[slidergirl2007]

Hi
I'm having a little trouble trying to figure out why these reaction rates are different. The reagent in all of the equations is CH3-OH.
The first reaction time is 20s and it is a cyclopropene with OTs group attatched The second is no reaction with a straight propanal carbon again with OTs attatched. The second is a reaction time of 180s and it is a straight propene chain with an OTs group at the end. Can anyone help me brainstorm why these reaction times might be different

[orgopete]

Hint, carbocation stability. Draw the resultant carbocations (are you studying aromaticity?).

[slidergirl2007]

We have been, I guess I understand why there's no reaction with the alkane but I assumed that the cyclopropene would be more stable than the straight chain propene, which is not the case since the reaction time is faster, so I got a little lost

[stewie griffin]

I assumed that the cyclopropene would be more stable than the straight chain propene, which is not the case since the reaction time is faster, so I got a little lost

I think you're confusing yourself 
As orgopete stated, this ultimately comes down to which carbocation is more stable. Our choices are a primary carbocation, an allylic carbocation, and a cyclopropenyl cation. You need to rank those in order of stability, and it would help to be familiar with aromaticity and the 4N + 2 rule.
Your confusion seems to be that you think a more stable carbocation must mean slower reaction. I can understand where this stems from... students often think "well if it's more stable then it should be more happy to sit around by itself all day and not need to react." Not quite though. This is an S_N1 reaction right... so the slowest step is formation of the carbocation (the resultant attack by CH₃OH on the carbocation is going to be quite quick compared to the time it takes to form the carbocation). Therefore the reaction times are really a reflection of the time required to form the carbocation. The more stable the carbocation, the faster/more likely it is to form.
So again, stable carbocation doesn't mean it won't react quickly. All carbocations are electron deficient and still love to get attacked by nucleophiles. However the more stable the carbocation, the faster the carbocation will form, and the faster the net reaction is.
Hope that helps.