The hydrolysis of $(CH X_{3}) X_{3} C - Br$ in aqueous acetone follows SN1 kinetics and has a half-life of 30 min when no base is added. When the reaction is repeated with $1.0 M$ $NaOH$ at the same temperature, the time needed for 87.5% of the bromide to react is

A $30 min$
B $45 min$
C $90 min$
D $15 min$

Answer: C

The SN1 rate does not depend on hydroxide concentration, so the half-life stays 30 min (k = ln2/30 = 0.0231 per min). A conversion of 87.5% corresponds to

ln 8/ k = 90

min, i.e. three half-lives,

3 \times 30 = 90

min.

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The hydrolysis of (CHX3​)X3​C−Br in aqueous acetone follows SN1 kinetics and has a half-life of 30 min when no base is added. When the reaction is repeated with 1.0 M NaOH at the same temperature, the time needed for 87.5% of the bromide to react is

Answer: C

More questions on SN1 mechanism, rate, stereochemistry, rearrangement

The hydrolysis of $(CH X_{3}) X_{3} C - Br$ in aqueous acetone follows SN1 kinetics and has a half-life of 30 min when no base is added. When the reaction is repeated with $1.0 M$ $NaOH$ at the same temperature, the time needed for 87.5% of the bromide to react is