Consider the reaction between tert-butyl alcohol and acetadelhyde in the presence of $\ce{HBr}$ in aqueous solution:
$$\ce {(CH_3)_3COH(aq) + (CH_3)CHO(aq)} \longrightarrow ?$$
Here is my assumed solution to the reaction mechanism:
Essentially, the $\ce{H+}$ ion removes the alcohol from the tert-butyl alcohol allowing the acetadelhyde to bond with the carbocation. In this process the double bond between the oxygen and a carbon becomes a single leaving a positive region on the respective carbon. This allows the bromide ion to attach forming the molecule in the last step.
Is the product correct? Is the mechanism to get to this product correct?