Chapter 1: Problem 25
The species having bond order different from that in \(\mathrm{CO}\) is (A) \(\mathrm{NO}^{-}\) (B) \(\mathrm{NO}^{+}\) (C) \(\mathrm{CN}^{-}\) (D) \(\mathrm{N}_{2}\)
Short Answer
Expert verified
(A) NO-
Step by step solution
01
- Calculate the bond order of CO
To find out which species has a bond order different from CO, first calculate the bond order of CO. According to Molecular Orbital (MO) theory, CO has 10 valence electrons from carbon and 6 from oxygen, giving a total of 10+6=16. Bond order is half the difference between bonding and antibonding electrons, so for CO: Bond order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2.In CO, 10 electrons are in bonding orbitals and 6 are in antibonding orbitals, so bond order = (10-6)/2 = 2.
02
- Identify bond orders for each option
Calculate the bond order for each of the given species using MO theory. (A) NO-: This has 8 (N) + 6 (O) + 1 (extra electron) = 15 electrons. (B) NO+: This has 8 (N) + 6 (O) - 1 (missing electron) = 13 electrons. (C) CN-: This has 6 (C) + 7 (N) + 1 (extra electron) = 14 electrons. (D) N2: This has 7 (N) + 7 (N) = 14 electrons.For each species, bond order is calculated as half the difference between the number of electrons in bonding and antibonding orbitals.
03
- Compare bond orders with CO
Compare the calculated bond order for each species with that of CO to determine which has a different bond order.(A) NO- likely has a bond order of 2.5 (15 electrons gives us 8 bonding, 5 antibonding).(B) NO+ likely has a bond order of 3 (13 electrons gives us 7 bonding, 4 antibonding).(C) CN- likely has a bond order of 3 (14 electrons gives us 7 bonding, 3 antibonding).(D) N2 likely has a bond order of 3 (14 electrons gives us 7 bonding, 3 antibonding).Since CO has a bond order of 2, only option (A) NO- has a bond order that is different from CO.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molecular Orbital Theory
Molecular Orbital (MO) Theory provides a profound method for understanding the electronic structure of molecules.
In essence, it describes electrons in a molecule by combining atomic orbitals to form molecular orbitals that are delocalized over the entire molecule, unlike in the simpler Valence Bond Theory where electrons are localized to a particular bond or lone pair.
These molecular orbitals can be classified as bonding or antibonding, with bonding orbitals stabilizing the molecule and antibonding doing the opposite.
Bonding orbitals are lower in energy than the atomic orbitals they originate from, whereas antibonding orbitals are higher in energy.
Electrons will fill available molecular orbitals based on the principles of the Aufbau principle (fill the lowest energy orbitals first), Pauli exclusion principle (each orbital can hold a maximum of 2 electrons with opposite spins), and Hund's rule (occupy orbitals singly as far as possible before pairing).
The resulting electronic configuration allows us to predict magnetic properties, bond strength, and, importantly, bond order.
In essence, it describes electrons in a molecule by combining atomic orbitals to form molecular orbitals that are delocalized over the entire molecule, unlike in the simpler Valence Bond Theory where electrons are localized to a particular bond or lone pair.
These molecular orbitals can be classified as bonding or antibonding, with bonding orbitals stabilizing the molecule and antibonding doing the opposite.
Bonding orbitals are lower in energy than the atomic orbitals they originate from, whereas antibonding orbitals are higher in energy.
Electrons will fill available molecular orbitals based on the principles of the Aufbau principle (fill the lowest energy orbitals first), Pauli exclusion principle (each orbital can hold a maximum of 2 electrons with opposite spins), and Hund's rule (occupy orbitals singly as far as possible before pairing).
The resulting electronic configuration allows us to predict magnetic properties, bond strength, and, importantly, bond order.
Bond Order Calculation
Bond order is a concept that indicates the stability and strength of a bond in a molecule.
It is obtained from the electronic configuration of a molecule as predicted by MO theory, following a straightforward formula:\br> ewline Bond order = \frac{(Number \text{ of } electrons \text{ in } bonding \text{ orbitals } - \text{ Number of } electrons \text{ in } antibonding \text{ orbitals})}{2}.
For example, a dioxygen molecule \text{(O\(_2\))} with 16 electrons might have 10 in bonding orbitals and 6 in antibonding orbitals, thus yielding a bond order of 2. This bond order implies a double bond between the two oxygen atoms.
Higher bond orders correlate with stronger, shorter bonds and greater stability of the molecule. Single bonds have a bond order of 1, double bonds have a bond order of 2, and triple bonds have a bond order of 3. Zero or negative bond orders suggest the molecule or ion is unstable or does not exist.
It is obtained from the electronic configuration of a molecule as predicted by MO theory, following a straightforward formula:\br> ewline Bond order = \frac{(Number \text{ of } electrons \text{ in } bonding \text{ orbitals } - \text{ Number of } electrons \text{ in } antibonding \text{ orbitals})}{2}.
For example, a dioxygen molecule \text{(O\(_2\))} with 16 electrons might have 10 in bonding orbitals and 6 in antibonding orbitals, thus yielding a bond order of 2. This bond order implies a double bond between the two oxygen atoms.
Higher bond orders correlate with stronger, shorter bonds and greater stability of the molecule. Single bonds have a bond order of 1, double bonds have a bond order of 2, and triple bonds have a bond order of 3. Zero or negative bond orders suggest the molecule or ion is unstable or does not exist.
Comparing Bond Orders
Comparing bond orders among different molecules or ions is a key application of MO Theory, as seen in the exercise to discern structures with differing degrees of stability.
When we compare the bond order of CO to other species like \text{NO\(^-\)}, \text{NO\(^+\)}, \text{CN\(^-\)}, and \text{N\(_2\)}, we are essentially assessing their relative stability and bond strength.
For a detailed comparison, we calculate the bond order for each given species and observe which one differs from CO. Bond order not only determines the type of bond but also the bond distance and the molecule's energy state.
Species with higher bond orders than another are typically more stable with shorter and stronger bonds. This comparative analysis of bond orders aids in predicting chemical reactivity and the nature of the chemical bond in unfamiliar molecules.
When we compare the bond order of CO to other species like \text{NO\(^-\)}, \text{NO\(^+\)}, \text{CN\(^-\)}, and \text{N\(_2\)}, we are essentially assessing their relative stability and bond strength.
For a detailed comparison, we calculate the bond order for each given species and observe which one differs from CO. Bond order not only determines the type of bond but also the bond distance and the molecule's energy state.
Species with higher bond orders than another are typically more stable with shorter and stronger bonds. This comparative analysis of bond orders aids in predicting chemical reactivity and the nature of the chemical bond in unfamiliar molecules.
