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.
