Acetic acid $($CH$3$COOH$)$ is cracked to produce the intermediate ketene $($CH$2$CO$($g$))$ in a furnace.

CH$3$COOH$($g$)->$ CH$2$CO$($g$)+$ H$2$O $($g$)1$H$$R$(298$K$)=132$ kJ$/$mol

The following side reaction also occurs to an appreciable extent.

CH$3$COOH$($g$)->$ CH$4($g$)+$ CO$2($g$)2$H$$R$(298$K$)=-33\mathrm{.}53$ kJ$/$mol

A conversion of acetic acid is $80\%$ and a fractional yield of ketene is $0\mathrm{.}0722.$ Yield is defined as the mole of ketene formed $/$ the maximum ketene would be obtained when all reactant completely consumed without side reaction.

a$.$ Complete mass balance calculation.

b$.$ Calculate required furnace heating rate for a furnace feed of $100$ mol$/$h acetic acid by using Heat of Reaction Method $.$ The temperature of the feed is $300$C and the temperature of the products is $700$C$.$

Cp Data in J$/$K$,$ T in K

Acetic acid $($CH$3$COOH$($g$))$ Cp$=6\mathrm{.}899+0\mathrm{.}257$ T

Ketene $($CH$2$CO$($g$))$ Cp$=17\mathrm{.}2+0\mathrm{.}123$ T

Metan CH$4($g$)$ Cp$=38\mathrm{.}38-0\mathrm{.}00736$ T

Water H$2$O $($g$)$ Cp$=34-0\mathrm{.}00965$ T

Carbondioxide CO$2($g$)$ Cp$=19+0\mathrm{.}0796$ T