Question

Which of the following pairs of species have the same bond order ?

• A. $O_2 , NO^+$
• B. $CN^- , CO$
• C. $N_2, O^-_2$
• D. $CO, NO$

Answer 1

The Correct Option is B

To determine which of the given pairs of species have the same bond order, we need to understand the concept of bond order and how to calculate it from molecular orbital theory. Bond order can be calculated using the formula:

Bond\ Order = \frac{(Number\ of\ bonding\ electrons) - (Number\ of\ antibonding\ electrons)}{2}

We will calculate the bond order for each species in the options and compare them.

1. O_2 and NO^+
   • O_2: The electron configuration is \sigma_{1s}^2 \sigma^*_ {1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^1. The bond order is \frac{10 - 6}{2} = 2.
   • NO^+: The electron configuration is similar to that of N_2 due to an extra positive charge (loss of an electron), making it \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2. The bond order is \frac{10 - 4}{2} = 3.
2. CN^-\ and CO
   • CN^-\: The electron configuration is \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 for a total of 14 electrons. The bond order is \frac{10 - 4}{2} = 3.
   • CO: The electron configuration is similar to the N_2 molecule's configuration but with a slight variation due to the heteronuclear nature of CO. It effectively also results in a bond order of 3.
   • Both have a bond order of 3.
3. N_2 and O_2^-\
   • N_2: Electron configuration is \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2. The bond order is 3.
   • O_2^-\: The extra electron goes into an antibonding orbital, making the bond order \frac{10 - 7}{2} = 1.5.
4. CO and NO
   • As calculated, CO has a bond order of 3.
   • NO: The bond order is \frac{8 - 3}{2} = 2.5.

Based on this analysis, the correct answer is the pair that has the same bond order: CN^- and CO, both of which have a bond order of 3.