Generally in a multistep reaction, the slowest step will determine the overall reaction rate law. Why? That can be interpreted as bottle-neck effect. For example, if you pour soda from a plastic Pepsi bottle to a cup, the rate/speed that the soda is coming out from the bottle is determined by the size of the opening of the bottle. No matter how fast the soda inside the bottle can move, it will eventually be slowed down by the small opening of the bottle. And this bottle-neck effect applies to multistep reaction as well. No matter how fast the other sub-reactions in the multistep reaction can react, it will be slowed down by the slowest step.

            Let’s do a sample question. Consider the following multistep reaction:

A + B --> AB (Fast Reaction)

AB + B --> AB₂ (Slowest Reaction)

AB₂ + B --> AB₃ (Very Fast Reaction)

Overall Reaction: A + 3B --> AB₃

Based on this multistep reaction, determine the rate law for the overall reaction.

 

Solution and Analysis:

As I said before, the overall reaction is determined by the slowest reaction, so that will be AB+B --> AB₂. For the other two reactions, one is fast, the other is very fast, but they don’t matter because they are not the slowest reaction.

So now the rate law for the overall reaction will be the same as the rate law of the slowest reaction and it will be: k[AB][B]

However, for the rate law of the overall reaction, we cannot include intermediate product (that is AB in this case) in the rate law. Therefore we are going to replace the AB according to the rate law of the first reaction A+B àAB (Rate Law for this is k[A][B] and it equals k[AB]. So in the rate law for the overall reaction we can substitute [AB] with [A][B], so we get k[A][B][B] and the final answer will be k[A][B]²

 

--Jason