Explain a possible mechanism for the `S_N1` reaction of `Me_(3)C-Br` and MeOH.

Explanation

`Me_(3)C-Br+H-OMerarrunderset("(An ether)")(Me_(3)C-OMe)+HBr`
Step 1. The substrate undergo heterolytic fission forming a carbocation. This is the slow rate determining step.
`Me_(3)C-Broverset("Slow step")rarrMe_(3)C^(+)+Br^(-)`
Step. The fast step in the attack of nucleophile, MeOH on the carbocation to form protonated ether, and is followed by the rapid loss of its proton to a second molecule of nucleophile to form an ether.
`Me_(3)overset(+)C+H-OMeoverset("Fast")underset("Step")rarrunderset("Protonated ether")(Me_(3)C-overset(+)underset(H)underset(|)OMe)overset(H-OMe)rarrunderset("(An ether) ")(Me_(3)C-OMe+Meoverset(+)OH_(2))`
In general,
`[R-Loverset("Slow")rarr:L^(-)+R^(+)overset(":NuH")underset("Fast")rarrR-NuH^(+)overset(-H^+)underset("Fast")rarrR-Nu]`