Answer to Question #259578 in General Chemistry for Anonymous005

Question

Magnesium has three stable isotopes: 24 Mg, 25 Mg, and 26 Mg. The lightest isotope has an abundance of 78.90 %. Calculate the percentage abundance of the other isotopes.

Answer 1

Isotopic mass of 24Mg= 23.9850amu

Isotopic mass of 25Mg=24.9858amu

Isotopic mass of 26Mg=25.9826amu

Atomic mass of Mg=24.3050amu

Isotopic abundance of 24Mg=78.90%

Isotopic abundance of 25Mg and 26Mg;

=100%-78.90%

=21.1%

Let isotopic abundance of 25Mg= x%

Therefore isotopic abundance of 26Mg

=(21.1 -x)%

=$\frac {78.90}{100} (23.9850)+\frac{x}{100}(24.9858)$

$+\frac{21.1-x}{100}(25.9826)=24.3050$

Solving for x;

$0.9968x=10.1494$

$x=10.18$ $\%$

$21.1-x=21.1-10.198$

$10.92\%$

Isotopic abundance of $25Mg=10.18\%$

Isotopic abundance of$\>26Mg=10.92\%$