Does E1 mechanism always imply first order reaction?

[Oxford University Press, Okuyama & Maskill: Organic Chemistry — Chapter 13: Multiple Choice Questions, Question 1](https://global.oup.com/uk/orc/chemistry/okuyama/student/mcqs/ch13/):



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> Which of the following statements regarding the E1 mechanism is wrong?
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> **a**) Reactions by the E1 mechanism are unimolecular in the rate-determining step.  
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> **b**) Reactions by the E1 mechanism are generally first order.  
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> **c**) Reactions by the E1 mechanism usually occur in one step.  
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> **d**) Reactions by the E1 mechanism are multi-step reactions.
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> 


Option **c** is the correct answer, but I have a few questions regarding option **b** being true:


1. Is the reaction which follows E1 mechanism *always* a first order reaction? Are there any examples with the second or higher orders?
2. Dehydration of secondary alcohol in the presence of concentrated sulfuric acid follows E1. What is the order for this reaction?
3. Does the number one in E1 represent molecularity or order of the reaction? According to me, it is usually molecularity of RDS, not the order, because option **b** says E1 reactions are *generally* 1st order, not *always*.




I think the problem lies in definition of terminologies. There are various kinds of reaction which occur in multiple steps, but just because one of the elementary step reaction follows SN1 or E1, it does not mean the whole reaction will have the first order.


Same thing here. The cation formed when alcohol attacks on $\ce{H+}$ undergoes SN1 and the rate will be only proportional to concentration of this cation. Further, the concentration of this cation is proportional to both hydrogen ion concentration and alcohol concentration.


In conclusion, E1 is always the first order reaction, but the dehydration of alcohols is the second order reaction (or pseudo first order if proton is abundant) because water expulsion is just one of the elementary steps happening in the reaction.


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