Methane Combustion and Chemical Equilibrium

[HinduHammer]

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:

[URL]http://upload.wikimedia.org/wikipedia/en/math/a/e/1/ae1ea56f2e557025e57022730f141861.png[/URL]

[URL]http://upload.wikimedia.org/wikipedia/en/math/2/b/1/2b116a1f13940176246dd9e08a0c0be3.png[/URL]

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.

Thanks for your help!

 

[Borek]

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

 

[HinduHammer]

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.

 

[Borek]

Check if this helps: http://en.wikipedia.org/wiki/ICE_table