+R power of the given groups is in the order:

(a) 1 > 2 > 3 > 4
(b) 4 > 3 > 2 > 1
(c) 1 > 3 > 2 > 4
(d) 1 > 4 > 3 > 2
Answer
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Hint: The higher the electron density and lesser the electronegativity, higher is the ability for +R groups. Now, apply this concept to the given question.
Complete Step-by-Step Solution:
Let us first look at mesomeric (resonance) effects in detail, so as to apply these concepts to help solve this question.
>The electron withdrawing or releasing effect attributed to a substituent through delocalization of π electrons, which can be visualized by drawing various canonical forms, is known as mesomeric effect or resonance effect. It is symbolized by M or R.
1) Negative resonance or mesomeric effect (-M or -R): It is shown by substituents or groups that withdraw electrons by delocalization mechanism from the rest of the molecule and are denoted by -M or -R. The electron density on the rest of the molecular entity is decreased due to this effect.
E.g. \[-N{{O}_{2}}\], Carbonyl group (C=O), -C≡N, -COOH, \[-S{{O}_{3}}H\] etc.
2) Positive resonance or mesomeric effect (+M or +R): These groups show positive mesomeric effect when they release electrons to the rest of the molecule by delocalization. These groups are denoted by +M or +R. Due to this effect, the electron density on the rest of the molecular entity is increased.
E.g. -OH, -OR, -SH, -SR, \[N{{H}_{2}}\], \[-N{{R}_{2}}~\] etc.
Now, let us apply these concepts to the given +R groups.
> Of all these groups, $-{{O}^{-}}$ has the highest electron density, making it the most effective +R group.
> The \[-NHCOC{{H}_{3}}\] group is stabilised by resonance and thus possesses the least electron density of the given groups. Therefore, it is the least effective +R group.
> Now, analysing \[-N{{H}_{2}}\] and -OH, of the two the latter is significantly more electronegative than the former due to Oxygen being much more electronegative than Nitrogen. Therefore, \[-N{{H}_{2}}\]is a much better +R group than -OH.
With this analysis, we can safely conclude that the order of +R effect is 1 > 2 > 3 > 4.
Therefore, the answer is a).
Note: In general, when it comes to organic chemistry, be very careful between the differences in Inductive and Resonance effect as in most cases, resonance effect is stronger and outweighs inductive effect.
For example, the -OH and \[-N{{H}_{2}}\] groups withdraw electrons by inductive effect (-I). However, they also release electrons by delocalization of lone pairs (+R effect). Since the resonance effect is stronger than the inductive effect the net result is electron releasing to the rest of the molecule.
Complete Step-by-Step Solution:
Let us first look at mesomeric (resonance) effects in detail, so as to apply these concepts to help solve this question.
>The electron withdrawing or releasing effect attributed to a substituent through delocalization of π electrons, which can be visualized by drawing various canonical forms, is known as mesomeric effect or resonance effect. It is symbolized by M or R.
1) Negative resonance or mesomeric effect (-M or -R): It is shown by substituents or groups that withdraw electrons by delocalization mechanism from the rest of the molecule and are denoted by -M or -R. The electron density on the rest of the molecular entity is decreased due to this effect.
E.g. \[-N{{O}_{2}}\], Carbonyl group (C=O), -C≡N, -COOH, \[-S{{O}_{3}}H\] etc.
2) Positive resonance or mesomeric effect (+M or +R): These groups show positive mesomeric effect when they release electrons to the rest of the molecule by delocalization. These groups are denoted by +M or +R. Due to this effect, the electron density on the rest of the molecular entity is increased.
E.g. -OH, -OR, -SH, -SR, \[N{{H}_{2}}\], \[-N{{R}_{2}}~\] etc.
Now, let us apply these concepts to the given +R groups.
> Of all these groups, $-{{O}^{-}}$ has the highest electron density, making it the most effective +R group.
> The \[-NHCOC{{H}_{3}}\] group is stabilised by resonance and thus possesses the least electron density of the given groups. Therefore, it is the least effective +R group.
> Now, analysing \[-N{{H}_{2}}\] and -OH, of the two the latter is significantly more electronegative than the former due to Oxygen being much more electronegative than Nitrogen. Therefore, \[-N{{H}_{2}}\]is a much better +R group than -OH.
With this analysis, we can safely conclude that the order of +R effect is 1 > 2 > 3 > 4.
Therefore, the answer is a).
Note: In general, when it comes to organic chemistry, be very careful between the differences in Inductive and Resonance effect as in most cases, resonance effect is stronger and outweighs inductive effect.
For example, the -OH and \[-N{{H}_{2}}\] groups withdraw electrons by inductive effect (-I). However, they also release electrons by delocalization of lone pairs (+R effect). Since the resonance effect is stronger than the inductive effect the net result is electron releasing to the rest of the molecule.
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