Sodium only has one naturally occuring isotope, 23 Na, with a relative atomic mass of 22.9898 u. A synthetic, radioactive isotope of sodium, 22 Na, is used in positron emission tomography. 22 Na has a relative atomic mass of 21.9944 u. A 1.8385 g sample of sodium containing a mixture of 23 Na and 22 Na has an apparent "atomic mass" of 22.9573 u. Find the mass of 22 Na contained in this sample?

Question

Chemistry

Aspen Browning

26 September, 12:34

Sodium only has one naturally occuring isotope, 23 Na, with a relative atomic mass of 22.9898 u. A synthetic, radioactive isotope of sodium, 22 Na, is used in positron emission tomography. 22 Na has a relative atomic mass of 21.9944 u. A 1.8385 g sample of sodium containing a mixture of 23 Na and 22 Na has an apparent "atomic mass" of 22.9573 u. Find the mass of 22 Na contained in this sample?

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Rigoberto Jackson · Answer 1

Mass of 22-Na contained in the sample = 0.0599 g

Explanation:

Mass of the isotope mixture = 1.8385g

Isotope mixture has apparent mass of 22.9573 u

23-Na has a relative atomic mass of 22.9898 u

22-Na has a relative atomic mass of 21.9944 u

Let the relative abundance of 23-Na be X

Then the relative abundance of 22-Na would be (1-X)

21.9944 (1-X) + 22.9898 X = 22.9573

21.9944 - 21.9944X + 22.9898X = 22.9573

22.9898X - 21.9944X = 22.9573 - 21.9944

0.9954X = 0.9639

X = 0.9674

Relative abundance of 23-Na = 0.9674

Relative abundance of 22-Na = 1 - 0.9674 = 0.0326

Mass of 22-Na in the 1.8385g of sample is

Relative abundance of 22-Na * Mass of sample = 0.0326 * 1.8385g = 0.0599 g