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Lady_Fox [76]
2 years ago
15

The half-life of the first-order decay of radioac- . 14C . b l:Ive 1s a out 5720 years. Calculate the rate constant for the reac

tion. (b) The natural abundance of 14C isotope is 1.1 x I 0-13 mol % in living matter. Radiochemical analysis of an object obtained in an archeological excavation shows that the 14 C isotope content is 0.89 x 10-14 mol %. Calculate the age of the object. State any assumptions.
Chemistry
1 answer:
Alinara [238K]2 years ago
4 0

Answer:

a. Rate constant: 1.2118x10⁻⁴ yrs⁻¹

b. The age of the object is 20750 years

Explanation:

a. We can solve the rate constant in an isotope decay by using Half-Life, as follows:

K = Ln 2 / Half-life

K = ln 2 / 5720 years =

<h3>1.2118x10⁻⁴ yrs⁻¹</h3><h3 />

b. The general equation of isotope decay is:

Ln [A] = -kt + Ln [A]₀

<em>Where [A] is concentration of the isotope after time t, </em>

<em>k is rate constant</em>

<em>and [A]₀ initial concentration of the isotope.</em>

<em />

Computing the values of the problem:

Ln [0.89x10⁻¹⁴] = -1.2118x10⁻⁴ yrs⁻¹t + Ln [1.1x10⁻¹³]

-2.5144 = -1.2118x10⁻⁴ yrs⁻¹t

20750 years = t

The age of the object is 20750 years

<em />

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<u>Answer:</u>

<u>For A:</u> The number of arsenic atoms are 3.4\times 10^{21}

<u>For B:</u> The percent composition of mercury, thallium and chromium in their complexes are 61.76 %, 62.2 % and 29.51 % respectively.

<u>Explanation:</u>

  • <u>For A:</u>

To calculate the number of moles, we use the equation:

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Given mass of dimercaprol = 696 mg = 0.696 g    (Conversion factor:  1 g = 1000 mg)

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We know that:

Molar mass of dimercaprol = 124.21 g/mol

Molar mass of mercury = 200.59 g/mol

Molar mass of thallium = 204.38 g/mol

Molar mass of chromium = 51.99 g/mol

Also, 1 molecule of dimercaprol binds with 1 metal atom.

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Mass of mercury = 200.59 g

Putting values in equation 1, we get:

\%\text{ composition of mercury}=\frac{200.59g}{324.8g}\times 100=61.76\%

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Mass of thallium = 204.38 g

Putting values in equation 1, we get:

\%\text{ composition of thallium}=\frac{204.38g}{328.59g}\times 100=62.2\%

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Mass of Cr-complex = (51.99 + 124.21) = 176.2 g

Mass of chromium = 51.99 g

Putting values in equation 1, we get:

\%\text{ composition of chromium}=\frac{51.99g}{176.2g}\times 100=29.51\%

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