Calculating the equilibrium constants for parallel reactions

Question

So, I am attempting to calculate the equilibrium constant for two separate reactions.

$$\ce{A + B<=>C + D}$$ $$\ce{A + B <=> C + E}$$

I have figured out the final pressures at equilibrium for $\ce{A}$, $\ce{B}$, $\ce{C}$, $\ce{D}$, and $\ce{E}$.

I was wondering if the equilibrium constant is calculated as normal using just the final pressures and molar ratios in the equations, or if the final pressures have to be adjusted somehow to compensate for the fact that the second reaction is also consuming the same products and producing one of the same reactants.

Answer 1

You can combine the two chemical reactions into a single global reaction scheme by adding them: \begin{align} \ce{A + B&<=>C + D}\tag{1}\\ \ce{A + B&<=>C + E}\tag{2} \\ \hline \ce{2A + 2B &<=> 2C + D + E} \tag{Global} \end{align} and the equilibrium constant for this overall reaction scheme is equal to the products of the two equilibrium constants: \begin{align} K_\mathrm{eq,global} &= K_\mathrm{eq,1} K_\mathrm{eq,2} \\ &= \frac{\ce{[C]^2[D][E]} } {\ce{[A]^2[B]^2}} \end{align} (where $\ce{[i]}$ denotes either molar concentration or partial pressure of component i). You do not need to adjust the final total pressure or mole amounts.