Sodium only has one naturally occuring isotope, Na23 , with a relative atomic mass of 22.9898 u. A synthetic, radioactive isotope of sodium, Na22 , is used in positron emission tomography. Na22 has a relative atomic mass of 21.9944 u. A 1.5909 g sample of sodium containing a mixture of Na23 and Na22 has an apparent "atomic mass" of 22.9785 u . Find the mass of Na22 contained in this sample

0.000399316  g

Explanation:

We can start with the molar fraction for each isotope:

We can say that the abudandance of is an unknow value "X" and the molar fraction of is "Y". We have to keep in mind that the molar fractions can be added:

Y + X = 1

So, we can put the molar fraction of in terms of , so:

Y=1-X

So, we will have the molar fraction of each isotope:

: X-1

: X

And the atomic mass:

: 21.9944

: 22.9898

If we multiply the molar mass by the each atomic mass of each isotope we will have:

Now we can solve for "X" :

The molar fraction of is 0.999749. Now we can calculate the molar fraction of , so:

Now, if we multiply the molar fraction by the mass we can find the mass of , so:

The mass of is 0.000399316  g

I hope it helps!

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