Why is SN1 mechanism favoured by low concentration of nucleophilic reagent? It is a first order reaction so shouldn't the reagent be in excess? Also higher the concentration of reagent faster the reaction right?
Let us assume that the competing reaction is a Sn2 based pathway.
Relative rate of products formed=(ie.. Sn1 to Sn2 product)=k'/(k[nucleophile]
Sn1 Reaction doesnot depend on concentration of the nucleophile , so more the concentration of nucleophile, the relative rate of Sn1 product diminishes.
Hence ,when the competing reaction is a Sn2 pathway, lesser concentration of nucleophile would favour the Sn1 pathway.
Hope this helps.