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The increasing order of the bond order of $O_{ 2 },\quad O_{ 2 }^{ + },\quad O_{ 2 }^{ - },\quad O_{ 2 }^{ -2 }$ is:A- $O_{ 2 }^{ + },\quad O_{ 2 },\quad O_{ 2 }^{ - },\quad O_{ 2 }^{ -2 }$B- $O_{ 2 }^{ -2 },\quad O_{ 2 }^{ - },\quad O_{ 2 }^{ + },\quad O_{ 2 }$C- $O_{ 2 },\quad O_{ 2 }^{ + },\quad O_{ 2 }^{ - },\quad O_{ 2 }^{ -2 }$D- $O_{ 2 }^{ -2 },\quad O_{ 2 }^{ - },\quad O_{ 2 },\quad O_{ 2 }^{ + }$

Last updated date: 10th Aug 2024
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Hint: Try to find the configuration of oxygen molecules following molecular orbital theory. Bond order is the number of bonding electrons – the number of antibonding molecular orbitals divided by 2. Electrons configuration will be different for species with electrons less than 14 and greater than 14.

We know that molecules form bonding and antibonding molecular orbitals by intermixing of atomic orbitals. In the intermixing of atomic orbitals, there are two types of interference. Constructive interference and destructive interference. Constructive interference has lower energy and it leads to the formation of bonding molecular orbital. Destructive interference has higher energy and it leads to the formation of antibonding molecular orbitals. Atomic orbitals in the atom mix with the same atomic orbitals of another atom.
The electronic configuration will be different for species with less than or equal to 14 electrons and for species with more than 14 electrons.
For species with electrons, less than or equal to 14 electronic configuration is
$\sigma _{ 1s },\quad \sigma ^{ \ast }_{ 1s },\quad \sigma _{ 2s },\quad \sigma ^{ \ast }_{ 2s },\quad \pi _{ 2p_{ x } },\quad \pi _{ 2p_{ y } },\quad \sigma _{ 2p_{ z } },\quad \sigma ^{ \ast }_{ 2p_{ z } },\quad \pi ^{ \ast }_{ 2p_{ x } },\quad \pi ^{ \ast }_{ 2p_{ y } }$
For species with electrons greater than 14 electronic configuration is
$\sigma _{ 1s },\quad \sigma ^{ \ast }_{ 1s },\quad \sigma _{ 2s },\quad \sigma ^{ \ast }_{ 2s },\quad \sigma _{ 2p_{ z } },\quad \pi _{ 2p_{ x } },\quad \pi _{ 2p_{ y } },\quad \pi ^{ \ast }_{ 2p_{ x } },\quad \pi ^{ \ast }_{ 2p_{ y } },\quad \sigma ^{ \ast }_{ 2p_{ z } }$
All the given species of oxygen contain more than 14 electrons so they follow the second type of electronic configuration.
Each orbital can accommodate 2 electrons each. $O_{ 2 }$ has 16 electrons, $O_{ 2 }^{ + }$ has 15 electrons, $O_{ 2 }^{ - }$ has 17 electrons and $O_{ 2 }^{ -2 }$ has 18 electrons.
Configuration of $O_{ 2 }$ is $\sigma ^{ 2 }_{ 1s },\quad \sigma ^{ \ast 2 }_{ 1s },\quad \sigma ^{ 2 }_{ 2s },\quad \sigma ^{ \ast 2 }_{ 2s },\quad \sigma ^{ 2 }_{ 2p_{ z } },\quad \pi ^{ 2 }_{ 2p_{ x } },\quad \pi ^{ 2 }_{ 2p_{ y } },\quad \pi ^{ \ast 1 }_{ 2p_{ x } },\quad \pi ^{ \ast 1 }_{ 2p_{ y } }$.
Configuration of $O_{ 2 }^{ + }$ is $\sigma ^{ 2 }_{ 1s },\quad \sigma ^{ \ast 2 }_{ 1s },\quad \sigma ^{ 2 }_{ 2s },\quad \sigma ^{ \ast 2 }_{ 2s },\quad \sigma ^{ 2 }_{ 2p_{ z } },\quad \pi ^{ 2 }_{ 2p_{ x } },\quad \pi ^{ 2 }_{ 2p_{ y } },\quad \pi ^{ \ast 1 }_{ 2p_{ x } }$.
Configuration of $O_{ 2 }^{ - }$ is $\sigma ^{ 2 }_{ 1s },\quad \sigma ^{ \ast 2 }_{ 1s },\quad \sigma ^{ 2 }_{ 2s },\quad \sigma ^{ \ast 2 }_{ 2s },\quad \sigma ^{ 2 }_{ 2p_{ z } },\quad \pi ^{ 2 }_{ 2p_{ x } },\quad \pi ^{ 2 }_{ 2p_{ y } },\quad \pi ^{ \ast 2 }_{ 2p_{ x } },\quad \pi ^{ \ast 1 }_{ 2p_{ y } }$.
Configuration of $O_{ 2 }^{ -2 }$ is $\sigma ^{ 2 }_{ 1s },\quad \sigma ^{ \ast 2 }_{ 1s },\quad \sigma ^{ 2 }_{ 2s },\quad \sigma ^{ \ast 2 }_{ 2s },\quad \sigma ^{ 2 }_{ 2p_{ z } },\quad \pi ^{ 2 }_{ 2p_{ x } },\quad \pi ^{ 2 }_{ 2p_{ y } },\quad \pi ^{ \ast 2 }_{ 2p_{ x } },\quad \pi ^{ \ast 2 }_{ 2p_{ y } }$.
Bond order = $\dfrac { number\quad of\quad bonding\quad electrons\quad -\quad number\quad of\quad antibonding\quad electrons }{ 2 }$
Bond order of $O_{ 2 }$ is 2, bond order of $O_{ 2 }^{ + }$ is 2.5, bond order of $O_{ 2 }^{ - }$ is 1.5, bond order of $O_{ 2 }^{ -2 }$ is 1.
Therefore, increasing the order of the bond order is $O_{ 2 }^{ -2 },\quad O_{ 2 }^{ - },\quad O_{ 2 },\quad O_{ 2 }^{ + }$. Option D is correct.

Note: Bond is not always an integer for molecules. Not all molecules obey this molecular orbital theory. Molecules containing unpaired electrons exhibit paramagnetism. Antibonding molecular orbitals have higher energy so they are filled after Bonding molecular orbitals.