QUESTION $1$

$5k\frac{g}{s}$ of methane is burned in a furnace using pure stream of $5\%$ excess oxygen according to the reaction provided to produce $C{O}_2$ and $H_{2}O.$ The methane is completely consumed, and both it and the oxygen are fed in at $300$ K $,$ and all the products leave the furnace at $2073\mathrm{.}15$ K $.$

$C{H}_4+2O_{2}C{O}_2+2H_{2}O$

$1\mathrm{.}1$ Determine the standard heat of reaction, where both the reactants and products leave at $298\mathrm{.}15$ K $?$

$1\mathrm{.}2$ What is the overall heat of reaction if the reactants and products leave the furnace at the conditions initially specified?

DATA:

Molar mass $(C{H}_4)=16\mathrm{.}04\frac{g}{m}ol$;

$CP(O_2)=31{10}^3\frac{J}{k}$mol.$K$;

$CP(C{H}_4)=[85\mathrm{.}8127+11\mathrm{.}26467T]$;

$CP(H_{2}O)=75429\mathrm{.}64\frac{J}{k}$mol. $K$;

$CP(C{O}_2)=36{10}^3\frac{J}{k}$mol. $K$;

$H_{f}CH{H}_{4}O=-74\mathrm{.}87{10}^6\frac{J}{k}$mol;

$H_f{H}_{2}O=-241\mathrm{.}83{10}^6\frac{J}{k}$mol;

$H{f}_{f}C{O}_2=-395\mathrm{.}52{10}^6\frac{J}{k}$mol.

PLEASE EXPLAIN IF I MUST USE INTEGRATION AND WHY OR WHY NOT. SOME PEOPLE ARE USING INTEGRATION AND OTHERS AREN'T.