Step 1 : A + B → C + E (slow)
Step 2 : B + E → D (fast)
Predict the rate law if step 1 is slow.
A + B → C + E (slow)
Step 2 : B + E → D (fast)
rate = k(A)(B)
To predict the rate law for a reaction, you need to identify the rate-determining step, which is the slowest step in the reaction mechanism. In this case, step 1 is identified as the slow step.
The rate law is an expression that relates the rate of a chemical reaction to the concentrations of reactants. To determine the rate law, you need to examine the stoichiometry of the slow step and determine the rate expression based on the reactant concentrations.
Based on step 1: A + B → C + E (slow)
The stoichiometry of the slow step indicates that the reaction is first order with respect to both reactants, A and B. This means that the rate of the reaction is directly proportional to the concentration of A and B.
Therefore, the rate law for the slow step 1 is:
Rate = k[A][B]
Where k is the rate constant for the slow step.
As the reaction is not happening in one step, it is important to consider the overall reaction rate law. To do that, you need to consider the fast step 2, which follows the slow step.
Step 2: B + E → D (fast)
Since step 2 is fast compared to the slow step, the concentration of the intermediate E will be very low, and it can be assumed that it is in equilibrium with its reactants and products.
As a result, the concentration of E will remain constant throughout the reaction, and it won't affect the rate law.
So, in the case where step 1 is slow, the predicted rate law for the overall reaction is:
Rate = k[A][B]