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 $=\dfrac{1}{2}$ (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 $~$ $=\dfrac{1}{2}(1-0)=0.5$
The bonding order of $H_{2}^{-}$ is $=\dfrac{1}{2}(2-1)=0.5$
$H_{2}^{+}$ 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.