The diatomic molecule OH exists in the gas phase. The bond lengthand bond energy have been measured to be 97.06 pm and 424.7 kJ/mol.Knowing that only the 2p orbitals of will interact significantlywith mol, respectively. Assume that the OH molecule is analogous tothe HF molecule discussed in the chapter and that molecular orbitalresult from the overlap of a lower-energy pz orbital from oxygenwith the higher energy 1s orbital of hydrogen(the O-H bond liesalong the z axis).
a.Which of the 2 molecular orbitals will have the greater hydrogen1s character?
b. Can the 2px orbital of oxygen from molecular orbital with the 1sorbital of hydrogen? Explain.
c. Knowing that only the 2p orbital of oxygen will interact significantly with 1s orbital of hydrogen, complete the molecularorbital energy-level diagram for OH. Place the correct number ofelectrons in the energy levels.
d.Estimate the bond order for OH.
e. Predict whether the bond order of OH+ will be greaterthan, less than or the same as that of OH.Explain
In order to answer these questions, we need to understand the concept of molecular orbital theory and how the orbitals of different atoms combine to form molecular orbitals. Let's break down each question and explain how to find the answers.
a. To determine which molecular orbital has greater hydrogen 1s character, we need to consider the overlap between the hydrogen 1s orbital and the oxygen 2p orbitals. Since the 1s orbital is closer to the nucleus, it has higher energy than the 2p orbitals. As a result, the molecular orbital formed from the overlap will have more hydrogen 1s character if there is more overlap with the hydrogen 1s orbital. Consequently, the molecular orbital with higher energy (the bonding molecular orbital) will have greater hydrogen 1s character.
b. To check if the oxygen 2px orbital can form a molecular orbital with the hydrogen 1s orbital, we need to consider their relative energies. The 2px orbital of oxygen has similar energy to the 2py and 2pz orbitals. However, the hydrogen 1s orbital has a significantly lower energy. Therefore, the energy difference between the oxygen 2px orbital and the hydrogen 1s orbital is too large for them to overlap and form a molecular orbital. Hence, the oxygen 2px orbital cannot contribute to the bonding in OH.
c. To complete the molecular orbital energy-level diagram for OH, we need to consider the relative energies of the atomic orbitals involved. The diagram should include the oxygen 2p orbitals (2px, 2py, and 2pz) and the hydrogen 1s orbital. Since the 2pz orbital of oxygen has the correct symmetry to overlap effectively with the hydrogen 1s orbital along the z-axis, it will have the lowest energy and form the bonding molecular orbital. The 2px and 2py orbitals will be higher in energy and give rise to non-bonding molecular orbitals. The energy levels should be labeled accordingly. To determine the number of electrons, we need to consider the electron configuration of oxygen (1s^2 2s^2 2p^4) and hydrogen (1s^1). Following Hund's rule and the Pauli exclusion principle, we distribute the electrons in the molecular orbitals following the Aufbau principle.
d. The bond order for OH can be calculated as (Number of bonding electrons - Number of anti-bonding electrons) / 2. By assigning the electrons to the energy levels in the molecular orbital diagram, we can determine the number of bonding and anti-bonding electrons. Subtracting the two and dividing by 2 will give us the bond order.
e. To predict the bond order for OH+, we first need to determine the number of electrons in OH+. OH+ has one less electron than OH because it has lost a negative charge. Therefore, we would remove one electron from the molecular orbital diagram previously created for OH. With this new electron configuration, we calculate the bond order following the same procedure as in part (d).
By following these steps, we can answer each question and gain a deeper understanding of molecular orbital theory and its application to diatomic molecules like OH.