The Question is from neet-chemistry chemical-kinetics order-and-molecularity, and it was created by the author Mr. S M HUSSAIN

Question

The hydrolysis of tert-butyl bromide in an aqueous medium follows the $S_N1$ mechanism.  If the concentration of tert-butyl bromide is doubled, and the concentration of water is tripled, how will the rate of the reaction be affected?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: $S_N1$ reaction kinetics
	**Related Topics**: Nucleophilic substitution, reaction rates, concentration dependence
	**Prerequisites**: Understanding of rate laws and $S_N1$ reaction mechanisms.
## SOLUTION PATHWAY
**Given Information**:
	The reaction follows an $S_N1$ mechanism.
	The concentration of tert-butyl bromide is doubled.
	The concentration of water is tripled.
**Method & Steps**:
	1. **Understanding $S_N1$ Kinetics**: In an $S_N1$ reaction, the rate-determining step is the formation of the carbocation intermediate. This step only involves the substrate (tert-butyl bromide in this case) and is independent of the nucleophile (water).  Therefore, the rate law for an $S_N1$ reaction is:
		$Rate = k[tert-butyl bromide]$
		where $k$ is the rate constant.
	2. **Applying the Rate Law**: If the concentration of tert-butyl bromide is doubled, the rate will also double, because the rate is directly proportional to the concentration of the substrate.
		$New Rate = k[2 	imes tert-butyl bromide] = 2k[tert-butyl bromide] = 2 	imes (Original Rate)$
	3. **Effect of Water Concentration**: Since the rate-determining step does not involve water, changing the concentration of water will not affect the rate of the reaction.
		The rate remains doubled.
		Result: The rate doubles.
		Verification: The rate law confirms that the reaction rate is only dependent on the concentration of tert-butyl bromide for an $S_N1$ mechanism.
## OPTION ANALYSIS
A ✓: Doubles: Correct. The rate is directly proportional to the concentration of tert-butyl bromide in an $S_N1$ reaction. Doubling the concentration doubles the rate.
B :x: Triples: Incorrect.  The rate is independent of the water concentration in an $S_N1$ reaction.
C :x: Increases six-fold: Incorrect. This would only be true if the reaction was first order in both tert-butyl bromide and water.
D :x: Remains unchanged: Incorrect. Doubling the concentration of the substrate will change the rate in an $S_N1$ reaction.
## LEARNING AIDS
	**Common Mistakes**:
		1. Applying $S_N2$ kinetics to an $S_N1$ reaction: Remember that $S_N1$ reactions are unimolecular and their rate depends only on the substrate concentration.
		2. Considering the nucleophile (water) in the rate law:  The rate-determining step does not involve the nucleophile in $S_N1$ reactions.
	**Quick Tips**:
		1. For $S_N1$ reactions, focus solely on the substrate's concentration when determining rate changes.
		2. Remember that carbocation formation is the rate-determining step in $S_N1$ reactions.

Mr. S M HUSSAIN · Answer

The correct Option is "Doubles"

Mr. S M HUSSAIN · Answer

Triples

Mr. S M HUSSAIN · Answer

Increases six-fold

Mr. S M HUSSAIN · Answer

Remains unchanged

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