What is the reaction order of SN1

[shredder666]

Sorry the title is bit misleading, I'm actually talking about the rate determining step of SN1 mechanisms. I thought it was first order, but my teacher disagrees.

he argues that it is zeroth order because in the appropriate solvent, the leaving group leaves spontaneously regardless of its concentration, thus the rate expression

rate=k[substrate]^0

my argument is that first, it is unimolecular substitution, thus the name SN1 (I'm only talking about the rate determining step, not the whole reaction).
Second only the substrate was involved in the reaction itself. The solvent just modifies the K value. Thus the rate expression
rate=k[substrate]^1

I do realize that a lot of texts (that I know of) tends towards my argument, but please ignore it for now, for most mechanisms are only proposed.
thank u

 

[neeraj93]

As a your teacher says, that the leaving group will leave spontaneously in the appropriate solvent. So that isn't good enough to generalisation that all SN1 reactions are of zeroth order.
But let's assume that the Formation of the carbocation,i.e, the rate-determining step, is spontaneous. Then it will no longer remain the slowest step. It will, in fact, proceed faster than the second step of the reaction. And automatically the second step will become the slowest step and determine the rate. So, you end up with a second order reaction, anyway. A total contradiction.
Further, The rate of a reaction depends on all the steps in the reaction. If you have a step which is prominently slower than all others, it becomes the rate determining step, because here, the rates of the other steps do not greatly affect the rate of the overall reaction. If the rates of the steps involved are comparable, you will have a complicated rate law equation. So even by this argument you may get a complicated rate law, but zero order isn't probable.

 

[chemisttree]

...he argues that it is zeroth order because in the appropriate solvent, the leaving group leaves spontaneously regardless of its concentration, thus the rate expression...

If that is what your teacher said, then teacher is wrong. Spontaneity is not the correct term to use in a reaction order or rate of reaction discussion. How the concentration of the species that is ionizing affects the overall rate of the reaction is the only pertinent point to discuss.

It is well known that solvent effects affect the rate of reaction but not the reaction order. A high dielectric solvent might lower the energy barrier leading to the reactive intermediate and thus increase the rate, but how the concentration of that species affects the overall rate remains unchanged... first order for SN1.