Please Help Me in Predicting the product(s) for the Organic Chemistry reactions:?

Question

1. trans-1-bromo-2-methyl cyclohexane + sodium tert-butoxide in tert-butanol with heat

2. cis-1-bromo-2-methyl cyclohexane + sodium tert-butoxide in tert-butanol with heat

Answer 1

The base can remove a proton from two different beta carbons: the one with the methyl group (tertiary), and the one without the methyl group (secondary).

1: The only product is 3-methylcyclohexene.

Because the bromine and methyl group are trans to each other, the bromine and the tertiary hydrogen are cis to each other. E2 elimination requires that the bromine and hydrogen be antiperiplanar (in a chair, this is accomplished when these two are trans and both axial). The secondary carbon has a hydrogen that can be trans to the bromine.

2. The major product is 3-methylcyclohexene.

Both possible eliminations can occur, since the bromine can be trans to a proton on either side. However, a bulky base tends to eliminate according to Hoffman's rule, which says that a sterically hindered base will remove the least substituted proton. In the case here, that is also the secondary proton. So the major product will again be 3-methylcyclohexene, although some 1-methylcyclohexene will form.

Answer 2

You need to understand that the butoxide ion attacks nucleophilically from the back of the carbon atom holding the leaving group - the halide ion. So the product will be an ether, and cis will turn into trans, and trans into cis.
Now you can work it out for yourself.