Why does Kequilibrium increase 4x forward when 2 product species are the same?

Posted on 2016-05-04 18:43:00 in Chemistry by BOBY

Say I have a polyatomic molecule XY2, which would dissociate to X+2 and 2Y+. 
In order to calculate the Keq, I would need to square the concentration of XY2 and then multiply it by 4. 
4x^3 where x is the moles of the polyatomic reactant XY2. 

In other words: 
Keq=[X+2][2Y-]^2/[XY2] 

Now, say instead of 2 Y, I swapped in a very similar molecule Z in place of 1 of the Y, so my polyatomic molecule would now be XYZ. The Keq for that would be: 

Keq=[X+2][Y-][Z-]/[XYZ] 

but now since we don't have any 'twin' species, (ie no 2Y but 1Y and 1Z), the Keq =x^3. 

Now my question is, why does the Keq of the molecule with two 'twin' species (XY2) always 4 times more product favored than XYZ, even though they both are one mole of reactant dissociating into 3 moles of reactant. Keq=4x^3 vs Keq=x^3 

How does the system 'know' that 2 of the 3 species formed are the same, and thus the reaction should be 4x more in the forward direction? 

I hope I'm making sense!

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