Comparison of rate of dehydration of primary, secondary & tertiary alcohols on cyclohexane Rate of dehydration when given compounds are treated with conc. $\ce{H2SO4}$ is 



According to me the answer should be $R &gt; Q &gt; S &gt; P$ but my textbook solution gives the answer as R > Q > P > S (Sadly, there is no explanation).

Dehydration of secondary &amp; tertiary alcohols in the presence of conc. $\ce{H2SO4}$ proceed through E1 mechanism whereas most primary alcohols proceed through E2 mechanism.

In the molecular R, the carbocation formed after the alcohol group leaves the molecule after protonation is a tertiary carbocation and not just that, it is resonance stabilized as well.

In the molecule Q, you get a secondary carbocation and this is resonance stabilized as well.

In molecule S, you get a secondary carbocation but there is no resonance stabilization. 

In molecule P, the dehydration goes via E2 mechanism and there is a bulky cyclohexene group attached to the $\alpha$-carbon which should be contributing to steric hindrance.

If the question did not have molecule P, then its pretty much obvious that the answer is R > Q > S but with molecule P, I am not quite sure where to place it.

I thought that P will be least reactive since it proceeds via E2 mechanism and there is one bulky group attached to the carbon.

So how do I come up with a concrete answer to justify why molecule P should react faster than molecule S but slower than molecule Q.
The rate of dehydration is related to the ease of formation of the carbocation and the energy of the carbocation intermediate.

The ease of formation of carbocation is tertiary>secondary>primary. That is the ease of abstraction of $\ce{OH2+}$ COULD BE be R>Q/S>P.

Let's look at a comparison of the energy of the carbocation intermediates in all these cases.


  A carbocation may be stabilized by resonance by a carbon-carbon double bond next to the ionized carbon. Such cations as allyl cation $\ce{CH2=CH–CH2+}$ and benzyl cation $\ce{C6H5–CH2+}$ are more stable than most other carbocations. Molecules that can form allyl or benzyl carbocations are especially reactive. These carbocations where the C+ is adjacent to another carbon atom that has a double or triple bond have extra stability because of the overlap of the empty p orbital of the carbocation with the p orbitals of the $\pi$ bond. This overlap of the orbitals allows the charge to be shared between multiple atoms – delocalization of the charge - and, therefore, stabilizes the carbocation. 




Let's look at them individually,


P - allylic cation, primary alcohol
Q - allylic cation, secondary alcohol
R - allylic cation, tertiary alcohol
S - NOT an allylic cation, secondary alcohol


$\ce{R}$ is clearly the winner.

Now we may conclude that the charge dispersal is better in resonance than it is in hyperconjugation (explanation)

Here are the 3D diagrams of the P carbocation. Hydrogen cation doesn't look like it has to face significant steric hindrance to perform protonation of the alcohol.