Final answer:
To calculate the percentage of the reactant consumed after 3 half-lives, divide the total time by the number of half-lives to find the time per half-life. Multiply the time per half-life by the number of half-lives to calculate the total time for 3 half-lives. Finally, multiply the total time by the percentage of completion for each half-life to determine the percentage of the reactant consumed after 3 half-lives.
Step-by-step explanation:
To calculate the percentage of the reactant consumed after 3 half-lives, we first need to determine the time it takes for 3 half-lives to occur. Since the reaction is first-order, the time for each half-life is constant, which is found by dividing the total time by the number of half-lives. In this case, 500 seconds/2 = 250 seconds per half-life. Therefore, after 3 half-lives (250 seconds x 3 = 750 seconds), the reaction will be 87.5% complete. So, the correct answer is option C, 87.5%.
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