Consider the reaction:

The rate equation for the forward reaction happens to be:

The rate equation for the reverse reaction (reformation of reactants) is :

As the reaction continues the formation of products is matched by the reformation of reactants. When the forward reaction rate is matched by the reverse reaction rate, the system has attained equilibrium.

Note that in the above graph equilibrium is attained when Rate_(f) = Rate_(r)

Since Rate_(f) = Rate_(r), by substitution the equation becomes:

k_f[NO₂][CO] = k_r[NO][CO₂]. Collecting terms we get

k_r/k_f = [NO][CO₂]/[NO₂][CO] and since the k_f/k_r represents a steady or constant condition the equilibrium constant expression can be developed.

From an instructional perspective, this approach usually is the easiest to begin with when approaching the topic of chemical equilibrium.