Chemistry · Differential and integral forms of zero and first-order reactions, their characteristics and half-lives

The rate constant of a first order reaction is 0.0693 min Time (in minutes) requ

The rate constant of a first order reaction is 0.0693 min\( ^{-1} \) Time (in minutes) required for reducing an initial concentration of 20 mol \( l i t^{-1} \) to 2.5 mol \( l i t^{-1} \) is :

  • A. 40
  • B. 30
  • C. 20
  • D. 10

Step-by-step solution

For a first-order reaction, t = (1/k) ln([A]0/[A]) = (1/0.0693) ln(20/2.5) = (1/0.0693) ln(8). Since ln(8) = 3 ln 2 ≈ 3×0.693 = 2.079, t = 2.079/0.0693 ≈ 30 minutes.
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