knowing that only the \(2 p\) orbitals of oxygen will interact significantly with the \(1 s\) orbital of hydrogen, complete the molecular orbital energy- level diagram for OH. Place the correct number of electrons in the energy levels. d. Estimate the bond order for OH. e. Predict whether the bond order of \(\mathrm{OH}^{+}\) will be greater than, less than, or the same as that of \(\mathrm{OH}\). Explain.

Short answer

In summary: a. The bonding molecular orbital will have more hydrogen 1s character. b. No, the 2px orbital of oxygen cannot form molecular orbitals with the 1s orbital of hydrogen due to their different orientation. c. MO energy-level diagram: Bonding (σ) MO (2 electrons), Non-bonding 2px and 2py orbitals (4 electrons), Antibonding (σ*) MO (1 electron). d. The bond order for OH is 1/2. e. The bond order of OH+ (1) is greater than that of OH (1/2).

Step-by-step solution

Determine the molecular orbitals involved in the overlapping process

We are given that the molecular orbitals result from the overlap of a lower-energy pz orbital from oxygen and the higher-energy 1s orbital of hydrogen. So, the molecular orbitals involved are the pz orbital from oxygen and the 1s orbital of hydrogen.

Identify the molecular orbital with more hydrogen 1s character

Since hydrogen's 1s orbital is higher in energy than oxygen's pz orbital, when overlapping occurs, the bonding molecular orbital formed will have a lower energy but greater hydrogen 1s character, and the antibonding molecular orbital formed will have higher energy but less hydrogen 1s character. Thus, the bonding molecular orbital will have the greater hydrogen 1s character. Answer (a): The bonding molecular orbital will have more hydrogen 1s character.

Determine if 2px orbital of oxygen can form molecular orbitals with 1s orbital of hydrogen

Orbital overlap requires matching symmetry. The 2px orbital of oxygen is oriented along the x-axis, while the 1s orbital of hydrogen lies along the z-axis. As the orbitals are oriented in different axes, they cannot have matching symmetry, so the 2px orbital of oxygen cannot form molecular orbitals with the 1s orbital of hydrogen. Answer (b): No, the 2px orbital of oxygen cannot form molecular orbitals with the 1s orbital of hydrogen due to their different orientation.

Complete the molecular orbital energy-level diagram for OH

Knowing that only the 2p orbitals of oxygen will interact with the 1s orbital of hydrogen, we can construct the molecular orbital energy-level diagram: 1. In the energy level diagram, start with the pz bonding and antibonding orbitals from step 2. 2. Add the non-bonding px and py orbitals. 3. Place electrons in energy levels: oxygen has 6 valence electrons and hydrogen has 1, so there are a total of 7 electrons in OH. 4. Fill the electrons from the lowest to the highest energy level following the Aufbau principle. Answer (c): MO energy-level diagram: - Bonding (σ) MO (2 electrons) - Non-bonding 2px and 2py orbitals (4 electrons) - Antibonding (σ*) MO (1 electron)

Estimate the bond order for OH

Bond order can be calculated with the formula: Bond order = (Number of electrons in bonding MO - Number of electrons in antibonding MO) / 2 Following the energy levels from step 4: Bond order = (2 - 1) / 2 = 1/2 Answer (d): The bond order for OH is 1/2.

Compare the bond order of OH+ with OH

To form OH+, one electron is removed from OH, leaving 6 electrons. The electrons will be removed from the highest occupied molecular orbital (HOMO), which is the antibonding σ* MO. Construct the new energy-level diagram for OH+: - Bonding (σ) MO (2 electrons) - Non-bonding 2px and 2py orbitals (4 electrons) - Antibonding (σ*) MO (0 electrons) The bond order of OH+: Bond order = (2 - 0) / 2 = 1 Answer (e): The bond order of OH+ (1) is greater than that of OH (1/2).

Key concepts

Bond Order

Bond order is a concept from molecular orbital theory that helps us understand the stability of a molecule. It indicates the number of chemical bonds between a pair of atoms. In simpler terms, it gives us an idea about how strong or weak a bond might be. In molecular orbital theory, you can calculate bond order using the formula:\[ \text{Bond order} = \frac{\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals}}{2} \]This calculation shows the net count of stabilizing bonding interactions over the destabilizing antibonding interactions. A higher bond order suggests a stronger bond. It also predicts the molecular stability: higher bond order often implies greater stability and shorter bond lengths. In the case of the OH molecule, the bond order was calculated to be 1/2, while for the positive ion OH+, it increased to 1, indicating a stronger bond.

Molecular Orbitals

Molecular orbitals are the centerpiece of molecular orbital theory, providing a new way to look at electron distribution in molecules compared to atomic orbitals. When two atomic orbitals combine, they form molecular orbitals, which spread over the entire molecule, rather than being localized around individual atoms. The overlap of atomic orbitals, such as a hydrogen 1s orbital with an oxygen pz orbital, forms these molecular orbitals. This overlap results in a pair of molecular orbitals: a lower-energy bonding orbital and a higher-energy antibonding orbital. The bonding orbital is stable and typically filled first by electrons, leading to bond formation. The antibonding orbital, being less stable, tends to remain unfilled in stable molecules. In the OH molecule, for example, the molecular orbitals result from the overlapping of orbitals along the z-axis, due to how the oxygen's p orbitals and hydrogen's s orbitals come together.

OH Molecule

The hydroxyl radical (OH) is a diatomic molecule with interesting bonding characteristics due to its structure. When considering molecular orbitals, OH can be compared to other similar diatomic molecules like HF. In OH, the molecular orbitals form from the overlap of the oxygen's p orbitals and hydrogen's s orbital along the z-axis. Something unique about the OH molecule is its unpaired electron, which results in specific chemical properties, such as high reactivity and participation in chemical reactions like combustion. Understanding the OH molecule using molecular orbital theory is crucial because it highlights how important the orientation and energy of orbitals are when predicting the behavior of molecules. By visualizing and calculating aspects like the bond order, scientists can predict not only stability and reactivity but also physical properties like bond length and bond energy, which, for OH, were measured to be 97.06 pm and 424.7 kJ/mol, respectively.