Consider the reaction sequence given below: Which of the following statements is true?

Step 1: Analyze the rate laws

Reaction (1): $\text{Rate} = k[t\text{-}BuBr]$

• First-order in substrate only
• Zero-order in base
• Independent of $[\ce{OH-}]$
• This is $S_N1$ mechanism

Reaction (2): $\text{Rate} = k[t\text{-}BuBr][\ce{OH-}]$

• First-order in substrate
• First-order in base
• Depends on both concentrations
• This is $S_N2$ mechanism

Step 2: Evaluate each statement

(a) "Changing [base] will have no effect on reaction (2)"

FALSE - Reaction (2) is first-order in $[\ce{OH-}]$, so changing base concentration will affect the rate.

(b) "Changing [base] will have no effect on reaction (1)"

TRUE - Reaction (1) is zero-order in base (rate doesn't depend on $[\ce{OH-}]$). This is characteristic of $S_N1$ mechanism where rate-determining step is ionization.

(c) "Changing base from $\ce{OH-}$ to $\ce{^-OR}$ will have no effect on reaction (2)"

FALSE - Different bases have different nucleophilicity. Changing the base will affect the rate of $S_N2$ reaction.

(d) "Doubling [base] will double the rate of both reactions"

FALSE - Only affects reaction (2). Reaction (1) is independent of base concentration.

Answer: (b)

Key Concepts:

$S_N1$ vs $S_N2$ Rate Laws:

| Mechanism | Rate Law | Order | |-----------|----------|-------| | $S_N1$ | Rate = $k[\ce{RX}]$ | First-order overall | | $S_N2$ | Rate = $k[\ce{RX}][\ce{Nu}]$ | Second-order overall |

Why $S_N1$ is independent of nucleophile:

• Rate-determining step: Carbocation formation
• Nucleophile attacks in fast step (after RDS)
• Changing nucleophile concentration doesn't affect overall rate

Solvent effects:

• Reaction (1) in $\ce{H2O}$ (polar protic) → favors $S_N1$
• Reaction (2) in $\ce{CH3OH}$ (polar protic) → can do $S_N2$ with strong base