Question
Match the rate expressions in LIST-I for the decomposition of \( X \) with the corresponding profiles provided in LIST-II. \(X_s\) and \( k \) are constants having appropriate units.
JEE Advanced
Chemistry
Chemical Kinetics
2022
JEE Advanced 2022 (Paper 1)
JEE Advanced Chemistry Question (2022) — Solution
Options
- A. I → P ; II → Q ; III → S ; IV → T
- B. I → R ; II → S ; III → S ; IV → T
- C. I → P ; II → Q ; III → Q ; IV → R
- D. I → R ; II → S ; III → Q ; IV → R
Answer
A. I → P ; II → Q ; III → S ; IV → T
Step-by-step solution
I rate = k X X S + X Case-1: X > > X s ; X + X s ≈ X rate = k X X = k (Zero order w.r.t. X ) I → P , S Case-2: X ≪ X s ; X + X s ≈ X s ∴ rate = k X X S = k ' X ( 1 st order w.r.t. X ) ∴     I → Q , T Case-3: X ≈ X S rate = k X X s + X In this case curve- R given in List-II will match. ∴   I → P , Q , R , S , T (The graph of half-life should start from origin) II rate = k X X S + X ∵   X ≪ X S ∴   X s + X ≈ X s ∴ rate = k X X S = k ' X ( 1 st order w.r.t. X ) ∴   II → Q , T III rate = k X X s + X ∵   X > > X s ∴   X s + X ≈ X ∴ rate = k X X = k (Zero order w.r.t. X ) ∴     III → P , S IV rate = k X 2 X s + X ∵   X > > X S ∴   X S + X ≈ X ∴ rate = k X 2 X = k X ( 1 st order w.r.t. X ) ∴   IV → Q , T
Related: Chemistry — Chemical Kinetics · All PYQ Banks