When tert-butylchloride is added to an equal amount of ethanol in an inert solvent, one of the products is ethyl tert-butyl ether. When the concentration of ethanol is doubled, the rate of the reaction:
remains constant
This reaction of clearly SN1. The rate expression is:
Reaction rate=[tert−butylchloride]
Since the rate is independent of the concentration of ethanol, the rate remains constant provided the temperature is constant.