In an ionising solvent, (CH3)3C-Br has a half-life of 20 min for SN1 hydrolysis. Under identical conditions (CH3)3C-Cl reacts 40 times more slowly. If 1.0 M NaOH is present, the time needed for 87.5% of the chloride to react is

JEE Advanced levelSingle correct optionDifficulty 3 of 3o3043

In an ionising solvent, $(CH X_{3}) X_{3} C - Br$ has a half-life of 20 min for SN1 hydrolysis. Under identical conditions $(CH X_{3}) X_{3} C - Cl$ reacts 40 times more slowly. If $1.0 M$ $NaOH$ is present, the time needed for 87.5% of the chloride to react is

The half-life of the chloride is

20 \times 40 = 800

min (

13.3

h) and it is unaffected by the hydroxide, as the slow step is ionisation. A conversion of 87.5% takes three half-lives:

3 \times 800 = 2400

min

= 40.0

h. The other values correspond to one, two or four half-lives.