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.