Is My Chemical Equation for Fuel-Rich Ethylene Combustion Correct?

[engineer23]

Homework Statement

An engine is operated slightly fuel rich (phi>1). Ethylene (C2H4) and inert nitrogen (N2) are the reactants and there are 40 mol of nitrogen for every mol of ethylene. The hydrocarbons are burned over a catalyst and converted to carbon dioxide (CO2) and water vapor (H20) only. Ambient air at 298 K with a composition of 1 mol of oxygen to 4 mol of nitrogen (O2 + 4N2) is injected before the catalyst. The catalyst is maintained at 1000 K. The temperature before the injection of the catalyst is 400 K. Calculate moles of air to moles of ethylene.

Homework Equations

C2H4 + 40 N2 + (a/phi) (O2 + 4N2) --> b CO2 + c H20 (gas) + d N2, where phi is the equivalence ratio and a, b, c, and d are stoichiometric coefficients

Hr = Hp

The Attempt at a Solution

For the equation I have written in (2), should O2 be included in the products? Should N2 be included in the products? I think if I can write the equation correctly, I know how to use mass balance and Hr = Hp to solve for the stoichiometric coefficient of air.

So my major question is, is my chemical equation right? If not, how do I correct it?

 

[chemisttree]

All you need to start is to determine the stoichiometric ratio between pure ethylene and pure oxygen. Write that equation first. Next you will determine the ratio of air (oxygen plus nitrogen) to fuel (ethylene plus nitrogen).

Your problem gives you the information that the fuel is composed of a ratio of 40 moles Nitrogen to 1 mole of ethylene... or that ethylene is 1/41 parts of the fuel gas composition. Likewise the air contains 1 mole of oxygen (as O2) to 5 moles of air (oxygen plus nitrogen) or is 1/5 parts of the air composition.

Can you take it from here?

 

[Blueshift5]

Your chemical equation is close, but there are a few corrections that need to be made. First, the reactants should be C2H4, N2, and O2, not just ethylene and nitrogen. Second, the products should include only CO2, H2O, and N2, as the inert nitrogen is not involved in the reaction. Third, the number of moles of O2 in the reactants should be (a/phi), not just a. Finally, the stoichiometric coefficients for N2 and O2 should be equal, as they are both inert and do not participate in the reaction. The corrected equation would be:

C2H4 + 40 N2 + (a/phi) O2 --> b CO2 + c H2O + d N2

To solve for the stoichiometric coefficient of air, you can use the equation for heat of reaction (Hr) and heat of formation (Hp). Set the heat of reaction equal to the heat of formation of the products minus the heat of formation of the reactants. Then, solve for the stoichiometric coefficient of air (a/phi). Once you have that, you can solve for the moles of air to moles of ethylene ratio.