Question

How do you calculate the average atomic mass of magnesium, given the following percent abundances and isotopic masses: $78.99\mathrm{\%}.{}^{24}\mathrm{Mg}(23.98504\mathrm{u}),10.00{\mathrm{\%}}^{25}\mathrm{Mg}(24.98584\mathrm{u}),\mathrm{and}11.01\mathrm{\%}{.}^{26}\mathrm{Mg}(25.98259\mathrm{u})?$

Answer 1

Average atomic mass:

• The Average atomic mass of an element can be calculated by adding up the masses of its isotopes, which are each multiplied by its natural abundance divided by 100.
• For calculating the average atomic mass of Magnesium, the natural abundance of its isotopes is given as follows;

$$\begin{gathered} 78.99\%\mathrm{of}23.98504\mathrm{u}\mathrm{for}{}^{24}\mathrm{Mg} \\ 10.00\%\mathrm{of}24.98584\mathrm{u}\mathrm{fo}{}^{25}\mathrm{Mg} \\ 11.01\%\mathrm{of}25.98259\mathrm{u}\mathrm{for}{}^{26}\mathrm{Mg} \end{gathered}$$

• Hence the average atomic mass can be calculated as;

$$\begin{gathered} =(0.7899x23.98504)+(0.100x24.98584)+(0.1101x25.98259) \\ =24.30505\mathrm{u} \end{gathered}$$

Therefore, in an above-given way, as described, the average atomic mass of Magnesium can be calculated as $24.30505\mathrm{u}.$