Question

The correct order of increasing bond lengths of the following species is I. $C_2^{-}$ II. $C_2^{2-}$ III. $C_2$

• A. I < III < II
• B. II < III < I
• C. II < I < III
• D. III < II < I

Answer 1

Answer: (C)

Total number of electrons in $C_2$ molecule is 12
Electronic configuration is $\sigma 1s^2\sigma \ast 1s^2\sigma 2s^2\sigma \ast 2s^2\pi 2p_x^2=\pi 2p_y^2$
Bond order $=\frac{1}{2}(8-4)=2$
Electronic configuration of $C_2^{-}\sigma 1s^2\sigma \ast 1s^2\sigma 2s^2\sigma \ast 2s^2\left(\pi p_x^2=\pi 2p_y^2\right)$
Bond order $=\frac{1}{2}(9-4)=2.5$
Electronic configuration of $C_2^{2-}=\sigma 1s^2\sigma \ast 1s^2\sigma 2s^2\sigma \ast 2s^2\pi 2p_x^2=\pi 2p_y^2\sigma 2p_z^2$
Bond order $=\frac{1}{2}(10-4)=3$
Greater the bond order, shorter is the bond length
$\therefore$ Order of band lengths $C_2^{2-}<C_2^{-}<C_2$