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Question: The correct statement with regard to \( H_{2}^{+} \) and \( H_{2}^{-} \) (A) Both \( H_{2}^{+} \)...

The correct statement with regard to H2+H_{2}^{+} and H2H_{2}^{-}
(A) Both H2+H_{2}^{+} and H2H_{2}^{-} are equally stable
(B) Both H2+H_{2}^{+} and H2H_{2}^{-} do not exist
(C) H2H_{2}^{-} is more stable than H2+H_{2}^{+}
(D) H2+H_{2}^{+} is more stable than H2H_{2}^{-}

Explanation

Solution

Hint : The composition of H2+H_{2}^{+} and H2H_{2}^{-} defines the stability order. H2+H_{2}^{+} does not include any electron in the antibonding molecular orbital. H2H_{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 =12=\dfrac{1}{2} (Number of bonding electrons -Number of antibonding electrons)
The number of antibonding electrons in H2+H_{2}^{+} is 0
The number of antibonding electrons in H2H_{2}^{-} is 1
The bonding order of H2+H_{2}^{+} is  ~ =12(10)=0.5=\dfrac{1}{2}(1-0)=0.5
The bonding order of H2H_{2}^{-} is =12(21)=0.5=\dfrac{1}{2}(2-1)=0.5
H2+H_{2}^{+} and H2H_{2}^{-} molecule have the same bond order
Presence of anti-bonding electron decreases the stability of the molecule
Therefore, H2+H_{2}^{+} is more stable than H2H_{2}^{-}
Both H2+H_{2}^{+} and H2H_{2}^{-} are equally stable is incorrect statement
Both H2+H_{2}^{+} and H2H_{2}^{-} do not exist is incorrect statement
H2H_{2}^{-} is more stable than H2+H_{2}^{+} is incorrect statement
The correct statement is H2+H_{2}^{+} is more stable than H2H_{2}^{-}
Due to the electron-electron repulsion in H2H_{2}^{-} , the stability of H2H_{2}^{-} is low
The configuration of H2+H_{2}^{+} is 11 electron in 11 s bonding orbital
The configuration of H2H_{2}^{-} is 11 electron in 11 s bonding orbital and 11 electron in 11 s antibonding orbital
Even though the bond order of both H2+H_{2}^{+} and H2H_{2}^{-} are same, the stability is different
Therefore, H2+>H2H_{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 H2H_{2}^{-} , the stability of H2H_{2}^{-} is low.