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Out of (Ch3)3 C-br and (Ch3)3 C-i, Which One is More Reactive Towards Sn1 and Why?

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Question

Out of (CH3)3 C-Br and (CH3)3 C-I, which one is more reactive towards SN1 and why? 

Answer in Brief
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Solution

In SN1 reactions, reactivity depends on the stability of carbocation after removing the leaving group form the reactant. Since the carbocation is the same here, so, we will see the tendency of leaving the group. As we can see in the following reactions Br and r are the leaving groups, out of them r is a better leaving group. Hence SN1 reaction will be faster in (CH3)3 C-I (CH3)3 - Br

\[\begin{array}{cc}
\ce{CH3}\phantom{..............}\ce{CH3}\\
\phantom{.}|\phantom{.................}|\phantom{...}\\
\ce{CH3-C-Br->CH3-C^+ + Br^-}\\
\phantom{.}|\phantom{.................}|\phantom{...}\\\ce{CH3}\phantom{..............}\ce{CH3}\\
\end{array}\]

\[\begin{array}{cc}
\phantom{...}\ce{CH3}\phantom{............}\ce{CH3}\\
\phantom{...}|\phantom{...............}|\phantom{...}\\
\ce{CH3-C-I->CH3-C^+ + I^-}\\
\phantom{...}|\phantom{...............}|\phantom{...}\\
\phantom{...}\ce{CH3}\phantom{............}\ce{CH3}\\
\end{array}\]

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