Problem 116 - Chemistry The Molecular Nature of Matter

Question

Assume that in the \(\mathrm{NO}\) molecule the molecular orbital energy level sequence is similar to that for \(\mathrm{O}_{2}\). What happens to the NO bond length when an electron is added to \(\mathrm{NO}\) to give \(\mathrm{NO}^{-} ?\) How would the bond energy of \(\mathrm{NO}\) compare to that of \(\mathrm{NO}^{-} ?\)

Step-by-Step Solution

Answer

Adding an electron to form NO- places it in an antibonding orbital, increasing bond length and decreasing bond energy compared to NO.

Step 1: Review Molecular Orbital Theory

Understand that according to molecular orbital (MO) theory, atomic orbitals combine to form molecular orbitals, which are spread over the entire molecule. Electrons in these orbitals contribute to the bond order of the molecule. Bond order is determined by the formula: Bond Order = (number of electrons in bonding MOs - number of electrons in antibonding MOs) / 2. A higher bond order implies a stronger and shorter bond.

Step 2: Consider the Electron Configuration of NO and NO-

Analyze the electron configuration of the NO molecule based on the molecular orbital energy level sequence of O₂. NO has 11 valence electrons, and according to Hund's rule and the Aufbau principle, the additional electron to form NO- would be placed in the next available molecular orbital, which is an antibonding orbital if the energy level sequence is indeed like that of O₂.

Step 3: Determine the Effect on Bond Length

Because the extra electron in NO- occupies an antibonding orbital, it weakens the bond, leading to a decrease in bond order. A decrease in bond order from NO to NO- suggests that the bond length in NO- will be longer than in NO.

Step 4: Compare Bond Energies

With the addition of an electron, the bond order of NO⁻ decreases, indicating that the bond is weaker than in NO. Weaker bonds require less energy to break so the bond energy of NO- is less than that of NO.

Key Concepts

NO Bond Length

Understanding the NO bond length requires a basic grasp of how molecular structures behave when electron configurations change. In the case of the nitrogen monoxide (NO) molecule, we delve into its bond length alteration upon gaining an extra electron to become an anion, referred to as NO-. According to molecular orbital (MO) theory, the addition of an electron to the molecular orbitals changes the dynamics of the electrons within.

By adding an electron to NO, we populate an antibonding orbital based on the similarity to O₂'s electron configuration. Antibonding orbitals are designed to weaken the bond between two atoms. Therefore, when NO becomes NO-, the added electron causes the bond length to increase. In simpler terms, think of the bond between the nitrogen and oxygen atoms as a spring; adding an electron is like adding weight to the spring, causing it to stretch out more.

Molecular Orbitals

To thoroughly comprehend this concept, envision molecular orbitals (MOs) as the housing for electrons in a molecule. These orbitals are formed by the combination or mixing of the individual atomic orbitals (AOs) when atoms bond together. They spread across the molecule and describe the regions in space where there is a high probability of finding electrons.

Bonding and Antibonding Orbitals

MOs are classified into bonding and antibonding types.

• Bonding orbitals foster strong attractions between atoms, leading to a robust bond.
• Antibonding orbitals do the opposite, they work against the bond, making it weaker and longer when electrons occupy these spaces.

The energy level sequence, like in the molecule O₂, guides us in predicting where the electrons will reside, influencing bond properties, and stability.

Bond Order

The discussion of bond order is vital for predicting the strength and length of a bond in molecular orbital theory. It's calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{number of electrons in bonding MOs} - \text{number of electrons in antibonding MOs})}{2} \]
An increase in bond order signifies a stronger, shorter bond, while a decrease indicates a weaker, longer bond. When examining NO and its anion NO-, we find an intriguing situation. Adding an electron to NO to form NO- introduces it to an antibonding orbital, impacting the bond order negatively. This decrease translates to a reduction in bond strength and higher bond length for NO- when compared to NO. Such insights allow us to not only foresee changes in the bond's physical characteristics but also support the prediction of molecular reactivity and stability.