Methanol may be synthesized from hydro$-$

gen and carbon monoxide in the presence of an

appropriate catalyst.

$CO+2H_{2}C{H}_{3}OH$

If one has a feed stream containing these gases in

stoichiometric proportions $(\frac{H_2}{C}O=2)$ at $200$

atm and $275C,$ determine the effluent composi$-$

tion from the reactor:

$($a$)$ If it operates isothermally and equilibrium

is achieved.

$($b$)$ If it operates adiabatically and equilibrium

is achieved. $($Also determine the effluent

temperature.$)$

Data:

$(1)H^0=-17,530-18\mathrm{.}19T+0\mathrm{.}0141T^2$ for

$H^0$ in calories per gram mole and $T$ in

degrees Kelvin.

$(2)$ Molal heat capacities at constant pressure

$H_2,C_p=6\mathrm{.}65+0\mathrm{.}00070T$

$CO,C_p=6\mathrm{.}89+0\mathrm{.}00038T$

$C{H}_{3}OH,C_p=2\mathrm{.}0+0\mathrm{.}03T$

for $C_p$ in calories per gram mole$-$degree

Kelvin.

$(3)$ Equilibrium constant expressed in terms of

fugacities

$lo{g}_{10}{K}_f=\frac{3835}{T}-9\mathrm{.}150lo{g}_{10}T$

$+3\mathrm{.}08{10}^{-3}T+13\mathrm{.}20$

$(4)$ Note that in part $($b$)$ a trial and error solu$-$

tion is required. $($Hint$.$ The effluent tempera$-$

ture will be close to $700K.)$