Show the mechanism that illustrates the following reaction.

1-methyl-1-methanol-cyclopentane + acid -> 1-methyl-cyclohexene

So, there is an elimination reaction, *AND* the carbon ring grows from a five carbon ring to a six carbon ring.

(I hope my IUPAC name for 1-methyl-1-methanol-cyclopentane is correct. One methyl group and one methanol group are attached to the same carbon on a cyclopentane structure).

I don't know the mechanism for your reaction but I'm posting this to let you know that we simply can't draw mechanisms on these boards. Sorry about that.

To illustrate the reaction between 1-methyl-1-methanol-cyclopentane and an acid that leads to the formation of 1-methyl-cyclohexene, we can propose a mechanism based on the given information.

First, let's clarify the IUPAC name for the starting material. What you described as "1-methyl-1-methanol-cyclopentane" is ambiguous and could have multiple interpretations. Assuming you meant "1-methyl-1-methoxycyclopentane," the structure would be as follows:

CH3 O
| |
H3C - C - C - C - C
|
H

Now, let's outline a plausible mechanism for the reaction:

Step 1: Protonation
The acid (represented as HA) protonates the oxygen of the methoxy group. This is often the first step in acid-catalyzed reactions and helps increase the reactivity of the leaving group.

CH3 OH2 O
| || |
H3C - C - C - C - C
|
H

Step 2: Carbocation formation
The electron pair of the O-H bond attacks the β-carbon (adjacent to the positively charged carbon) forming a new bond. This leads to the formation of a carbocation intermediate and leaves the oxygen with a positive charge.

CH3 O+ H2O
| || |
H3C - C - C - C - C
|
H

Step 3: Ring expansion
In a ring expansion, the carbocation of the five-membered cyclopentane rearranges to stabilize the positive charge. This results in a six-membered cyclohexyl carbocation.

CH3 O H2O
| || |
H3C - C - C - C+ - C
|
H

Step 4: Deprotonation
A base (represented as B: :) abstracts a proton from the adjacent carbon in the cyclohexyl carbocation, leading to the formation of a double bond and stabilizing the system.

CH3 O H2O
| || |
H3C - C = C - C+ - C
|
H

Step 5: Deprotonation (optional)
If additional acid is present, the double bond can be protonated to restore the aromaticity of the cyclohexene product.

CH3 O H2O
| || |
H3C - C = C - C+ - C
|
H

Overall, these steps describe the conversion of 1-methyl-1-methoxycyclopentane to 1-methyl-cyclohexene through an acid-catalyzed elimination reaction and a ring expansion.