Equilibrium occurs when the forward and reverse reaction rates are equal, and catalysts change reaction rates.  So what effect does a catalyst have on a reaction's rate?
 
 

One of the major factors affecting the rate constant (k) for a reaction is activation energy.  Since an equilibrium occurs when two processes are in opposition, there are always two rate constants -- one for the forward, and one for the reverse reaction.  As can be seen in this diagram, the activation energy in the forward (R  P) direction is not the same as the activation energy in the reverse (R  P) direction.  Therefore  kf does not normally equal kr.

The effect of a catalyst is to provide a new pathway that has a lower activation energy (in the diagram the catalyzed pathway is shown in green, and the uncatlayzed activation energies have been slightly dimmed.  The critical point is that the reduction in activation energy is exactly the same for both directions.  A catalyst makes it equally easy for the reaction to go faster in the forward direction, and in the reverse direction.

 
To see what effect a catalyst will have on an equilibrium, load this Excel simulation onto your computer, and then run it.  This simulation calculates and plots both an uncatalyzed and catalyzed reaction at the same time.  Use the simulation¹ to do the following:

1. Observe when equilibrium is achieved in the uncatalyzed reaction.  What is the equilibrium concentration of the cis- and trans-2-butene?  What is the value of the equilibrium constant, K_eq?

2. Add a catalyst that reduces the activation energy by 10 kJ.  Repeat the same observations made in question 1.

3. Repeat, this time adding a catalyst the reduces the activation energy even more.  What are the results?

4. Summarize what the effect of a catalyst is on the time required to reach equilibrium, the value of K_eq, and the equilibrium concentrations.