# Methane Combustion and Chemical Equilibrium

This may belong in the Chemistry section but this is a problem from my Thermodynamics class, so I'll post it here and then move to the Chem section if need be.

## Homework Statement

Methane (CH4) is the principal constituent of natural gas and is often used to represent natural gas. Consider the operation of a natural gas fired water heater operating with 15% excess air. Assuming the fuel to be CH4 and the products of the reaction to be CO2, H2O, N2, O2 , and CO, calculate the concentration (percent by volume) of each product if the temperature in the products is 1000K.

## Homework Equations

CH4 + (a)(m)(O2 + 3.76N2 → bCO2 + cH2O + dN2 + eO2 + fCO

2CO2 $\Leftrightarrow$ 2CO + O2

where:
a=moles for stoichiometric combustion
m=excess air ratio (1.15 in this case)
b,c,d,e,f = moles of products

## The Attempt at a Solution

To balance equation:

From combustion reaction:
C: 1 = b+f
H: 4 = 2; c=2
O: 2*a*1.15 = c+2e+f
N: 3.76*1.15*a*2 = 2d

From dissociation reaction:
2b = 2f + e (2 CO2 makes 2CO and 1O2)

I still only have 5 equations and 6 unknowns.

There is also the equilibrium constant K that we are given a table of:

I know how to solve the problem when CO is not created. It becomes a much simpler problem. However, when CO enters the problem, I end up with not enough equations.

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Borek
Mentor
Are you given K value? Look to me like it can be just a stoichiometry problem, where you are to assume reaction proceeded to the end.

Alternatively, the only equilibrium to be taken into account is 2CO + O2 <-> 2CO2

Yes, we are given a K value. However, we haven't been taught this type of Chemistry yet, so I'm having difficulty solving the K equation.

I know that the equation for 2CO + O2 <-> 2CO2 is used to find concentrations of the substances, but I'm not exactly sure how...

Edit: K = 3.68 x 10^-21

After I set up K = ((Y_CO)^2 x (Y_O2))/ (Y_CO2)^2 I get stuck on solving for the terms. I assume Y_CO2 = 1 because it is the only term on the right side. However, I am unsure on how to find Y_CO and Y_O2.

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