$1$ mole of pure H$2$O is fed into a porous solid carbon bed at $1000$ K and $0\mathrm{.}5$ bar to produce H$2$ and CO gases. H$2$O$($g$)+$ C $($s$)->$H$2($g$)+$ CO$($g$)$ Assuming that DHrxn does not change with temperature, answer the following questions: a$)$ At equilibrium, find the amount of H$2$ produced per mole of supplied steam? b$)$ If the flow rate of steam entering the reactor is $2$ mol$/$s$,$ how much heat must be added and removed to keep the system at $1000$ K$?$