Problem $4$: Textbook $10\mathrm{.}4\mathrm{.}4$

$**10\mathrm{.}4\mathrm{.}4.$ The chemist for a gas company finds a gas analyzes $9\mathrm{.}2\%C{O}_2,0\mathrm{.}4\%C_2{H}_4,20\mathrm{.}9\%CO,15\mathrm{.}6\%H_2,1\mathrm{.}9\%C{H}_4,$ and $52\mathrm{.}0\%N_2.$ What should the chemist report as the gross heating value of the gas?

Assume complete oxidation of the components in the gas, except nitrogen, which is treated as inert for fuel.

a$)$ Write and balance the chemical reaction equation $(5$ points$)$

b$)$ Calculate the reaction heat of the fuel in BTU$/$Ibmol and BTU$/$SCF$.$ Note that the specific volume of the gas is $379\mathrm{.}4SC\frac{F}{\text{I}}$bmol. SCF is defined as "gas volume in cubic feet at the standard condition, $T=520R,$ and $p=14\mathrm{.}7$ psia." $(10$ points$)$