Question

Arrange the following species in the correct order of their stability $C_2,L{i}_2,O_2^{+},H{e}_2^{+}$

• A. $L{i}_2<H{e}_2^{+}<O_2^{+}<C_2$
• B. $C_2<O_2^{+}<L{i}_2<H{e}_2^{+}$
• C. $H{e}_2^{+}<L{i}_2<C_2<O_2^{+}$
• D. $O_2^{+}<C_2<L{i}_2<H{e}_2^{+}$
• E. $C_2<L{i}_2<H{e}_2^{+}<O_2^{+}$

Answer 1

Answer: (C)

Higher the bond order, more is the stability. The bond order of the given species can be calculated as

$MO$ configuration of $C_2=(6+6=12)$

$=\sigma 1s^2,{\sigma }^{\ast }1s^2,\sigma 2s^2,{\sigma }^{\ast }2s^2,\pi 2p_x^2\approx \pi 2p_Y^2$

$BO=\frac{N_b-N_a}{2}=\frac{8-4}{2}=\frac{4}{2}=2$

$MO$ configuration of $L{i}_2=(3+3=6)$

$=\sigma 1s^2,{\sigma }^{\ast }1s^2,\sigma 2s^2$

$BO=\frac{4-2}{2}=1$

$MO$ configuration of $O_2(8+8-1=15)$

$=\sigma 1s^2,{\sigma }^{\ast }1s^2,\sigma 2s^2,{\sigma }^{\ast }2s^2,\sigma 2p_z^2,\pi 2p_x^2$

$\approx \pi 2p_{Y^{{}^{\prime }}}^2,{\pi }^{\ast }2p_x^1$

$BO=\frac{10-5}{2}=2.5$

$MO$ configuration of $H{e}_2=(2+2-1=3)$

$=\sigma 1s^2,{\sigma }^{\ast }1s^1$

$BO=\frac{2-1}{2}=\frac{1}{2}=0.5$

Thus, the order of bond orders of the given species is

$H{e}_2^{+}<L{i}_2<C_2<O_2^{+}$

Since, bond order $\alpha$ stability.

Thus, order of stability will also be the same.