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Chemical Kinetics

Question
CBSEENCH12006355

For the reaction A → B, deduce the integrated form of rate law. What will be the nature of the curve when concentration is plotted against time for such reaction?

Solution

For the reaction:    A → B.

Let a is the initial concentration of A in g moles L–1 and (a – x) is the concentration in g moles L–1 after time t, then according to law of mass action

          Rate of reaction  (a - x)
or               dxdt (a-x)or               dxdt=k(a-x)or                dx(a-x)= k dt

    Integrating the above equation, we get

       -In (a-x) = kt+c                             [where In is natural log]

when t=0,  x=0, c=-In a

or         -In(a-x) = kt-In a

or                 kt=Ina(a-x)

or                k=1tIna(a-x)

   Changing natural log to base 10, we get

              k=2.303tloga(a-x)

Nature of the curve: Hypothetical variation of conc. of reactant [R] and product [P] during the course of reaction.



Fig. Instantaneous and average rate of a reaction.