Equilibrium: why exponents?

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This question has many possible answers, depending on how deep you want to go into the philosophy of chemical thermodynamics.

As a simple response, K values are calculated as ratio of products over reactants. If your equation is

A + B + C => D
then the K is D/ABC

But what if A and B are really the same chemical?

A + A + C => D
then the K is D/AAC

In another words,

2A + C => D
has a K of D/A^2C

The coefficients become exponents because the K calculations involve multiplication and division, not addition and subtraction.


If you want to discuss this further, by all means ask a deeper question. For instance, why are K values based on multiplications and not additions? Or, is there a way to convert from concentration multiplications to additions of something else? I've spent a lot of time pondering these issues.
 
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