The correct option is D Rate depends on R-X
E1 reaction is a two step process.
In step 1, leaving group leaves and form a carbocation.
In step 2, the base will attack the proton and proton abstraction takes place.
In E1, formation of carbocation is the slowest step. Hence, it is the rate determining step.
Polar protic solvent solvates the halide ion formed due to C-X bond breaking. Therefore, polar protic solvent favours the E1 reaction.
The base is not involved in the RDS in E1 reaction. thus it does not affect the rate of E1 reaction.
However, a stronger base is not necessary for the E1, it may lead to side reactions. So, weak & moderate bases are preferred.
Rate of the reaction ∝[R−X]1[Base]0
Hence, correct option is d.