Question

Michaelis and Menten derived their rate law by assuming a rapid pre-equilibrium
of E, S, and ES.

a) Derive the rate law in this manner: pre-equilibrium

b) Identify the conditions under which it becomes the same as that based on the steady·
state approximation.

Answer 1

The rapid equilibrium that Michaelis and Menten considered during their Enzyme Kinetic model,the following equilibrium was considered-

Let's now come to the Steady-State approximation. Here we consider,the concentration of the intermediate in a multistep reaction doesn't chnage with time i.e. .Uning this concept,we now derive the rate law of the above equilibrium-

Now compare the two equations i.e equation 5 and eqn 7. The difference is in the expression of rate constant which is oversimplified in equation 5.So, the equation 5 can also be alike equation 7 if we did not impose the condition that " species 'E' 'S' and 'ES' are considered to be in rapid equilibrium during the entire course of reaction" i.e the Pre-equilibrium concept has to be lifted for the intermediate. The only option was then that the intermediate concentration is constant which is the Steady-Stare approximation itself.