Derivation of the Equilibrium Constant

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Discussion Overview

The discussion focuses on the derivation of the equilibrium constant from Gibbs Free Energy, specifically examining the mathematical expressions involved and their interpretations. Participants are exploring the meaning of certain terms and the assumptions behind them.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the origin of the equation \(\Sigma v_{j} A_{j} = 0\), seeking clarification on what it sums and whether it assumes the products side is negative.
  • Another participant suggests that the equation represents mass conservation and agrees that the products are negative.
  • A further inquiry is made regarding why the summation only goes up to \(n\), with a participant expressing confusion over the inclusion of additional products in the derivation.
  • Another participant asserts that the summation includes all \(j\), challenging the previous assumption about the limit of the summation.

Areas of Agreement / Disagreement

Participants express differing interpretations of the summation in the equation, with some agreeing on the concept of mass conservation while others question the limits of the summation. The discussion remains unresolved regarding the assumptions and implications of the equation.

Contextual Notes

There are limitations in the clarity of the assumptions made in the derivation, particularly regarding the definitions of terms and the scope of the summation. The discussion does not resolve these ambiguities.

gsingh2011
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I'm trying to understand this: http://en.wikipedia.org/wiki/Equilibrium_constant#Derivation_from_Gibbs_Free_Energy
And there are few steps that I don't get. My first question is probably a stupid one, but where does the [tex]\Sigma[/tex]v[tex]_{j}[/tex]A[tex]_{j}[/tex]=0 come from? What exactly is it summing up, the number of atoms? Are you assuming that the products side is negative? (Because I don't see how else you would get zero) And why does it only go up to n?

I'll ask my other questions after I get some replies because it's possible I'll figure them out after I read the replies.
 
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gsingh2011 said:
where does the [tex]\Sigma[/tex]v[tex]_{j}[/tex]A[tex]_{j}[/tex]=0 come from? What exactly is it summing up, the number of atoms? Are you assuming that the products side is negative? (Because I don't see how else you would get zero) And why does it only go up to n?

My guess is it is just a mass conservation, and yes, products are negative.
 
Borek said:
My guess is it is just a mass conservation, and yes, products are negative.

Ok, but why does it only sum up to n? The first equation in the derivation shows the first product being n but then shows more products after that. If it was mass conservation, wouldn't it have to sum passed n?
 
Where does it sum only to n? It sums for all j.
 

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