The catalytic dehydration of methanol $($ME$)$ to form dimethyl ether $($DME$)$ and water was

carried out over an ion exchange catalyst. The packed bed was initially filled with nitrogen. At

$t=0$ a feed of pure methanol vapour entered the reactor at $413K,100$kPa and $0\mathrm{.}2c{m}^3{s}^{-1}.$ The

following partial pressures were recorded at the exit to the differential reactor containing $1\mathrm{.}0g$

of the catalyst in $4\mathrm{.}5c{m}^3$ of reactor volume.

Propose a possible mechanism and derive a rate expression.