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

In summary, the problem involves an engine operating with a fuel rich mixture of ethylene and nitrogen being burned over a catalyst to produce carbon dioxide and water vapor. The composition of the reactants and the temperature before and after the catalyst are given. The task is to calculate the moles of air needed for every mole of ethylene. To solve this, the stoichiometric ratio between ethylene and oxygen must first be determined, followed by the ratio of air to fuel.
  • #1
engineer23
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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?
 
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  • #2
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?
 
  • #3


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.
 

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

1. What is a chemical equation?

A chemical equation is a symbolic representation of a chemical reaction, which shows the reactants and products involved in the reaction as well as the relative amounts of each substance.

2. How do I write a chemical equation?

To write a chemical equation, you first need to identify the reactants and products of the reaction. Then, write the chemical formulas for each substance and use the appropriate symbols to indicate the state of each substance (solid, liquid, gas, or aqueous). Finally, balance the equation by making sure that the number of atoms of each element is equal on both sides of the equation.

3. What are coefficients and subscripts in a chemical equation?

Coefficients are the numbers written in front of a chemical formula, which indicate the relative amounts of each substance involved in the reaction. Subscripts are the numbers written below and to the right of an element's symbol in a chemical formula, which indicate the number of atoms of that element in a molecule.

4. How do I know if a chemical equation is balanced?

A chemical equation is balanced when the number of atoms of each element is equal on both sides of the equation. This can be achieved by adjusting the coefficients of the reactants and products until the number of atoms of each element is the same on both sides.

5. Can a chemical equation be changed?

Yes, a chemical equation can be changed by adjusting the coefficients of the reactants and products. However, the number of atoms of each element must remain the same on both sides in order for the equation to be balanced.

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