Gas phase reaction of methanol $($A$)$ in water forming formaldehyde and hydrogen at $300$ C

and $101$ kPa $($assuming both are constant$)$ with the reaction

CH$3$OH $->$ HCHO $+$ H$2.$

The reaction takes place in a Plug Flow Reactor $($PFR$)$ without a catalyst. If the reaction proceeds first order with a value of kA $=0\mathrm{.}53/$sec$.$ Determine:

a$.$ Is the reaction exothermic or endothermic? Prove it$!$

b$.$ Determine the reactor volume to achieve $85\%$ methanol conversion where the mol flow rate of the feed is $200$ kmol$/$det

Data known:

R$=8\mathrm{.}314$ Kpa. m$3/$kmol$.$K

$Hf(HCHO)=115,9K\frac{j}{m}ol$

$$Hf$($H$2)=0$ Kj$/$mol

$$Hf$(CH3OH)=201,2$ Kj$/$mol