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 tert-butyl chloride is doubled, the rate of the reaction:
doubles
This reaction of clearly SN1. The rate expression is:
Reaction rate=[tert−butylchloride]
Since the rate is only dependant on the concentration of tert-butyl chloride, the rate doubles with the doubling of the concentration of tert-butyl chloride.