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Chemical Kinetics

Question
CBSEENCH12010939

In first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is

  • 30 minutes

  • 60 minutes

  • 7.5 minutes

  • 15 minutes

Solution

A.

30 minutes

Order = 1
Concentration changes from 0.8 M to 0.4 M(50%) in 15 min, thus half - life is 15 min = T50
A change from 0.1 M to 0.025 M is 75% and for first order reaction
T75 = 2 x T50
= 2 x 15 = 30 min
T50 = 15 min
straight k space equals space fraction numerator 2.303 space log space 2 over denominator straight T subscript 50 end fraction space equals space fraction numerator 2.303 space log 2 over denominator 15 end fraction
straight a space equals space 0.1 space straight M
left parenthesis straight a minus straight x right parenthesis space equals space 0.025 space straight M
For space first space order space straight k space equals space fraction numerator 2.303 over denominator straight t space end fraction space log space open parentheses fraction numerator straight a over denominator straight a minus straight x end fraction close parentheses
fraction numerator 2.303 space log space 2 over denominator 15 end fraction space equals space fraction numerator 2.303 over denominator straight t end fraction space log space fraction numerator 0.1 over denominator 0.025 end fraction
space equals space fraction numerator 2.303 over denominator straight t end fraction space log space 4
therefore space fraction numerator 2.303 space log space 2 over denominator 15 end fraction space equals space fraction numerator 2 space straight x space 2.303 space log space 2 over denominator straight t end fraction
straight t space equals space 30 space min