Which elimination reactions, E1 or E2, depend on the concentration of the substrate?
With this, we need to differentiate between the reactant and what is being reacted with.
The substrate is what is being reacted with. There must be something reacting with it, since in order for the concentration of the substrate to matter, it has to matter with respect to another reactant. Therefore, it must be a bimolecular reaction---a reaction involving two molecules.
It is clear that a bimolecular reaction is one that depends on the concentration of the substrate (whether it's the substrate itself or its conjugate base), because if there are two dependent reactants, when one runs out, the reaction is over. (It is the basic type of reaction you learned in General Chemistry where you have a limiting reactant and an excess reactant.)
A second-order reaction is either second order with respect to one reactant or first order with respect to each of two reactants.
#r(t) = k[A]^2#
#r(t) = k[A][B]#
#\mathbf"E2"#is first order with respect to each of two reactants.
There is a faster scenario, which occurs in one step. It is first order with respect to the substrate. This is known as
The slower scenario is also first order with respect to the substrate, but there is another step---a slower second step---and that is first order with respect to the conjugate base of the substrate. This only happens if the carbanion is stabilized and the leaving group is a poor one. This is known as the less-common
An example one-step
The proton eliminated was on the