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

Question

Using MO theory predict which of the following species has the shortest bond length? (A) O2+ (B) O2- (C) O22 - (D) O22 +

Tardigrade Admin · Accepted Answer

Bond length propto (1/ text bond order ) Bond length =( text no. of bonding bare- text no. of antibonding bare/2) Bond orders of O2+, O2-, O22- and O22+ are respectively 2.5, 1.5,1 and 3 Hence O22+ is shortest in bond length as have max. bond order.

Q. Using MO theory predict which of the following species has the shortest bond length?

$O_{2}^{+}$

$O_{2}^{-}$

$O_{2}^{2 -}$

$O_{2}^{2 +}$

Bond length $\propto \frac{1}{bond order}$
Bond length $= \frac{no. of bonding e ˉ - no. of antibonding e ˉ}{2}$
Bond orders of $O_{2}^{+}, O_{2}^{-}, O_{2}^{2 -}$ and $O_{2}^{2 +}$ are respectively $2.5$ , $1.5, 1$ and $3$
Hence $O_{2}^{2 +}$ is shortest in bond length as have max. bond order.

Q. Using MO theory predict which of the following species has the shortest bond length?

O2+​

O2−​

O22−​

O22+​

Bond length ∝bond order 1​ Bond length =2 no. of bonding eˉ− no. of antibonding eˉ​ Bond orders of O2+​,O2−​,O22−​ and O22+​ are respectively 2.5, 1.5,1 and 3 Hence O22+​ is shortest in bond length as have max. bond order.

$O_{2}^{+}$

$O_{2}^{-}$

$O_{2}^{2 -}$

$O_{2}^{2 +}$

Bond length $\propto \frac{1}{bond order}$
Bond length $= \frac{no. of bonding e ˉ - no. of antibonding e ˉ}{2}$
Bond orders of $O_{2}^{+}, O_{2}^{-}, O_{2}^{2 -}$ and $O_{2}^{2 +}$ are respectively $2.5$ , $1.5, 1$ and $3$
Hence $O_{2}^{2 +}$ is shortest in bond length as have max. bond order.