In class we discussed stoichiometric (ideal) combustion of hydrocarbons in ideal dry air, and introduced the equivalence ratio Φ. Consider the combustion of hydrocarbon CxHy, where x and y are known for a given hydrocarbon (e.g., for methane, CH4, x = 1, y = 4). The general equation for non-ideal combustion of hydrocarbon CxHy is CxHy +a(O2+3.76N2) = bCO2+cH2O+dN2 +eCO+fO2 +trace where molar coefficients a, b, c, d, e, and f need to be calculated to balance the equation, and "trace" means small quantities of other pollutants, such as alcohols, NOx, aldehydes, etc.

(a) Generate algebraic expressions for coefficients a, b, c, d, e, and f as functions of each other and of (known) x and y as far as possible. In particular, provide equations for b, c, d, and f as functions of x, y, a, and e. Hint: You will not be able to solve explicitly for all the coefficients, since there are 6 unknowns and only 4 elements in the equation with which to generate expressions (C, H, O, and N).

(b) Consider the stoichiometric case in which there is no excess air, a = astoich, and there is no CO or excess air on the RHS (e = f = 0). Generate expressions for coefficients a (a = astoich), b, c, and d as functions of only x and y.

(c) Gasoline is mostly octane, C8H18. For octane, calculate the molar coefficients and write the final chemical equation for the stoichiometric case.

(d) Now consider combustion of octane with Φ = 0.833333... Also, molar coefficient e is known to be 2 in this particular case. Calculate the molar coefficients and write the final chemical equation for this case. Is this rich or lean combustion?

(e) Calculate the mol fraction of CO (in PPM) of the exhaust gas products of the case of Part (d).