[Shagbark]

Last night I went to the bookstore and went thru an enormous pile of textbooks, none of which had the answer to this simple problem:

Suppose I have 2 equilibrium reactions in solution:
A + B <-> X
A + C <->Y

I know everything about these reactions in general: their equilibrium constants, free energy changes, enthalpy changes, etc.  I also know the starting concentrations of all the reactants (starting concentation of products is zero).

How can I compute the equilibrium concentrations?
Or even just the relative concentrations of X and Y at equilibrium?

[Borek]

It's about pH, but first paragraph contains the most general answer to your question:

http://www.chembuddy.com/?left=pH-calculation&right=general-pH-calculation

[Yggdrasil]

Are there any simplifying assumptions that can be made?  (I assume this is relating to your other posts on the forum) For example, can you assume that [A] >> , [C] so that [A] remains approximately constant throughout the reaction?

[lavoisier]

If you can assume that the reactions are at equilibrium, you don't need any information about their kinetics. You have the two K's and the initial conditions --> you have the answer.

The method is always the same (I guess I already answered you on a similar problem. Have you seen my reply?). Write the mass conservation laws for all the compounds you have:

[A]0 = [A] - [X] - [Y]
0 = - [X]
[C]0 = [C] - [Y]

(for X and Y you would have identities, so you don't consider them).

Then you write you eq. constants:

K1 = [X]/([A])
K2 = [Y]/([A][C])

You have a system of 5 independent equations in 5 variables (the equilibrium concentrations of A, B, C, X, Y). You solve it and you have the result. It's just algebra.
The real issue is that you get a third order algebraic equation, therefore you may want to use a PC to compute the roots.