[koolman]

AMONG THE compounds which of the following reacts faster in an SN1 reaction?
 I. cis-4-tert-butylcyclohexyl bromide
 II. trans-4-tert-butylcyclohexyl bromide

I think II compound beacuse of stable carbocation.

[Babcock_Hall]

Can you explain in what way the carbocations are different?

[koolman]

As trans is more stable due to dipole moment.

[clarkstill]

The carbocations formed from these two starting materials are identical. I guess any difference in rates will correlate with the relative stabilities of the starting materials, but it's a weird question. This is normally the example they use to make a point about antiperiplanar arrangements in E2 eliminations.

[Babcock_Hall]

clarkstill,

Is there any requirement that the leaving group leaves from an axial (or equatorial) position in forming a carbocation from a substituted cyclohexane?  Obviously my question only pertains to E1 or S_N1 processes.

[clarkstill]

I'm certain there isn't a requirement. Whether there is a preference is another issue... You could well imagine that the stabilization by hyperconjugation is slightly different in the two transition states leading to the common intermediate, as well as the two starting materials having different energies, so it's likely the rates would differ to some extent.

Just thinking out loud, there are two main factors I can think of that would affect the rate. Assuming the t-Bu remains as an equatorial 'lock' throughout:
1. If the halogen is axial it will experience greater steric destabilization, raising the energy of the SM and making loss of the halogen more favourable to relieve strain.
2. If the halogen is equatorial, then adjacent electron-rich C-C bonds can donate into the C-X sigma*, weakening the bond and making loss of the halogen easier.

I don't know which effect wins, but I'd be happy to hear people's thoughts?

[orgopete]

Without looking it up, I believe it is the less stable axial bromide that reacts faster.

[Dan]

Another vote for faster SN1 with the axial bromide here (on the basis of 1,3-diaxial strain relief).