Question
Which of the following options represents the correct bond order?
A.
$$O_2^ - > {O_2} > O_2^ + $$
B.
$$O_2^ - < {O_2} < O_2^ + $$
C.
$$O_2^ - > {O_2} < O_2^ + $$
D.
$$O_2^ - < {O_2} > O_2^ + $$
Answer :
$$O_2^ - < {O_2} < O_2^ + $$
Solution :
$${\text{Bond order of}}\,\,O_2^ - $$
$$O_2^ - = \sigma 1{s^2},\mathop \sigma \limits^* 1{s^2},\sigma 2{s^2},$$ $$\mathop \sigma \limits^* 2{s^2}\,\sigma 2p_z^2\left( {\pi 2p_x^2 = \pi 2p_y^2} \right)$$ $$\left( {{\pi ^*}2p_x^1 = {\pi ^*}2p_y^1} \right)$$
$$\eqalign{
& {\text{Bond}}\,\,{\text{order}} \cr
& = \frac{{{\text{number}}\,\,{\text{of}}\,\,{\text{electron}}\,\,{\text{in}}\,\,BMO - {\text{number}}\,\,{\text{of}}\,\,{\text{electrons}}\,\,ABMO}}{2} \cr
& = \frac{{10 - 7}}{2} \cr
& = \frac{3}{2} \cr
& = 1.5 \cr} $$
$$O_2^ + = \sigma 1{s^2},\mathop \sigma \limits^* 1{s^2},\sigma 2{s^2},$$ $$\mathop \sigma \limits^* 2{s^2}\,\sigma 2p_z^2\left( {\pi 2p_x^2 = \pi 2p_y^2} \right)$$ $$\left( {{\pi ^*}2p_x^1 = {\pi ^*}2p_y^0} \right)$$
$$\eqalign{
& BO = \frac{{10 - 5}}{2} \cr
& \,\,\,\,\,\,\,\,\,\, = \frac{5}{2} \cr
& \,\,\,\,\,\,\,\,\,\, = 2.5 \cr} $$
$${O_2} = \sigma 1{s^2},\mathop \sigma \limits^* 1{s^2},\sigma 2{s^2},$$ $$\mathop \sigma \limits^* 2{s^2}\,\sigma 2p_z^2\left( {\pi 2p_x^2 = \pi 2p_y^2} \right)$$ $$\left( {{\pi ^*}2p_x^1 = {\pi ^*}2p_y^1} \right)$$
$$\eqalign{
& BO = \frac{{10 - 6}}{2} \cr
& \,\,\,\,\,\,\,\,\,\, = \frac{4}{2} \cr
& \,\,\,\,\,\,\,\,\,\, = 2 \cr
& {\text{So, the correct sequence is}} \cr
& O_2^ - < {O_2} < O_2^ + \cr} $$