# Chemical equilibrium for simultaneous dissociation reactions

While calculating the adiabatic flame temperature for the following combustion reaction:

$$\ce{\Phi\, C2H6 + 3.5\,(O2 + 3.76\,N2) -> a\,CO2 + b\,CO + d\,H2O + e\,H2 + f\,O2 + g\,N2}$$

Where $\Phi$ is the equivalence ratio.

To determine the product composition ratios $a$, $b$, $d$, $e$, $f$ I need to make mass balance on $\ce{C}$, $\ce{O}$ and $\ce{H}$ and then use two $K_{p}$ (Chemical equilibrium constant) relations. Then solve this system of equation simultaneously.

My question is about the elementary reactions of dissociation I should use to apply $K_{p}$ equations, As I could have the following scenarios happening (regarding dissociation): \begin{align} \ce{CO + H2O &<=> CO2 + H2}\\ \ce{CO2 &<=> CO + $0.5$\,O2}\\ \ce{H2O &<=> H2 + $0.5$\,O2}\\ \end{align}

I only need two equations for $K_{p}$ which two should I use and why?

## 2 Answers

Short answer (After some trials): It does not matter which dissociation reaction you use, The system of equation will be solved anyway since the reactions are not independent.

However, using the first reaction as a dissociation mechanism would generate a Kp equation that's a lot easier to solve than the others.

• This question was flagged very low quality. I think it is okay, since it answers the premise. However, could you explain that a little more, I cannot really grasp what you are trying to tell us here. You could at the same time also accept your answer and make this question solved this way. – Martin - マーチン Apr 24 '15 at 6:52

We should use only those equations which are linearly independent. For example, of the three equations specified eqn.(1) can be written by linearly combining eqn(2) and eqn(3). So use eqn (2) and (3) only.