Using `MO` theory predict which of the following sepcies has the shortest bond length ?

Options

A. `O_2^(2+)`
B. `O_2^(+)`
C. `O_2^(-)`
D. `O_2^(2-)`

Answer

A

Explanation

The MO configuration for `O_2` is
`KK(sigma2s)^2(sigma^**2s)^2(sigma2p_z)^2(pi2p_x^2=pi2p_y^2)(pi^**2p_x^1=pi^**2pi_y^1)`
It has `N_b` 10 and `N_a` 6. Thus,
`O_2^(2+) bo=(10-4)/(2)=3`
`O_2^(+) bo=(10-5)/(2)=2.5`
`O_2^(-) bo=(10-7)/(2)=1.5`
`O_2^(2-) bo=(10-8)/(2)=1.0`
Since bo is inversely related to bond length, `O_2^(2+)` with the highest bo of 3 has the shortest bond length.