Concept:For a first-order reaction, the percentage of reactant remaining can be calculated by halving the concentration successively over consecutive half-lives.
Solution:- If 87.5% of the reaction is completed, the amount of reactant remaining is: \( 100\% - 87.5\% = 12.5\% \).
- Let's trace the decay through half-lives (\( t_{1/2} = 30 \text{ min} \)):
- After 1st half-life: 100% falls to 50% (30 mins elapsed).
- After 2nd half-life: 50% falls to 25% (60 mins elapsed).
- After 3rd half-life: 25% falls to 12.5% (90 mins elapsed).
- It takes exactly 3 half-lives to reach 12.5% remaining (87.5% complete).
- Total time = \( 3 \times 30 \text{ minutes} = 90 \text{ minutes} \).
Why other options are incorrect:60 minutes equals two half-lives (75% completion). 120 minutes equals four half-lives (93.75% completion).
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