For the reaction........
A+BrightleftharpoonsC+D
There is a "rate forward", k_f[A][B], where k_f is some constant....
And a "rate backwards", k_r[C][D], where k_r is some other constant....
Now, by definition, a condition of "chemical equilibrium" occurs not when chemical change ceases, but when there is equality of forward and reverse rates, and thus.........
"rate backwards", k_r[C][D]-="rate forwards", k_f[A][B]. And so we take the quotient......
k_r/k_f=([C][D])/([A][B])
We more commonly call the quotient k_r/k_f, K_c, the thermodynamic equilibrium constant.