# Derivation of equilibrium constant [duplicate]

In general chemistry, we learn that the equilibrium constant, defined in terms of activities, for the reaction

$$\ce{aA + bB -> cD + dD}$$

is given by

$$K_\mathrm{eq} = \frac{(\ce{C})^c(\ce{D})^d}{(\ce{A})^a(\ce{B})^a}$$

But I can't find any explanation as to why stoichiometric coefficients should be exponentiated rather than appearing as coefficients in the equilibrium expression or something else.

• This question has been asked a number of times before, please see: chemistry.stackexchange.com/questions/6924/… chemistry.stackexchange.com/questions/14836/… – Buck Thorn Apr 7 '19 at 5:19
• There are indeed alot of answers to this question. In my opinion... ignore the answers that use rate constants. Thermo does not care about time. – B. Kelly Apr 7 '19 at 5:23
• @CharlieCrown True that thermo does not care about time, but if one is looking at relative rate constants, the time factor cancels, so there's no reason to ignore those answers. And I think many find the rate equation arguments more intuitive and easier to understand than the stat mech multiplicative possible states derivation. – Andrew Apr 7 '19 at 11:41
• @Andrew I don't think anything makes more sense than equivalency of chemical potentials :) – B. Kelly Apr 7 '19 at 16:29