Would this reaction be exothermic or endothermic?

[Beowulf_8991]

Summary:: A tertiary allylic alcohol rearranges to become a primary allylic alcohol, would it be exothermic because the final product is more stable and lower in energy?

Hi all, this problem's been on my mind for a couple of days now and I'm not making any progress with it. My problem is that with part c), I can't figure out if the reaction as a whole is exothermic or endothermic; the only data they've given me is that the entropy of activation is +20 Jmol-1K-1 and that the solvent isotope effect value is KH/KD = 0.33.

I think I've figured out the main bulk of the energy diagram but it's the product's energy level that's giving me problems. As far as I understand it, the final product is a tertiary allyl (primary alcohol) but the reactant is a primary allyl (tertiary alcohol) and since the tertiary allyl is a more stable alkene, it should be at a lower energy level therefore making the reaction exothermic. However, the fact it also goes from a tertiary alcohol to a primary one (less stable) makes me think it could be endothermic because of the decreased stability.

It's been a while since I covered energy diagrams so apologies for any rookie mistakes! I'm grateful for any pointers you guys can give me :)

 

[Thomas Michael]

To determine the relative stability of the reactant vs the product, try thinking about how the R group induction will stabilize the carbocation formed in the Sn1 reaction.

 

[chemisttree]

Why is a primary alcohol less stable than a tertiary alcohol?