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3 years ago

The radioisotope radon-222 has a half life of 3.8 days. How much of a 10 gram sample of radon-222 would be left after 15.2 days?

Chemistry

1 answer:

djyliett [7]3 years ago

4 0

Answer:

0.625 g

Explanation:

Given data:

Half life of radon-222 = 3.8 days

Total mass of sample = 10 g

Mass left after 15.2 days = ?

Solution:

Number of half lives = T elapsed / Half life

Number of half lives = 15.2 / 3.8

Number of half lives = 4

At time zero = 10 g

At first half life = 10 g/2 = 5 g

At 2nd half life = 5 g/ 2= 2.5 g

At third half life = 2.5 g/2 = 1.25 g

At 4th half life = 1.25 g/2 = 0.625 g

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$M_1V_1=M_2V_2$

where,

$M_1\text{ and }V_1$ are the molarity and volume of the concentrated glucose solution

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$M_1=0.860M\\V_1=35.0mL\\M_2=?M\\V_2=0.500L=500mL$

Putting values in above equation, we get:

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Now, calculating the mass of glucose by using equation 1, we get:

Molarity of glucose solution = 0.0602 M

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Volume of solution = 100 mL

Putting values in equation 1, we get:

$0.0602=\frac{\text{Mass of glucose solution}\times 1000}{180.2\times 100}\\\\\text{Mass of glucose solution}=\frac{0.0602\times 180.2\times 100}{1000}=1.085g$

Hence, the mass of glucose in final solution is 1.085 grams

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