Question

For an autocatalytic second-order reaction R $\rightarrow$ P, the rate law is
[where v is the rate of the reaction and k is the rate constant]

• A. $v = k [R]$
• B. $v = k [R][P]$
• C. $v = k [R]^2$
• D. $v = k [P]^2$

Hint:

Autocatalysis: product accelerates formation → rate law contains both [R] and [P].

Answer 1

The Correct Option is B

Step 1: Understand autocatalysis.
In an autocatalytic reaction, the product acts as a catalyst for its own formation. Hence, the rate depends not only on the reactant concentration [R] but also on the product concentration [P].
Step 2: Apply second-order kinetics.
A second-order autocatalytic rate law has contributions from both species. Therefore, the reaction rate must be proportional to [R][P], consistent with second-order behavior (1 + 1 order).
Step 3: Conclusion.
Thus, the correct rate law for an autocatalytic second-order reaction is $v = k [R][P]$, which matches option (B).