Gas containing $50\%$ methane $(C{H}_4)$ and $50\%$ propane $(C_3{H}_8)$ is fed to a boiler where it is burnt with $60\%$ excess air. Gas is supplied to the boiler at $20C$ and the combustion air enters at a temperature of $200C.$ The boiler stack temperature is $420C.$ The boiler is used to evaporate $100C$ liquid water to $150C$ steam. The standard state of reactants and products is gaseous.

$($a$)$ Draw a schematic diagram of the process including the balanced combustion reactions.

$($b$)$ Calculate the heat of combustion for both methane and propane.

$($c$)$ Use tables to show the mass balance and energy balance of the combustion reactions taking place inside the boiler.

$($d$)$ Determine the mass of steam produced for each mole of gas fed to the boiler. Write down clearly all the assumptions used.

NOTE:

Relevant Data:

Air consists of $21\%O_2$ and $79\%N_2$ on a volume basis at $30C$

$C_p(O_2)=33Jmo{l}^{-1}{K}^{-1}$

$C_p(N_2)=31Jmo{l}^{-1}{K}^{-1}$

$C_p(H_{2}O)=35Jmo{l}^{-1}{K}^{-1}$

$C_p(C{O}_2)=39Jmo{l}^{-1}{K}^{-1}$

$C_p(C{H}_4)=36Jmo{l}^{-1}{K}^{-1}$

$C_p(C_3{H}_8)=74Jmo{l}^{-1}{K}^{-1}$

Latent heat of vaporisation of water at $100C=2257kJk{g}^{-1}$

Molar mass of water $18gmo{l}^{-1}$

Energies of formations refer to each mole formed at a datum temperature of $20C.$

$H(C{H}_4)=-75kJmo{l}^{-1}$

$H(C_3{H}_8)=-104kJmo{l}^{-1}$

$H{o}_f(C{O}_2)=-394kJmo{l}^{-1}$

$H(H_{2}O)=-242kJmo{l}^{-1}$