An unknown paraffinic hydrocarbon is defined by the chemical formula C_xH_2x.2. The paraffin is burned with air, and there is no CO in the combustion products.

(a) Use a degree-of-freedom analysis to determine how many variables must be specified to determine the flow rates of all components entering and leaving the combustion unit. Express the fraction excess air as y and write elemental balances in terms of x, y, and the molar flow rate of C_xH_2x.2.

(b) Calculate the molar composition of the combustion product gas in terms of x for each of the following three cases: (i) theoretical air supplied (y = 0), 100% conversion of the paraffin; (ii) 20% excess air (y = 0.2), 100% conversion of the paraffin; (iii) 20% excess air, 90% conversion of the paraffin.