$7.$ Acetic acid $($CH$-$COOH$)$ is cracked to produce the intermediate ketene $($CH$-$CO$($g$)$ in a furnace. CH$,$COOH$($g$)-$ CH CO$($g$)+$ H$20(8))$ AH$(298$K$)-132$ kJ$/$mol $+$ The following side reaction also occurs to an appreciable extent CH$,$COOH$($g$)-$CH $(8)+$ CO$2(8)$ C AH$$x$(298$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 $300\backslash$deg C and the temperature of the products is $700\backslash$deg C$.$ C$.$ Data in J$/$K Tin K Acetic acid $($CH$3$COOH$(8))$ Cp$6\mathrm{.}899+0\mathrm{.}257$ T Ketene $($CH$3$COg$))$ Cp $17\mathrm{.}2+0\mathrm{.}123$T Metan CH $(8)$ Cp $38\mathrm{.}38-0\mathrm{.}00736$ T Water H$20(8)$ Cp $34-0\mathrm{.}00965$ T Carbondioxide CO$2($g$)$ Cp $19+0\mathrm{.}0796$ T