How Can I Solve for the Equilibrium Constants in These Equations?

[Air]

Homework Statement
With the 5 equations, the equilibrium contants can be calculated at the bottom. (See image)

My complication
I am aware that $X = 200$ thus that value remains at that. Also, From the fourth equation $K_{out}$ = $Cl_{out}$. But, I cannot seem to work out the values. If not simple algebra, what am I missing?

 

[Borek]

Won't hurt if you would explain what is the question that you are solving, at the moment you just posted a bunch of equations describing some undefined system.

 

[Air]

From this, finding the concentrations at equilibrium.

 

[Air]

I understand how the equations are set up but I can't seem to solve the maths to get the equilibrium constants. Is there something I am missing? Like I said, I am aware that $X = 200$ thus that value remains at that. Also, From the fourth equation $K_{out}$ = $Cl_{out}$.

 

[Borek]

Simple algebra.

My bet is your problem is related to the fact you have too many equations - they are not all independent, which makes you getting 0=0 type result.

 

[epenguin]

By equilibrium constants are we to guess that the protein forms complexes we might call XCl^- and XCl₂ in non-coperative fashion so it is characterised by a single equilibrium constant which it is required to calculate from the data?

I think you had better cite the entire question.

 

[Air]

By equilibrium constants are we to guess that the protein forms complexes we might call XCl^- and XCl₂ in non-coperative fashion so it is characterised by a single equilibrium constant which it is required to calculate from the data?

I think you had better cite the entire question.

The whole question is posted in post number 3. https://www.physicsforums.com/showpost.php?p=4410136&postcount=3

 

[Borek]

You do realize there is no problem with solving the question using your approach and the simple algebra, it is just a matter of ignoring superfluous information?

 

[Air]

You do realize there is no problem with solving the question using your approach and the simple algebra, it is just a matter of ignoring superfluous information?

When I substitute into each other, they all just cancel out to 0=0.

 

[Borek]

Which is exactly what I wrote in the post #5 - have you read it? That's because the linear equations are not independent. Ignore one of the linear ones and you will get the correct answer.