Acid catalysed dehydration of t-butanol is faster than that of n-butanol because

Explanation

Acid-catalysed dehydration of alcohols occurs through the formation of carbocation intermediate as:
`underset("tert- Butanol") (CH_(3) - overset(CH_(3))overset(|)underset(CH_(3))underset(|)(C)-OH) overset(H^(+))underset(-H_(2)O)(to) underset("tert- Butyl carbocation (more stable)") (CH_(3) - overset(CH_(3))overset(|)underset(CH_(3))underset(|)(C^(+)))`
`CH_(3)Cunderset("n- Butanol")(H_(2) CH_(2) CH_(2))OH overset(H^(+)) underset(-H_(2)O)(to) underset("n- Butyl carbocation (less stable)")(CH_(3) CH_(2)CH_(2)CH_(2)^(+))`
Since tert-butyl carbocation `(3^(@))` is more stable than n-butyl carbocation `(1^(@))`, therefore, acid-catalysed dehydration of tertbutanol takes place faster than that of n-butanol.