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Sodium-24 has a half-life of 15 hours. Suppose you had a sample containing 0.010 moles of Na-24. How many hours would be required to reduce your sample to 6.25 x 10-4 moles?
Accepted Answer
Here's the solution:
Each half-life reduces the amount of Na-24 by half. We need to figure out how many half-lives it takes to reduce 0.010 moles to 6.25 x 10^-4 moles.
Step 1: Determine the fraction remaining:
(6.25 x 10^-4 moles) / (0.010 moles) = 0.0625
Step 2: Find the number of half-lives:
Since each half-life reduces the amount by half, we need to find the power of 1/2 that equals 0.0625.
(1/2)^4 = 0.0625
Therefore, 4 half-lives are required.
Step 3: Calculate the total time:
4 half-lives
15 hours/half-life = 60 hours
Answer: It would take 60 hours to reduce the sample to 6.25 x 10^-4 moles.
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