Consider a complex reaction taking place in three steps with rate constants k₁$k_{1}$ , k₂$k_{2}$ and k₃$k_{3}$ respectively. The overall rate constant k is given by the expression k = k₁k₃k₂$k = \sqrt{\frac{k_{1}k_{3}}{k_{2}}}$ . If the activation energies of the three steps are 60, 30 and 10 kJ mol ⁻¹$^{-1}$ respectively, then the overall energy of activation in kJ mol ⁻¹$^{-1}$ is . (Nearest integer)

Related Formula

Core Logic

Since r = k[A]$r = k[A]$, the reaction follows first-order kinetics. The half-life (50%$50\%$ decomposition) is t1/2 = 120 minutes$t_{1/2} = 120\text{ minutes}$.

Step 1: Calculating for 90% decomposition

For 90%$90\%$ completion of the reaction, [A]₀ = 100$[A]_0 = 100$ and [A]ₜ = 100 - 90 = 10$[A]_t = 100 - 90 = 10$.

Rounding off to the nearest integer, we get 399 minutes$399\text{ minutes}$.

Pattern Recognition

For a first order reaction, t90% ≈ 3.32 × t50%$t_{90\%} \approx 3.32 \times t_{50\%}$. 120 × 3.32 = 398.4$120 \times 3.32 = 398.4$, so roughly 399$399$.

Chapter Mix

Class 12 Chemistry: Chemical Kinetics

Core Logic

Consider a general gas phase reaction: A arrow B + C$A \rightarrow B + C$

Initial (t=0$t=0$): Pᵢ 0 0$\quad P_i \quad\quad 0 \quad\quad 0$ At time t$t$: Pᵢ - x x x$\quad P_i - x \quad\quad x \quad\quad x$

Total pressure at time t$t$:

x = Pₜ - Pᵢ$x = P_t - P_i$

Partial pressure of A at time t$t$ (PA$P_A$): PA = Pᵢ - x$P_A = P_i - x$

For a first-order reaction:

Here, P₀ = Pᵢ$P_0 = P_i$ and the pressure of the reactant at time t$t$ is PA$P_A$.

Chapter Mix

Class 12 Chemistry: Chemical Kinetics