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The increasing order of the following compounds towards $HCN$ addition is:

(a) \[\left( {iii} \right){\text{ }} < {\text{ }}\left( i \right){\text{ }} < {\text{ }}\left( {iv} \right){\text{ }} < {\text{ }}\left( {ii} \right)\]
(b) \[\left( {iii} \right){\text{ }} < {\text{ }}\left( {iv} \right){\text{ }} < {\text{ }}\left( i \right){\text{ }} < {\text{ }}\left( {ii} \right)\]
(c) \[\left( i \right){\text{ }} < {\text{ }}\left( {iii} \right){\text{ }} < {\text{ }}\left( {iv} \right){\text{ }} < {\text{ }}\left( {ii} \right)\]
(d) \[\left( {iii} \right){\text{ }} < {\text{ }}\left( {iv} \right){\text{ }} < {\text{ }}\left( {ii} \right){\text{ }} < {\text{ }}\left( i \right)\]

Answer
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Hint: Nucleophile means nucleus loving. These are those species that attack electron deficient compounds. On the other hand, an electrophile is electron loving that attacks electron rich compounds. Electron withdrawing groups tend to withdraw the electron density towards itself, making the benzene ring electron deficient and susceptible to attack by the nucleophile.

Complete Step by Step Solution:
All the four compounds have benzaldehyde groups with different groups attached at ortho or meta positions. The effect of various groups attached determines the order of addition of$HCN$.

$C{N^{ - 1}}$Is the nucleophile so addition of nucleophile is favoured with an electron deficient compound.

$N{O_2}$ shows –M effect (withdrawing of electron density through pie bonds) only at the ortho position. But when $N{O_2}$group is attached at meta position, it no more shows resonance but withdraws electron density through sigma bond due to the fact that $N$of $N{O_2}$ is more electronegative than \[C\]of benzene ring. Hence, $N{O_2}$ at meta position shows –I effect.

Similarly \[OC{H_3}\]is an electron releasing group and donates the lone pair present on oxygen thus showing + M effect when attached at ortho position. \[OC{H_3}\] attached at meta position shows –I effect and not +I. This is because oxygen is more electronegative than carbon of benzene ring and withdrawing of electron density takes place through sigma bond. \[OC{H_3}\] at ortho position is least susceptible towards $HCN$ addition.
Mesomeric effect is stronger than inductive effect. Hence –M effect leads to stronger withdrawal of electrons than –I effect. Hence, $N{O_2}$at ortho is more electron withdrawing in nature.

Thus, order of electron withdrawing nature of groups is same as order towards $HCN$ addition
-M>-I>+M
-I effect of $N{O_2}$ is stronger than \[OC{H_3}\]
Hence the overall order is (a) (iii) < (i) < (iv) < (ii).

Note: Nucleophile is itself an electron rich species and usually carries a lone pair or negative charge. Positively charged species are generally called the electrophile. Inductive effect operates through sigma bonds and is dependent on electronegativity. Thus, inductive effect is observed at both meta and ortho position but mesomeric effect is only observed at ortho (and para).