Question

The correct statement with regard to $H_2^{+}$ and $H_2^{-}$
(A) Both $H_2^{+}$ and $H_2^{-}$ are equally stable
(B) Both $H_2^{+}$ and $H_2^{-}$ do not exist
(C) $H_2^{-}$ is more stable than $H_2^{+}$
(D) $H_2^{+}$ is more stable than $H_2^{-}$

Answer 1

Hint :The composition of $H_2^{+}$ and $H_2^{-}$ defines the stability order. $H_2^{+}$ does not include any electron in the antibonding molecular orbital. $H_2^{-}$ includes electrons in antibonding molecular orbital.The stability can be easily identified from the electron presence in bonding and antibonding molecular orbital.

Complete Step By Step Answer:
The electron presence in anti-bonding orbital result in repulsion and decrease of stability
The stability order follows the molecular orbital theory
The formula for bonding order can be regarded as follows
Bonding order $={\displaystyle \frac{1}{2}}$ (Number of bonding electrons -Number of antibonding electrons)
The number of antibonding electrons in $H_2^{+}$ is 0
The number of antibonding electrons in $H_2^{-}$ is 1
The bonding order of $H_2^{+}$ is $$ $={\displaystyle \frac{1}{2}}(1-0)=0.5$
The bonding order of $H_2^{-}$ is $={\displaystyle \frac{1}{2}}(2-1)=0.5$
 $H_2^{+}$ and $H_2^{-}$ molecule have the same bond order
Presence of anti-bonding electron decreases the stability of the molecule
Therefore, $H_2^{+}$ is more stable than $H_2^{-}$
Both $H_2^{+}$ and $H_2^{-}$ are equally stable is incorrect statement
Both $H_2^{+}$ and $H_2^{-}$ do not exist is incorrect statement
 $H_2^{-}$ is more stable than $H_2^{+}$ is incorrect statement
The correct statement is $H_2^{+}$ is more stable than $H_2^{-}$
Due to the electron-electron repulsion in $H_2^{-}$ , the stability of $H_2^{-}$ is low
The configuration of $H_2^{+}$ is $1$ electron in $1$ s bonding orbital
The configuration of $H_2^{-}$ is $1$ electron in $1$ s bonding orbital and $1$ electron in $1$ s antibonding orbital
Even though the bond order of both $H_2^{+}$ and $H_2^{-}$ are same, the stability is different
Therefore, $H_2^{+}>H_2^{-}$ .

Note :
The stability order follows the molecular orbital theory. The electron presence in anti-bonding orbital results in repulsion and decrease of stability. Electron-electron repulsion in $H_2^{-}$ , the stability of $H_2^{-}$ is low.