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Chapter 9: Problem 81

Determine the electron configurations for \(\mathrm{CN}^{+}, \mathrm{CN}\), and \(\mathrm{CN}^{-}\). (a) Which species has the strongest \(\mathrm{C}-\mathrm{N}\) bond? (b) Which species, if any, has unpaired electrons?

Short Answer

Expert verified
The electron configurations for CN+, CN, and CN- are as follows: CN+: \(\sigma_{1s}^2\sigma^*_{1s}^2\sigma_{2s}^2\sigma^*_{2s}^2\pi_{2p}^4\sigma_{2p}^0\pi^*_{2p}^0\sigma^*_{2p}^0\) CN: \(\sigma_{1s}^2\sigma^*_{1s}^2\sigma_{2s}^2\sigma^*_{2s}^2\pi_{2p}^4\sigma_{2p}^1\pi^*_{2p}^0\sigma^*_{2p}^0\) CN-: \(\sigma_{1s}^2\sigma^*_{1s}^2\sigma_{2s}^2\sigma^*_{2s}^2\pi_{2p}^4\sigma_{2p}^2\pi^*_{2p}^0\sigma^*_{2p}^0\) (a) The species with the strongest C-N bond is CN- because it has the highest bond order of 3. (b) CN is the only species with an unpaired electron, which is in the \(\sigma_{2p}\) orbital.

Step by step solution

01

Determine the total number of electrons in each species

For each molecule, find the atomic numbers of carbon (C) and nitrogen (N) and add or subtract the charge. Carbon has an atomic number of 6 and nitrogen has an atomic number of 7. For CN+: \(6 + 7 - 1 = 12\) electrons For CN: \(6 + 7 = 13\) electrons For CN-: \(6 + 7 + 1 = 14\) electrons
02

Identify the molecular orbital diagram

Since the number of atomic orbitals for C and N is closer to that of oxygen rather than to that of hydrogen, we will use the oxygen molecular orbital diagram.
03

Determine the electron configurations

Fill in the molecular orbitals according to the diagram. For species with fewer than 14 electrons (CN+ and CN), fill in the electrons from the lowest to the highest energy orbitals, abiding to the Aufbau Principle and Hund's Rule. For species with 14 electrons (CN-), all orbitals will be full. CN+: \(\sigma_{1s}^2\sigma^*_{1s}^2\sigma_{2s}^2\sigma^*_{2s}^2\pi_{2p}^4\sigma_{2p}^0\pi^*_{2p}^0\sigma^*_{2p}^0\) CN: \(\sigma_{1s}^2\sigma^*_{1s}^2\sigma_{2s}^2\sigma^*_{2s}^2\pi_{2p}^4\sigma_{2p}^1\pi^*_{2p}^0\sigma^*_{2p}^0\) CN-: \(\sigma_{1s}^2\sigma^*_{1s}^2\sigma_{2s}^2\sigma^*_{2s}^2\pi_{2p}^4\sigma_{2p}^2\pi^*_{2p}^0\sigma^*_{2p}^0\) Now we can use the electron configurations to answer parts (a) and (b).
04

Identify the species with the strongest C-N bond

The species with the highest bond order will have the strongest bond. Bond order is determined by subtracting the number of electrons in antibonding orbitals from the number of electrons in bonding orbitals and dividing by 2. CN+ \(Bond Order = (2-2 + 2-2 + 4 + 0)/2 = 4/2 = 2\) CN \(Bond Order = (2-2 + 2-2 + 4 + 1)/2 = 5/2 = 2.5\) CN- \(Bond Order = (2-2 + 2-2 + 4 + 2)/2 = 6/2 = 3\) The species with the strongest bond is CN- because it has the highest bond order of 3. (a)
05

Determine if any species has unpaired electrons

Observe the electron configurations and look for any orbitals with an unpaired electron. CN+ has paired electrons in all orbitals, so it has no unpaired electrons. CN has one unpaired electron in the \(\sigma_{2p}\) orbital. CN- has paired electrons in all orbitals, so it has no unpaired electrons. Therefore, CN is the only species with an unpaired electron. (b)

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Most popular questions from this chapter

Consider the molecule \(\mathrm{PF}_{4}\) Cl. (a) Draw a Lewis structure for the molecule, and predict its electron-domain geometry. (b) Which would you expect to take up more space, a \(\mathrm{P}-\mathrm{F}\) bond or a \(\mathrm{P}-\mathrm{Cl}\) bond? Explain. (c) Predict the molecular geometry of \(\mathrm{PF}_{4} \mathrm{Cl}\). How did your answer for part (b) influence your answer here in part (c)? (d) Would you expect the molecule to distort from its ideal electron-domain geometry? If so, how would it distort?

For each statement, indicate whether it is true or false. (a) \(\ln\) order to make a covalent bond, the orbitals on each atom in the bond must overlap. (b) A \(p\) orbital on one atom cannot make a bond to an \(s\) orbital on another atom. \((\mathbf{c})\) Lone pairs of electrons on an atom in a molecule influence the shape of a molecule. (d) The 1 s orbital has a nodal plane. \((\mathbf{e})\) The \(2 p\) orbital has a nodal plane.

(a) Predict the electron-domain geometry around the central \(\mathrm{S}\) atom in \(\mathrm{SF}_{2}, \mathrm{SF}_{4}\), and \(\mathrm{SF}_{6}\). ( \(\mathbf{b}\) ) The anion \(\mathrm{IO}_{4}^{-}\) has a tetrahedral structure: three oxygen atoms form double bonds with the central iodine atom and one oxygen atom which carries a negative charge forms a single bond. Predict the molecular geometry of \(\mathrm{IO}_{6}{ }^{5-}\).

How would we describe a substance that contains only paired electrons and is weakly repelled by a magnetic field? Which of the following ions would you expect to possess similar characteristics: $\mathrm{H}_{2}^{-}, \mathrm{Ne}_{2}^{+}, \mathrm{F}_{2}, \mathrm{O}_{2}^{2+} ?$

Draw sketches illustrating the overlap between the following orbitals on two atoms: (a) the \(2 s\) orbital on each atom, (b) the \(2 p_{z}\) orbital on each atom (assume both atoms are on the \(z\) -axis), \((\mathbf{c})\) the 2 s orbital on one atom and the \(2 p_{2}\) orbital on the other atom.
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