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.

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 ∴ rat