Butane is burned with air. No carbon monoxide is present in the combustion products.

a$.$ Use the degree$-$of$-$freedom analysis to prove that if the percentage excess air and the percentage conversion of butane are specified, the molar composition of the product gas can be determined.

b$.$ Calculate the molar composition of the product gas for each of the following three cases:

i$.$ Theoretical air supplied and $100\%$ conversion of butane

ii$.20\%$ excess air and $100\%$ conversion of butane.

iii. $20\%$ excess air, $90\%$ conversion of butane.