[cseil]

cis-1-bromo-4-tert-butylcyclohexane

or


trans-1-bromo-4-tert-butylcyclohexane

SN1 reaction has a carbocation as intermediate, so the nucleophile can attack from both sides (every carbocation is planar).
Because of that, I think that the reaction occurs at the same velocity.

It it had been a SN2 reaction, the cis would have reacted faster (because SN2 is a one step reaction, the nucleophile attacks from the back and on the back there's no substituent).

[orgopete]

If a starting material were less stable, how might that affect its reactivity?

By the way, they are not chiral.

[cseil]

I did not write "Chiral" but I don't know why it appeared 
The SMILES code was generated by ACD/ChemSketch!

Well, the less stable is more reactive. So the cis molecule is more reactive.

[cseil]

I don't want to start a new topic so I'll write it here.
It asks me to write them in order of decreasing reactivity in a E2 reaction.

I said that b is the least reactive, because it can remove only a distant proton.
Then c, because is more stable than "a" which is the most reactive (it has axial bonds, hence it is less stable).

Is that right?

[cseil]

I don't want to start a new topic so I'll write it here.
It asks me to write them in order of decreasing reactivity in a E2 reaction.

I said that b is the least reactive, because it doesn't have protons to remove.
Then c, because is more stable than "a" which is the most reactive (it has axial bonds, hence it is less stable).

Is that right?

[Altered State]

I agree with b being the least reactive. If fact, it will not react through E2, since you don't have any axial proton in an alpha position to the axial leaving group, so there won't be elimination in one step (E2).

But in regards to a and c, I wouldn't follow that reasoning. For an E2 reaction to occur a base has to attack an axial proton (situated in the Alfa position to the Br) at the same time that the bromine leaves the molecule.
I'd say that the base attack will take place more easily in c than in a, because in a you have an axial -CH3 that will hinder the attack of the base. In c these 1,3 diaxial interactions will be lower.

In addition, the larger your base is, the more reactive would be c respect to a towards an E2 reaction.

[orgopete]

I think you have to keep first order reactivity separate from second order. Strain can increase a first order reaction and decrease a second order reaction.

In this case, all axial b would the least stable, but it will convert to all equatorial b. All axial a would be less stable than all equatorial a, and all equatorial a more stable than either form of c.

For a second order reaction, the rates depend on concentration, higher will be faster. Therefore c should react the fastest. The concentration of all axial a will be the next most reactive, and it has one less proton that could be extracted. The concentration of all equatorial c would be the highest conformation, but equatorial elimination reactions occur at approximately 0.001 times the rate of a trans-diaxial elimination (as I recall).