Which reaction in each of the following pairs takes place...

Which reaction in each of the following pairs takes place more rapidly? (EtOH is ethyl alcohol; $\mathrm{Et}_{2} \mathrm{O}$ is diethyl ether.) a. $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{HO}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Br}^{-}$ $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{HBr}$ b. $\mathrm{CH}_{3} \mathrm{I}+\mathrm{HO}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{I}^{-}$ $\mathrm{CH}_{3} \mathrm{Cl}+\mathrm{HO}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Cl}^{-}$ c. $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{NH}_{3} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{3}+\mathrm{Br}^{-}$ $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{HBr}$ d. $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{HO}^{-} \stackrel{\mathrm{DMSO}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Br}^{-}$ $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{HO}^{-} \stackrel{\mathrm{EtOH}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Br}^{-}$ e. $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{NH}_{3} \stackrel{\mathrm{Et}_{2} \mathrm{O}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{NH}_{3}+\mathrm{Br}^{-}$ $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{NH}_{3} \stackrel{\mathrm{EtOH}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{NH}_{3}+\mathrm{Br}^{-}$

Which reaction in each of the following pairs takes place more rapidly? (EtOH is ethyl alcohol; $\mathrm{Et}_{2} \mathrm{O}$ is diethyl ether.)
a. $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{HO}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Br}^{-}$
$\mathrm{CH}_{3} \mathrm{Br}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{HBr}$
b. $\mathrm{CH}_{3} \mathrm{I}+\mathrm{HO}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{I}^{-}$
$\mathrm{CH}_{3} \mathrm{Cl}+\mathrm{HO}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Cl}^{-}$
c. $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{NH}_{3} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{3}+\mathrm{Br}^{-}$
$\mathrm{CH}_{3} \mathrm{Br}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{HBr}$
d. $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{HO}^{-} \stackrel{\mathrm{DMSO}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Br}^{-}$
$\mathrm{CH}_{3} \mathrm{Br}+\mathrm{HO}^{-} \stackrel{\mathrm{EtOH}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Br}^{-}$
e. $\mathrm{CH}_{3} \mathrm{Br}+\mathrm{NH}_{3} \stackrel{\mathrm{Et}_{2} \mathrm{O}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{NH}_{3}+\mathrm{Br}^{-}$
$\mathrm{CH}_{3} \mathrm{Br}+\mathrm{NH}_{3} \stackrel{\mathrm{EtOH}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{NH}_{3}+\mathrm{Br}^{-}$

Key Concepts

SN2 Mechanism

The SN2 mechanism involves a single, concerted step in which the nucleophile attacks the electrophilic carbon from the backside as the leaving group departs. This mechanism results in inversion of configuration at the carbon center, and the reaction rate depends linearly on both the concentration of the nucleophile and the substrate.

Nucleophile Strength

Nucleophile strength plays a key role in determining the rate of SN2 reactions. Stronger nucleophiles, which are often negatively charged or less sterically hindered, attack the electrophilic center more readily, accelerating the reaction. The reactivity can be influenced by factors such as basicity, polarizability, and the degree of solvation in the reaction medium.

Leaving Group Ability

Leaving group ability is critical in SN2 reactions; a good leaving group can stabilize the negative charge after departure, facilitating the overall process. Generally, weaker bases such as iodide and bromide tend to be better leaving groups compared to stronger bases like chloride, which directly correlates to the reaction speed.

Solvent Effects

The solvent has a significant impact on SN2 reaction rates by influencing both nucleophile reactivity and leaving group stabilization. Polar aprotic solvents, which do not strongly solvate anions, enhance nucleophilicity and thereby speed up the reaction, whereas polar protic solvents tend to stabilize nucleophiles through hydrogen bonding, potentially slowing down the reaction rate.

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