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A substance 'A' decomposes by a first order reaction starting initially with [A] = 2.00 m and after 200 min, [A] becomes 0.15 m. For this reaction t₁/₂ is
- 53.72 min
- 50.49 min
- 48.45 min
- 46.45 min
Correct answer: 53.72 min
Solution
For a first-order reaction, the half-life (t1/2) is independent of the initial concentration and can be calculated using the formula: t1/2 = 0.693 / k, where k is the rate constant. Given that [A] = 2.00 m and after 200 min, [A] becomes 0.15 m, we can calculate the rate constant k using the formula: k = ln([A]0 / [A]t) / t, where [A]0 is the initial concentration and [A]t is the concentration at time t. Substituting the values, we get k = ln(2.00 / 0.15) / 200 = 0.013 min^-1. Now, we can calculate the half-life using the formula: t1/2 = 0.693 / k = 0.693 / 0.013 = 53.72 min.
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