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Step-by-Step Explanation
Step 1: Write Down the General Reaction
We are considering the nucleophilic substitution (SN2) reaction:
$CH_3Br + Nu^- \to CH_3 - Nu + Br^-$
Here, $Nu^-$ represents different nucleophiles: (A) $PhO^-$ (phenolate), (B) $CH_3COO^-$ (acetate), (C) $HO^-$ (hydroxide), and (D) $CH_3O^-$ (methoxide).
Step 2: Recognize the Connection between Acid Strength and Conjugate Base Strength
A stronger acid produces a weaker conjugate base, and a weaker acid produces a stronger conjugate base. In other words, if the conjugate acid of a base is very strong, the base itself will be relatively weaker, and vice versa.
Step 3: Compare Conjugate Acids of the Given Bases
The conjugate acids of the nucleophiles are:
$CH_3O^-$ comes from $CH_3OH$ (methanol)
$HO^-$ comes from $H_2O$ (water)
$PhO^-$ comes from $C_6H_5OH$ (phenol)
$CH_3COO^-$ comes from $CH_3COOH$ (acetic acid)
The acid strength order among these conjugate acids is known to be:
$CH_3COOH > C_6H_5OH > H_2O > CH_3OH$
This tells us that $CH_3COOH$ is the strongest acid and $CH_3OH$ is the weakest acid among the four.
Step 4: Deduce the Basic (and Hence Nucleophilic) Strength
Because a stronger acid forms a weaker conjugate base, the reverse order (from weakest to strongest base) will be:
$CH_3COO^- < C_6H_5O^- < HO^- < CH_3O^-$
Thus, methoxide ($CH_3O^-$) is the strongest base/nucleophile, whereas acetate ($CH_3COO^-$) is the weakest.
Step 5: Relate Nucleophilicity to the Rate of SN2 Reaction
In an SN2 reaction, a stronger nucleophile attacks the carbon center more readily and leads to a faster reaction rate. Hence the nucleophile with the highest basicity usually has the fastest rate in an SN2 process (although other factors like steric hindrance can also play a part, these substituents are relatively small so basic strength dominates).
Step 6: Arrange the Shown Nucleophiles in Decreasing Order of Rate
Following the basicity (nucleophilicity) trend, the order is:
$CH_3O^- \ (D) > HO^- \ (C) > PhO^- \ (A) > CH_3COO^- \ (B)$
Therefore, the decreasing order of the rate of the reaction is:
D > C > A > B
