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Eddi Din [679]
3 years ago
7

The radioactivity due to carbon-14 measured in a piece of a wooden casket from an ancient burial site was found to produce 20 co

unts per minute from a given sample, whereas the same amount of carbon from a piece of living wood produced 160 counts per minute. The half-life of carbon-14, a beta emitter, is 5730 years. Thus we would estimate the age of the artifact to be about?
Chemistry
1 answer:
bekas [8.4K]3 years ago
3 0

Answer:

17202.6 years

Explanation:

Activity of the living sample (Ao) = 160 counts per minute

Activity of the wood sample (A) = 20 counts per minute

Half life of carbon-14 = 5730 years

t= age of the artifact

From;

0.693/t1/2= 2.303/t log Ao/A

Then;

0.693/ 5730= 2.303/t log Ao/A

Substituting values;

0.693/5730= 2.303/t log (160/20)

Then we obtain;

1.209×10^-4 = 2.0798/t

t= 2.0798/1.209×10^-4

Thus;

t= 17202.6 years

Therefore the artifact is 17202.6 years old.

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Answer: The molarity of each of the given solutions is:

(a) 1.38 M

(b) 0.94 M

(c) 1.182 M

Explanation:

Molarity is the number of moles of a substance present in liter of a solution.

And, moles is the mass of a substance divided by its molar mass.

(a) Moles of ethanol (molar mass = 46 g/mol) is as follows.

Moles = \frac{mass}{molar mass}\\= \frac{28.5 g}{46 g/mol}\\= 0.619 mol

Now, molarity of ethanol solution is as follows.

Molarity = \frac{moles}{Volume (in L)}\\= \frac{0.619 mol}{4.50 \times 10^{2} \times 10^{-3}L}\\= 1.38 M

(b) Moles of sucrose (molar mass = 342.3 g/mol) is as follows.

Moles = \frac{mass}{molar mass}\\= \frac{21.6 g}{342.3 g/mol}\\= 0.063 mol

Now, molarity of sucrose solution is as follows.

Molarity = \frac{moles}{Volume (in L)}\\= \frac{0.063 mol}{0.067 L}  (1 mL = 0.001 L)\\= 0.94 M

(c) Moles of sodium chloride (molar mass = 58.44 g/mol) are as follows.

Moles = \frac{mass}{molar mass}\\= \frac{6.65 g}{58.44 g/mol}\\= 0.114 mol

Now, molarity of sodium chloride solution is as follows.

Molarity = \frac{moles}{Volume (in L)}\\= \frac{0.114 mol}{0.0962 L}\\= 1.182 M

Thus, we can conclude that the molarity of each of the given solutions is:

(a) 1.38 M

(b) 0.94 M

(c) 1.182 M

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3 years ago
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