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Consider the following species:

$$ \underset{(\text{A})}{\ce{\overset{⊖}{O}H}} \quad \underset{(\text{B})}{\ce{CH3-\overset{⊖}{O}}} \quad \underset{(\text{C})}{\ce{\overset{⊖}{C}H3}} \quad \underset{(\text{D})}{\ce{\overset{⊖}{N}H2}} \quad $$

Arrange these species in their decreasing order of nucleophilicity.

(a) C > D > A > B
(b) B > A > C > D
(c) A > B > C > D
(d) C > A > B > D

My teacher taught in polar protic solvent nucleophilicity is inversely proportional to basic character. I assumed solvent to be $\ce{H2O}$ as solvent was not mentioned in the question. As acidity order is

$$\ce{H2O} > \ce{CH3OH} > \ce{NH3} > \ce{CH4},$$

so basicity order should be

$$\ce{CH3-} > \ce{NH2-} > \ce{CH3O-} > \ce{OH-},$$

therefore using above proportionality I arrived at the nucleophilicity order

$$\ce{OH-} > \ce{CH3O-} > \ce{NH2-} > \ce{CH3-},$$

but you can see the option is not even given. Why is it so?

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What you probably missed was that the order you mention is for the SAME GROUP elements. For example, down the group basicity of halide ions is-

F->Cl->Br->I-

But the the nucleophilicity order in polar protic solvents is-

I->Br->Cl->F-

This reverse in order is due to higher charge density of smaller halide ions and thus better interaction with polar protic solvents.

But along a period the charge density is similar and thus the interaction between solvent and nucleophile is almost similar. Thus, along a period the order follows basicity order.

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It is dangerous to relate nucleophilicity and basicity like that

To say that nucleophilicity follows basicity across a row means that, as basicity increases from right to left on the periodic table, nucleophilicity also increases. As basicity decreases from left to right on the periodic table, nucleophilicity also decreases. When it comes to nucleophilicity, do not assign this same rule when making comparisons between the halogens located in a column. In this case of moving up and down a column, nucleophilicity does not always follow basicity. It depends on the type of solvent you are using. (Nucleophile)

In general here are the rules for nucleophilicity along a group and across a period in a protic solvent

  1. Along a group nucleophilicity and basicity for the same order, reason for this is that charge density along a group is similar for the anions as there is not much size difference. So the better base is the better nucleophile. As the best nucleophiles are the good bases that want to share their electrons with an an electrophilic center.

  2. However when it comes to down a group nuceophilicty and basicity follow the exact opposite trend, reason for this is that charge is more dispersed in the larger anions and the extent of solvation is much lesser. Put in simpler words, the $\ce{H2O}$ molecules are in a surrounding the smaller ions and preventing them from acting as nucleophiles efficiently.

This will help you relate to what I mean This will help you relate to what I mean

References

  1. Nuclephile (Chemistry LibreTexts)
  2. Wikipedia
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