JEE Challenger
More from Chemical Kinetics
ChemEasyAdv 2007 • Paper 2

Overall Order of Reaction from Rate Dependences

Consider a reaction aG+bH→Productsa\text{G} + b\text{H} \rightarrow \text{Products}. When concentration of both the reactants G\text{G} and H\text{H} is doubled, the rate increases by eight times. However, when concentration of G\text{G} is doubled keeping the concentration of H\text{H} fixed, the rate is doubled. The overall order of the reaction is

Options

A

0

B

1

C

2

D

3

Correct

Topics & Concepts

Chemical KineticsChemical KineticsRate LawOrder of Reaction

Step-by-Step Solution

Let the rate law be:
r=k[G]x[H]yr = k [\text{G}]^x [\text{H}]^y

  1. When [G][\text{G}] is doubled keeping [H][\text{H}] constant:
    r′=k(2[G])x[H]y=2xrr' = k (2[\text{G}])^x [\text{H}]^y = 2^x r
    Given r′=2rr' = 2r, we have 2x=2  ⟹  x=12^x = 2 \implies x = 1.

  2. When both [G][\text{G}] and [H][\text{H}] are doubled:
    r′′=k(2[G])x(2[H])y=2x+yrr'' = k (2[\text{G}])^x (2[\text{H}])^y = 2^{x+y} r
    Given r′′=8rr'' = 8r, we have 2x+y=8=23  ⟹  x+y=32^{x+y} = 8 = 2^3 \implies x + y = 3.

Thus, the overall order of the reaction is x+y=3x + y = 3.

Correct Answer: D

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