Question

According to molecular orbital theory, place the following molecules in order of increasing bond length: CN, CN²⁻, and CN⁺.

a) CN⁺ < CN < CN²⁻
b) CN < CN⁺ < CN²⁻
c) CN²⁻ < CN < CN⁺
d) CN²⁻ < CN⁺ < CN

Answer 1

According to molecular orbital theory, the bond length of a molecule depends on the bond order. CN²⁻ has the lowest bond order, followed by CN, and CN⁺ has the highest bond order. Therefore, the correct order of increasing bond length is CN²⁻ < CN < CN⁺.

Step-by-step explanation:

According to molecular orbital theory, the bond length of a molecule depends on the bond order. Bond order is calculated as one-half the difference between the number of bonding electrons and the number of antibonding electrons. In the case of CN, CN²⁻, and CN⁺, their bond orders are as follows:

1. CN⁺: 2 bonding electrons, 1 antibonding electron, bond order = (2-1)/2 = 0.5
2. CN: 2 bonding electrons, 1 antibonding electron, bond order = (2-1)/2 = 0.5
3. CN²⁻: 2 bonding electrons, 2 antibonding electrons, bond order = (2-2)/2 = 0

Based on the bond orders, we can determine that CN⁺ and CN have the same bond order, while CN²⁻ has a lower bond order. Therefore, the correct order of increasing bond length is CN²⁻ < CN < CN⁺, so option c) is the correct answer.