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MHT CET20255 May 2025Evening ShiftChemistryChemical KineticsActual

What is half life of a first order reaction if time required to decrease concentration of reactant from 0.4 M to 0.1 M is x hour?

Options

  1. Ax hour
  2. B2 x hour
  3. Cx 2 hour
  4. D3 x 2 hour

Correct answer

C. x 2 hour

Step-by-step solution

The half-life of a first-order reaction relates to the rate constant k through t_ 1/2 = 0.693 k . Given the concentration decreasing from [A]₀ = 0.4 M to [A]_t = 0.1 M over time t = x hours, this represents a reduction by a factor of 4. Since [A]_t [A]₀ = 1 4 , exactly two half-lives have elapsed: [A]₀ [A]₀ 2 [A]₀ 4 . Therefore, x = 2t_ 1/2 , yielding t_ 1/2 = x 2 hours. Final answer: x 2 hour

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