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Arrange the following in order of their ...

Arrange the following in order of their increasing reactivity towards Lucas reagent.
Butan-2-ol, 2-methyl propan-2-ol, butan-1-ol.

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`underset("Butan-2-ol")(CH_(3)-CH_(2)-underset(OH)underset(|)CH-CH_(3)), underset("2-methyl propan-2-ol")(CH_(3)-underset(OH)underset(|)overset(CH_(3))overset(|)C-CH_(3))`
`CH_(3)-CH_(2)-CH_(2)-CH_(2)OH`
The increasing reactivity order towards Lucas reagent
`CH_(3)CH_(2)CH_(2)CH_(2)OH lt CH_(3)CH_(2)underset(2^(@) "alcohol")(underset(OH)underset(|)CHCH_(2)) lt underset(3^(@) "alcohol")(CH_(3)- underset(OH)underset(|)overset(CH_(3))overset(|)C-CH_(3))`
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