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