[Big-Daddy]

I have an isotopic exchange equilibrium,

(¹²C)₂(¹³C)₂H₁₀ + (¹²C)(¹³C)₃H₁₀  (¹²C)₃(¹³C)H₁₀ + (¹³C)₄H₁₀

I tried working out K for this by using natural abundances, and ended up with 1/6. But is this right? It forces a certain value of ΔG° on the reaction...

[Corribus]

I tried working out K for this by using natural abundances

Elaborate, please.

[Big-Daddy]

If we take the case

(³⁵Cl)₂ + (³⁷Cl)₂  2 ³⁵Cl³⁷Cl

And let x be the natural abundance of ³⁵Cl and y of ³⁷Cl. Then the fractional abundances of these isotopologues in nature's equilibrium is x^2 for the first reactant listed, y^2 for the product and 2! * x * y (2! due to permutations) for the product.

Then K = (2! * x * y)^2 / (x^2 * y^2) which as you see reduces to K = (2!)^2 = 4.

Firstly I'd like to know if I've applied the same method correctly to this new equilibrium. Secondly I'm wondering whether this is actually a robust way of working out something like K which leads to ΔG° for this reaction, and if not what the problem is.

[Corribus]

If you took pure ³⁵Cl and pure ³⁷Cl and mix them together in a sealed container, what makes you think that the amount of product has anything to do with what the natural abundances of these isotopes are?

[Big-Daddy]

Well, nature should be at or extremely close to equilibrium, right? Why not?

We discussed this problem once before, with respect to the Cl isotopic exchange. Link is here: http://www.chemicalforums.com/index.php?topic=67802.15 Wherein it was noted I should have pointed out that I'm using natural abundances (have done so here). There was a point made that the chemical equivalence of the isotopologues leads to 0 enthalpy changes (which is relevant for this but probably not necessary if you use natural abundances to calculate K as I have).

Can the same logic be safely extended to this larger/more complicated equilibrium?

[curiouscat]

I can't see how natural abundances have anything to do with this.

I could be wrong.

[Corribus]

Me neither. Natural abundances are the products of countless chemical and physical equilibria. I'm not sure how (and why) you'd try to pigeonhole that into determining the thermodynamics and kinetics for a single reaction. It really makes no sense to me. And we've apparently been down this road before, which I had forgotten.

EDIT: And most importantly, the other thread should have established that the equilibrium constant (standard thermodynamic properties) for a process do NOT depend on the amount of reactants or products available at the starting point. 

[curiouscat]

Me neither. Natural abundances are the products of countless chemical and physical equilibria. I'm not sure how (and why) you'd try to pigeonhole that into determining the thermodynamics and kinetics for a single reaction. It really makes no sense to me. And we've apparently been down this road before, which I had forgotten.

EDIT: And most importantly, the other thread should have established that the equilibrium constant (standard thermodynamic properties) for a process do NOT depend on the amount of reactants or products available at the starting point.

I hadn't forgotten. This felt like deja vu.

I feel bad because you had given some pretty neat and detailed explanations clarifying this the last time. This seems a repeat all over.

[Big-Daddy]

I haven't forgotten. I took careful notes the last time.

As curiouscat acknowledged in Reply #15, it is accurate to use natural abundances and say K=4 for the chlorine exchange equilibrium in that thread.

Why would that not be the case for this equilibrium, when it was for the Cl one?

And most importantly, the other thread should have established that the equilibrium constant (standard thermodynamic properties) for a process do NOT depend on the amount of reactants or products available at the starting point.

Yes but nature is at equilibrium presumably, not at a starting point?

If not then why is the logic correct/why did you (plural) accept the logic for the chlorine example? I quote curiouscat: "I just read the IChO problem. Nothing wrong with that problem at all." when the answer is K_x=4 for the chlorine example as deduced from natural abundances?

Surely K cannot take a different value in nature as opposed to in the lab, if we assume the same average temperature.