Answer to Question #96072 in General Chemistry for yenco

Question #96072
Direction: Solve the following problems. Show your solution and use the appropriate number of significant figures.

1.Problem(20 points):Radon-222 has a half-life of 3.8 days. The source water for drinking water treatment plant contains 1250 μmol/L of radon. How long must the water be stored to meet the US EPA limit of 300 μmol/L?
1
Expert's answer
2019-10-08T07:40:59-0400

Answer: 7.82 days

Solution:

"N=N_{0}\u00d7(1\/2)^{\\frac{t}{T_{1\/2}}}"

"\\ln{\\frac{N}{N_{0}}}=-{\\frac{t}{T_{1\/2}}}\u00d7\\ln2"

"t=-\\frac{\\ln{\\frac{N}{N_{0}}}\u00d7{T_{1\/2}}}{\\ln2}=-\\frac{\\ln{\\frac{C}{C_{0}}}\u00d7{T_{1\/2}}}{\\ln2}"

"t=-\\frac{\\ln{\\frac{300\\,\\mu mol\/L}{1250\\,\\mu mol\/L}}\u00d7{3.8\\,days}}{\\ln2}=7.82\\,days"


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