Why do copper ions amminate so slowly

The kinetic treatment of multi-step reactions, and the rate-determining step 

Addition of concentrated ammonia to a solution of copper(II) yields a deep-blue solution of [Cu(NH3)4]2+. The balanced reaction is given by 

A quick look at the reaction suggests that the rate of this ammination reaction should be k[Cu2+(aq)][NH3(aq)]4, where the power of 4 derives from the stoichiometry (provided that the reaction as written was the rate-determining step). It would be a fifth-order reaction, and we would expect that doubling the concentration of ammonia would cause the rate to increase 16-fold (because 24 = 16). But the increase in rate is not 16-fold and, as we have just seen, a fifth-order reaction is not likely. 

In fact, the ammination reaction forming [Cu(NH3)4]2+ occurs stepwise, with first one ammonia ligand bonding to the copper ion, then a second, and so forth until the tetra-amminated complex is formed. And if there are four separate reaction steps, then there are four separate kinetic steps - one for each ammination step, with each reaction having its own rate constant k - we call them k(i), k(2), k(3 and k(4. This observation helps explain why the increase in reaction rate is not 16-fold when we double the concentration of ammonia. 

Each step in a multi-step reaction sequence proceeds at a different rate. 

---