Question

5. Some heteronuclear d energy levels like th heteronuclear diatomic molecules have energy levels like those in Figure 3, while others to ey levels like those in Figure 4 (e.g., CN, CN-, and CNT). Write the molecular orbital electron configurations for these three species. For example electron configuration for H, is (015) b. Arrange these species in increasing bond order, increasing bond length, and increasing bond energy

Answer 1

The atomic numbers of C and N are 6 and 7 respectively.

Species	$CN$	$CN^-$	$CN^+$
Total number of electrons	$6+7=13$	$6+7+1=14$	$6+7-1=12$
MO electronic configuration	$\displaystyle \left ( \sigma _{1s} \right )^2 \left ( \sigma^* _{1s} \right )^2 \\ \ \left ( \sigma _{2s} \right )^2 \left ( \sigma^* _{2s} \right )^2 \\ \ \left ( \pi _{2px} \right )^2\left ( \pi _{2py} \right )^2 \\ \ \left ( \sigma _{2pz} \right )^1$	$\displaystyle \left ( \sigma _{1s} \right )^2 \left ( \sigma^* _{1s} \right )^2 \\ \ \left ( \sigma _{2s} \right )^2 \left ( \sigma^* _{2s} \right )^2 \\ \ \left ( \pi _{2px} \right )^2\left ( \pi _{2py} \right )^2 \\ \ \left ( \sigma _{2pz} \right )^2$	$\displaystyle \left ( \sigma _{1s} \right )^2 \left ( \sigma^* _{1s} \right )^2 \\ \ \left ( \sigma _{2s} \right )^2 \left ( \sigma^* _{2s} \right )^2 \\ \ \left ( \pi _{2px} \right )^2\left ( \pi _{2py} \right )^2$
Number of electrons in bonding MO $\left ( N_b \right )$	9	10	8
Number of electrons in antibonding MO $\left ( N_a \right )$	4	4	4
Bond order $=\frac{N_b-N_a}{2}$	$\frac{9-4}{2}=2.5$	$\frac{10-4}{2}=3$	$\frac{8-4}{2}=2$

Increasing order of bond order is $CN^&plus; < CN <CN^-$

Increasing order of bond energy is $CN^&plus; < CN <CN^-$

Increasing order of bond length is $CN^- <CN<CN^&plus;$

Higher is the bond order, higher is the bond energy and smaller is the bond length.