# Simultaneous equilibria

## Rephrasing:

The following reactions are a small example of my big system

$$(1)\ \ce{A + B <=> AB}$$ $$(2)\ \ce{AB -> CB}$$ $$(3)\ \ce{A -> C}$$ $$(4)\ \ce{C + B <=> CB}$$

with

$$\ce{\frac{[AB]}{[A][B]}} = 100 = K_e$$ $$\ce{\frac{[CB]}{[C][B]}} = 100 = K_e$$

I know the rate constants for reactions (2) and (3), and I know that $$\ce{[A] + [AB] + [C] + [CB] = T}$$

with T = some constant.

Now, although there is a fast equilibrium between $\ce{A + B}$ and $\ce{AB}$, and between $\ce{C + B}$ and $\ce{CB}$, I want to know how the concentration of each form changes with time.

But I dont know how to write down the differential equations of the system and include the equilibrium constant. Could someone please help me out? My only problem is how to include $K_e$ in the system of ordinary differential equations.

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Hmm, it's really hard to understand what you're asking here. COuld you edit your post and explain what your variables are? (eg what $k_8,k_9$ are). Also, what are you trying to find? (Maybe give a sample problem statement?) It's really confusing in its current form :/ –  ManishEarth Nov 30 '12 at 14:39
I agree with Manishearth. The best that can be said is that all equilibria must be simultaneously satisfied at equilibrium. –  Paul J. Gans Dec 5 '12 at 2:01
Thanks guys! I rephrased the problem! Thanks so much for all the help! –  Sosi Dec 5 '12 at 15:23
@SosiKun: Much better! Now its actually answerable... Hopefully someone will try soon :) –  ManishEarth Dec 5 '12 at 16:44
Yes, it was too confusing before! I'm sorry! thanks! –  Sosi Dec 5 '12 at 16:46