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Question

The rate constant of a first order reaction is 6.93×103 min1. If we start with 10 mol/L, it is reduced to 1.25 mol/L in:
  1. 100 minutes
  2. 200 minutes
  3. 300 minutes
  4. 30 minutes


Solution

The correct option is C 300 minutes
Given K=6.93×103min1
[A]0=10 M,  (A)t=1.25 M
Hence, for a 1st order reaction we can write
t=1Kln[A]0[A]t
t=16.93×103ln(101.25)
t=1036.93×ln8=3×103 ln 26.93
t=3×0.693×106.93=3×1031000×693693×100
t=300 minutes

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