Because alcohol protons are reasonably acidic and easily undergo exchange, it is important that the base be matched to the appropriate solvent. Explain why it would be virtually impossible to sort out the factors the size of the base or the stability of the alkenes formed if a reaction were carried out using methanol as the solvent and potassium t-butoxide as the base. In your answer draw a mechanism using methanol and tert-butoxide to illustrate your answer.

I don't understand how to do the mechanism at all.
but wouldn't the reasoning have to do with methanol being able to produce methoxide

To understand why it would be virtually impossible to sort out the factors of base size and stability of alkenes formed in a reaction using methanol as the solvent and potassium t-butoxide as the base, let's consider the mechanism involved.

When methanol is used as the solvent, it can act as a nucleophile itself because it can generate methoxide ions (CH₃O⁻) in solution. This means that during the reaction, both potassium t-butoxide (t-BuOK) and methanol can potentially act as bases.

Now, let's illustrate the mechanism using methanol and t-BuOK:

1. The oxygen atom in t-BuOK, which is negatively charged, acts as a base and abstracts a proton from methanol, forming methoxide (CH₃O⁻).

CH₃OH + t-BuOK → CH₃O⁻ + t-BuOH

2. The methoxide ion (CH₃O⁻) can then react with the starting material or substrate, which is denoted as R-X (where R is the alkyl group).

CH₃O⁻ + R-X → R-OCH₃ + X⁻

In this step, where R-X reacts with CH₃O⁻, there can be multiple possibilities. The reaction could occur via an E2 mechanism, leading to the formation of an alkene. However, the choice of base and solvent can greatly influence the outcome of this step.

If a strong base like t-BuOK is used, it can lead to a highly substituted alkene. On the other hand, if methoxide is present in high concentrations and reacts with the substrate, it can form a methoxy ether (R-OCH₃) instead of an alkene.

Due to the presence of methanol as the solvent, it can generate methoxide ions, thus competing with t-BuOK as a base. This makes it challenging to discern the sole influence of t-BuOK on the reaction outcome because both bases are present simultaneously.

Therefore, when using methanol as the solvent and t-BuOK as the base, it becomes difficult to attribute the outcome of the reaction solely to the base size or the stability of the alkenes formed. The presence of methoxide generated from methanol complicates the reaction pathway and makes it challenging to isolate the effects of different factors.

To overcome these complexities and be able to differentiate the influence of base size and alkene stability, alternative solvents without acidic protons, like dimethyl sulfoxide (DMSO) or acetonitrile, can be used. In these solvents, the influence of t-BuOK as the base would be more pronounced, facilitating a clearer understanding of the factors impacting the reaction outcome.