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zaharov [31]
3 years ago
14

Iron‑59 is used to study iron metabolism in the spleen. Its half‑life is 44 days. How many days would it take a 28.0 g sample of

iron‑59 to decay to 0.875 g?
Chemistry
1 answer:
RoseWind [281]3 years ago
5 0

The radioisotope will take 219 days to decay from 28 g to 0.875 g.

Explanation:

Any radioactive isotope is tend to decay with time. So the rate of decay of the radioactive isotopes is termed as disintegration constant. Since, the initial mass of the radioactive isotope is given along with the reducing mass. In order to determine the time required to reduce the mass of the radioisotope from 28 g to 0.875 g, first the disintegration constant is need to be determined. The disintegration constant can be obtained from half life time of the isotope. As half life time is the measure of time required to reduce half of the concentration of the isotope.

Half life time = 0.6932/disintegration constant

44 = 0.6932/λ

λ = 0.6932/44=0.0158

So, with this values of disintegration constant, initial mass and final mass, the time required to reduce from initial to final mass can be obtained using law of disintegration constant as follows.

N = Noe^(-λt)

t= -\frac{1}{disintegration constant}* ln(\frac{N}{N_{0} } )\\ \\t = -\frac{1}{0.0158}*ln(\frac{0.875}{28})\\  \\t = -\frac{1}{0.0158}*ln(0.03125)\\\\t = -63.29*(-3.466)\\\\t=219 days.

Thus, the radioisotope will take 219 days to decay from 28 g to 0.875 g.

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Carbon tetrachloride, CCl4, once used as a cleaning fluid and as a fire extinguisher, is produced by heating methane and chlorin
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1.882 g

Explanation:

Data Given

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Reaction Given:

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Solution:

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                    1 mol        4 mol

So 1 mole of CH₄ combine with 4 moles of Cl₂

Now

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Molar mass of Cl₂ = 2 (35.5)

Molar mass of  Cl₂  = 71 g/mol

mass of Cl₂

                mass in grams = no. of moles x molar mass

                mass of Cl₂ = 4 mol x 71 g/mol

                mass of Cl₂  = 284 g

Molar mass of CH₄= 12+ 4(1)

Molar mass of CH₄= 16 g/mol

mass of CH₄

                mass in grams = no. of moles x molar mass

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                mass of CH₄ = 16 g

So,

284 g of Cl₂  combine with 16 g of methane ( CH₄ ) then how many grams of CH₄ is needed to combine with 33.4 g of Cl₂  

Apply unity Formula

                           284 g of Cl₂  ≅ 16 g of methane ( CH₄ )

                           33.4 g of Cl₂  ≅ X g of methane ( CH₄ )

By cross multiplication

                          X g of methane ( CH₄ ) = 16 g x 33.4 g / 284 g

                          X g of methane ( CH₄ ) = 1.88 g

1.882 g of methane (CH₄) will needed to combine with 33.4 g of Cl₂

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