Dehydration is a reversible process. Which of the two set-ups, distillation or
single flask, will generate the most cyclohexene? Why?

             Distillation will generate the most cyclohexene.

Explanation:

                     Let us assume following attached reaction for the synthesis of cyclohexene from cyclohexanol which attains equilibrium after certain time.

As shown in figure the cyclohexanol upon treatment with phosphoric acid undergoes dehydration reaction (removal of water) and produces cyclohexene. On the other hand cyclohexene reacts with water (hydration reaction) and produces cyclohexanol.

Now, if this reaction is allowed in a single flask it will attain equilibrium and will not generate the cyclohexene in high quantity. On the other hand if we apply Le Chatelier's principle ( removal of product moves the equilibrium in right direction) and distillate cyclohexene (boiling the cyclohexene to convert it into vapors and then collect it after condensation) will move the reaction in forward direction and will allow us to generate cyclohexene in high amounts.

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.