Consider the following mechanism for the reaction 2A → P: 1. 2A xrightarrowk_1 I (slow) 2. I + A xrightarrowk_2 P (fast)

Consider the following mechanism for the reaction $2 A \to P$ : 1. $2 A x r i g h t a r r o w k_{1} I$ (slow) 2. $I + A x r i g h t a r r o w k_{2} P$ (fast)

hard 4 marks Class 12 · Chemistry · Chemical Kinetics

Answer

(a)

r = k_{1} [A]^{2}

; (b) Overall second order in

A

; (c) Step 1 is the RDS because it is slow and limits the rate.

The correct answer is (a) $r = k_{1} [A]^{2}$ ; (b) Overall second order in $A$ ; (c) Step 1 is the RDS because it is slow and limits the rate. — Justification: The overall rate equals the rate of the slow step, and the steady‑state approximation shows step 1 controls the concentration of $I$ .

Step-by-step solution

Write the steady‑state condition: $d [I] / d t = 0 = k_{1} [A]^{2} - k_{2} [I] [A]$ .
Solve for $[I]$ : $[I] = \frac{k _{1} [ A ] ^{2}}{k _{2} [ A ]} = \frac{k _{1} [ A ]}{k _{2}}$ .
Write the rate of product formation: $r = k_{2} [I] [A]$ .
Substitute $[I]$ into $r$ : $r = k_{2} c d o t \frac{k _{1} [ A ]}{k _{2}} c d o t [A] = k_{1} [A]^{2}$ .
Thus the rate law is $r = k_{1} [A]^{2}$ ; the reaction is second order overall and first order in $A$ .
Since step 1 is slow and step 2 is fast, step 1 limits the rate. Hence step 1 is the rate‑determining step.
Justification: The overall rate equals the rate of the slow step, and the steady‑state approximation shows step 1 controls the concentration of $I$ .

Common mistake: Assuming step 2 determines the rate or ignoring the steady‑state approximation

Concept tested: Mechanistic analysis using steady‑state approximation

Published 6 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked

← All Chemical Kinetics questions

Consider the following mechanism for the reaction 2A→P: 1. 2Axrightarrowk1​I (slow) 2. I+Axrightarrowk2​P (fast)

Step-by-step solution

Consider the following mechanism for the reaction $2 A \to P$ : 1. $2 A x r i g h t a r r o w k_{1} I$ (slow) 2. $I + A x r i g h t a r r o w k_{2} P$ (fast)