All The Stuff We Do with Equilibrium Constants

[modulus]

NONE OF IT MAKES ANY SENSE!

For example:

1. If we divide the molar coefficients all by 2, then we raise the original equilibrium constant by the same power (0.5).
2. If we write the reaction in the reverse, then the new equilibrium constant is the multiplicative inverse of the original constant.

But the problem with all of this is that, if, suppose I take some fixed amounts of the substances that will eventually form an equilibrium mixture (let's suppose that I take 2 moles of hydrogen gas, 1 mole of nitrogen gas, and 1 mole of ammonia gas; note that all of these numbers are completely random; nitrogen and hydrogen will form ammonia, and ammonia will dissociate into hydrogen and nitrogen) in a closed container. Eventually all the components will even out (equilibrium will be established).

And then, suppose, according to the final concentrations in the equilibrium mixture, I calculate the equilibrium constant for the reaction. Now this is where my dilemma begins: how am I to compare my experimental value with other values people have determined? It would be impossible, because, while one person may have determined it with some molar coefficients (1, 3, and 2, suppose), another person may have determined it using doubled molar coefficients (2, 6, and 4). And another person may have determined a value from an equation written in reverse.

The thing is, that the gases reacting in the container wouldn't 'know' what chemical equation we are writing out to determine the constant. So how are the such rules justified??

 

[Borek]

It is a matter of convention.

Stoichiometric coefficients in the 'correct' reaction equation should be the smallest possible integers. As long as you follow this rule your reaction is unambiguous - so the equilibrium constant is unambiguous as well. Whenever you think there is a place for confusion - just write the reaction for which you list the equilibrium constant.

 

[modulus]

Thank you.
That explains the problem with stoichiometric coefficients, but, now I still don't understand how we are to decide which is the 'forward' reaction and which is 'backward'. We could write the equilibrium reaction in any direction, and get different constants. So, what about that?

 

[Borek]

Still a matter of convention - and still it needs clarification whenever there is a chance of confusion. If you are given dissociation constant, it always means H⁺ is between products. If you are given X synthesis constant - X is between products. And so on.

Note: you are perfectly right that there is a place for ambiguity here. It is up to the people publishing/giving equilibrium constants to list them in a way that avoids any ambiguity.