Question #44793

Consider the complex consecutive first-order reaction sequence occurring in a closed vessel at $T = 298\text{ K}$:

\ce{A(g) ->[k_1] I(g) ->[k_2] P(g)}

The Arrhenius parameters for the two steps are such that their pre-exponential factors are equal ($A_1 = A_2$), and the difference in their activation energies is $E_{a1} - E_{a2} = 2.303 RT$.

A student attempts to apply the Steady-State Approximation (SSA) to the intermediate $I$. However, recognizing the 'induction period' before SSA becomes strictly valid, the student measures the instantaneous rate of formation of product $P$ at the exact moment $t = t_{max}$, where the concentration of intermediate $I$ reaches its absolute maximum.

If $R_{P, max}$ is the instantaneous rate of formation of $P$ at $t_{max}$, and $R_{A, 0}$ is the initial instantaneous rate of disappearance of $A$ at $t=0$, determine the exact ratio $\frac{R_{P, max}}{R_{A, 0}}$.