Acetic acid $(C{H}_3\frac{C}{O}OH)$ is cracked to produce the intermediate ketene $(C{H}_{2}CO(g))$ in a furnace.

$C{H}_3\frac{C}{O}OH(g)C{H}_{2}CO(g)+H_{2}O(g),{}_1,H_R^o(298K)=132k\frac{J}{m}ol$

The following side reaction also occurs to an appreciable extent.

$C{H}_3\frac{C}{O}OH(g)C{H}_4(g)+C{O}_2(g),{}_2,H_R^o(298K)=-33\mathrm{.}53k\frac{J}{m}ol$

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 $100mo\frac{l}{h}$ acetic acid by using Heat of Reaction Method $.$ The temperature of the feed is $300C$ and the temperature of the products is $700C.$

$C_p$ Data in $\frac{J}{K},T$ in $K$

Acetic acid $(C{H}_3\frac{C}{O}OH(g))C_p=6\mathrm{.}899+0\mathrm{.}257T$

Ketene $(C{H}_{2}CO(g))C_p=17\mathrm{.}2+0\mathrm{.}123T$

Metan $C{H}_4(g),C_p=38\mathrm{.}38-0\mathrm{.}00736T$

Water $H_{2}O(g),C_p=34-0\mathrm{.}00965T$

Carbondioxide $C{O}_2(g),C_p=19+0\mathrm{.}0796T$