What is the Default Equilibrium Constant for Chemical Reactions?

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Nikitin
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Let's say we have the reaction 2H2 + O2 -> 2H2O. The equilibrium constant for this reaction then is: K1=[H2O]2]/([H2]2*[O2]).

But the reaction can also be written as H2 + 0.5O2 -> H2O, and with the equilibrium constant becoming K2 = [H2O]1]/([H2]1*[O2]0.5)=K10.5

This phenomena with the coefficients goes generally for all reactions. So, what K is the default one? Is it the one where most coefficients are 1 (K2), or is it when all coefficients are at their smallest, while remaining integers (K1)? Or something else?
 
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There is no general default. Usually you have to give the reaction equation along with the equilibrium constant.
 
Most often you will see the equilibrium constant for the properly balanced reaction equation - that is, with all coefficients being the smallest possible integer numbers. So when there is no other information I would assume value given is K1. Serious sources of equilibrium constants usually define the convention used, to make the information unambiguous.

Which basically boils down to what DrDu wrote earlier.