For an isothermal batch reactor operating under first-order kinetics, 50% decomposition of a liquid takes 2 minutes. Approximately how many _______________ minutes are needed for 75% decomposition?
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Answer: B. 4
Explanation
First-order half-life is constant, meaning fifty percent decomposition takes exactly two minutes. Reaching seventy-five percent decomposition requires two successive half-lives to elapse in the reactor. Multiplying the two-minute half-life by two gives a total required time of four minutes. First-order reaction half-lives depend only on the rate constant and remain independent of concentration. Seventy-five percent decomposition leaves twenty-five percent unreacted, which equals one-half squared. Batch reactor performance equations for first-order kinetics simplify to logarithmic time relationships.
Chemical plant operators use half-life calculations to estimate batch reaction cycle times quickly. Waste treatment facilities apply first-order half-life models to predict pollutant removal timescales. Reactor scheduling benefits from knowing exact times required to reach target conversion thresholds. Three minutes assumes linear decomposition behavior, which violates exponential first-order kinetics. Six minutes would correspond to three half-lives, resulting in eighty-seven point five percent conversion. Ten minutes overestimates the required time significantly, leading to inefficient reactor scheduling.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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