Problem 71 - Chemistry: The Central Science

Question

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?

Step-by-Step Solution

Answer

(a) The strongest C-N bond is present in CN-. (b) CN is the only species with an unpaired electron.

Step 1: Determine the total number of electrons for each molecule

For CN+: C has 6 electrons, N has 7 electrons, and 1 electron is removed due to the positive charge, resulting in 12 electrons. For CN: C has 6 electrons, and N has 7 electrons, resulting in 13 electrons. For CN-: C has 6 electrons, N has 7 electrons, and 1 electron is added because of the negative charge, resulting in 14 electrons. Step 2: Assign Electrons to Molecular Orbitals

Step 2: Fill the molecular orbitals with given electrons

The molecular orbital diagram for CN molecules has σ and π orbitals. The order of energy levels for these orbitals is: σ1s < σ*1s < σ2s < σ*2s < π2px = π2py < σ2pz < π*2px = π*2py < σ*2pz. For CN+ (12 electrons): σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 π2px^2 π2py^2 (All orbitals are filled) For CN (13 electrons): σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 π2px^2 π2py^2 σ2pz^1 (π*2px and π*2py orbitals are unfilled) For CN- (14 electrons): σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 π2px^2 π2py^2 σ2pz^2 (Just the π*2px and π*2py orbitals are unfilled) Step 3: Evaluate C-N Bond Strength

Step 3: Compare the bond orders for different species

Bond order is calculated as (number of electrons in bonding orbitals - number of electrons in anti-bonding orbitals)/2. For CN+: Bond order = (10 - 4)/2 = 3 (strongest bond) For CN: Bond order = (10 - 4 + 1)/2 = 3.5 For CN-: Bond order = (12 - 4)/2 = 4 Therefore, based on bond order, CN- has the strongest C-N bond. Step 4: Identify Unpaired Electrons

Step 4: Identify molecules with unpaired electrons

We can examine the molecular orbitals of each molecule to identify unpaired electrons. For CN+: All orbitals are filled, with no unpaired electrons. For CN: σ2pz orbital has 1 unpaired electron. For CN-: All orbitals are filled, with no unpaired electrons. Only CN has an unpaired electron. In summary: (a) CN- has the strongest C-N bond. (b) CN is the only species with an unpaired electron.