Predict the ground configuration of (a) CO, (b) NO. For each species, decide which term lies lowest in energy, compute the bond order and identify the HOMO and LUMO.

Short Answer

Expert verified
For CO, the ground configuration is \( \sigma _{1s}^2 \, \sigma _{1s*}^2 \, \sigma _{2s}^2 \, \sigma _{2s*}^2 \, \pi _{2p}^4 \, \sigma _{2p}^2 \, \pi _{2p*}^2 \, \sigma _{2p*}^0 \), lowest energy term is \( \sigma _{2p}^2 \), bond order is 4, HOMO is \( \pi _{2p*} \), and LUMO is \( \sigma _{2p*} \). For NO, the ground configuration is \( \sigma _{1s}^2 \, \sigma _{1s*}^2 \, \sigma _{2s}^2 \, \sigma _{2s*}^2 \, \pi _{2p}^4 \, \sigma _{2p}^2 \, \pi _{2p*}^3 \, \sigma _{2p*}^0 \), lowest energy term is \( \sigma _{2p}^2 \), bond order is 4, and both HOMO and LUMO are \( \pi _{2p*} \).

Step by step solution

01

Predict the ground configuration of CO and NO

To predict the ground electron configuration, you should remember that the molecular orbitals are filled in order of increasing energy. The configuration for CO is \( \sigma _{1s}^2 \, \sigma _{1s*}^2 \, \sigma _{2s}^2 \, \sigma _{2s*}^2 \, \pi _{2p}^4 \, \sigma _{2p}^2 \, \pi _{2p*}^2 \, \sigma _{2p*}^0 \). For NO, the configuration is \( \sigma _{1s}^2 \, \sigma _{1s*}^2 \, \sigma _{2s}^2 \, \sigma _{2s*}^2 \, \pi _{2p}^4 \, \sigma _{2p}^2 \, \pi _{2p*}^3 \, \sigma _{2p*}^0 \)
02

Decide which term lies lowest in energy

The term that has the lowest energy is the one with the most electrons. For CO and NO, the lowest energy term is the one with the two sigma (σ) electrons in the 2p orbital.
03

Compute the bond order

Bond order can be calculated using the formula: Bond Order = 0.5 * (number of electrons in bonding orbitals - number of electrons in antibonding orbitals). Thus, for CO, Bond Order = 0.5 * (10 - 2) = 4 and for NO, Bond Order = 0.5 * (11 - 3) = 4.
04

Identify the HOMO and LUMO

The Highest Occupied Molecular Orbital (HOMO) is the one with the highest energy and has electrons in it. The Lowest Unoccupied Molecular Orbital (LUMO) is the one with the lowest energy among the unoccupied orbitals. For CO, HOMO is \( \pi _{2p*} \) and LUMO is \( \sigma _{2p*} \). For NO, HOMO is \( \pi _{2p*} \) and LUMO is the same \( \pi _{2p*} \) orbital which is not completely filled.

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