\[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}+2HI\xrightarrow{\Delta }2{{C}_{2}}{{H}_{5}}I+{{H}_{2}}O\]

Recall that oxymercuration-reduction of alkenes lead to hydration in Markovnikov’s way. Thus

The given reaction proceeds through $${S_N}^1$$  mechanism which involves carbocation as intermediate.
$$P{h}_{3}C-O-R\stackrel{H^{+}}{\rightleftharpoons }$$    $$P{h_3}C - \mathop O\limits_H^ + - R \rightleftharpoons P{h_3}{C^ + } + ROH$$
Thus, higher the stability of the carbocation, greater will be reactivity. Presence of electron releasing group $$\left( {e.g., - OC{H_3}} \right)$$    in $$p$$ - position of the phenyl group will disperse the positive charge of the carbocation by $$ + M$$   effect, hence stabilizes the carbocation.

\[C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}\xrightarrow{HBr/{{H}_{2}}{{O}_{2}}}C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}Br\xrightarrow{{{C}_{2}}{{H}_{5}}ONa}C{{H}_{3}}{{\left( C{{H}_{2}} \right)}_{3}}O{{C}_{2}}{{H}_{5}}\]
In presence of \[{{H}_{2}}{{O}_{2}},\]  $$HBr$$  adds in $$anti$$  - Markovnikov’s way (peroxide effect)

Phenol reacts with bromine water ( aqueous solution to give a precipitate of 2, 4, 6 - tribromophenol ) due to polar salvent.

Alkyl aryl ethers undergo substitution reactions.

Thinking process This problem is based on the acidic character of phenol. Electron - withdrawing group at $$o$$  and $$p$$ - position $$w.r.t.$$  $$-OH$$  group of Phenol, increase the acidic strength.
Picric acid ( 2, 4, 6 - trinitrophenol ) is extremely more acidic than given compounds because its $$pKa$$  value is close to zero also due to the presence of three strong electron withdrawing group ( $${ - N{O_2}}$$  group ) at $$ortho$$  and $$para$$  - positions, picric is more acidic compound.

Tertiary alchols reacts fastest with lucas reagnet as the rate of reaction is directly proportional to the stability of carbocation formed in the reaction. Since most stable $${3^ \circ }$$ carbocation is formed in the reaction hence it will react fastest further tetriary alcohols appears to react by $${S_N}1$$  mechanism.
$$\eqalign{ & {\text{step}}\,{\text{1}}{\text{.}}\,\,\,{\left( {C{H_3}} \right)_3}C - OH + H - Cl \rightleftarrows {\left( {C{H_3}} \right)_3} - \mathop {\text{O}}\limits^{\text{ + }} {H_2} + C{l^ - } \cr & {\text{step}}\,2.\,\,\,{\left( {C{H_3}} \right)_3}C - \mathop {\text{O}}\limits^{\text{ + }} {H_2} \rightleftarrows {\left( {C{H_3}} \right)_3}{C^ + } + {H_2}O \cr & {\text{step}}\,3.\,\,\,{\left( {C{H_3}} \right)_3}{C^ + } + C{l^ - } \to \mathop {{{\left( {C{H_3}} \right)}_3}C - Cl}\limits_{{\text{tert - Butyl chloride}}} \cr} $$