Which `S_(N)1` reaction would you expect to take place more rapidly ?
(a) (i) `(CH_(3))_(3)C Cl+H_(2)O to (CH_(3))_(3)COH+HCl`
Or
(ii) `(CH_(3))_(3)C Br+H_(2)O to (CH_(3))_(3)COH+HBr`
(b) (i) `(CH_(3))_(3)C Cl+H_(2)O to (CH_(3))_(3)COH + HCl`
Or
(ii) `C_(5)H_(5)Cl+H_(2)O to C_(5)H_(5)OH + HCl`
(c) (i) `(CH_(3))_(3)C Cl+ H_(2)O to (CH_(3))_(3)COH + HCl`
Or
(ii) `(CH_(3))_(3)C Cl+ CH_(3)OH to (CH_(3))_(3)COCH_(3)+ HCl`
(d) (i) `(CH_(3))_(3)C Cl(1.0M)+CH_(3)CH_(2)O^(-)(1.0M) overset(C_(2)H_(2)OH)to (CH_(3))_(3)COCH_(2)CH_(3)+Cl^(-)`
Or
(ii) `(CH_(3))_(3)C Cl(1.0M)+CH_(3)CH_(2)O^(-)(2.0M) overset(C_(2)H_(2)OH)to (CH_(3))_(3)COCH_(2)CH_(3)+Cl^(-)`

Explanation

(a) Reaction (ii) because `Br^(-)` ion is a better leaving group than `Cl^(-)` ion,
(b) Reaction (i) because the reactant is a tertiary halide. Moreover, phenyl halides are not reactive in `S_(N)1` reactions.
(c) Reaction (i) because water is more polar solvent than methanol and `S_(N) 1` reaction takes place faster in more polar solvent.
(d) Both reactions occur at the same rate because `S_(N)1` reactions are independent of the concentration of the nucleophile.