## Q. 4.5

Magnesium is a macromineral needed in the contraction of muscles and metabolic reactions. Using Table 4.7, calculate the atomic mass for magnesium using the weighted average mass method.

 TABLE 4.7 Isotopes of Magnesium Atomic Symbol $^{24}_{12}Mg$ $^{25}_{12}Mg$ $^{26}_{12}Mg$ Name Mg-24 Mg-25 Mg-26 Number of Protons 12 12 12 Number of Electrons 12 12 12 Mass Number 24 25 26 Number of Neutrons 12 13 14 Mass of Isotope (amu) 23.99 24.99 25.98 Percent Abundance 78.70 10.13 11.17

## Verified Solution

Table 1

STEP 1   Multiply the mass of each isotope by its percent abundance divided by 100.

Table 2

STEP 2   Add the contribution of each isotope to obtain the atomic mass.
Atomic mass of Mg = 18.88 amu + 2.531 amu + 2.902 amu
$\space$                                    = 24.31 amu (weighted average mass)

Table 1

 ANALYZE THE PROBLEM Given Need Connect percent abundance, atomic mass atomic mass of Mg weighted average mass

Table 2

 Atomic Symbol Mass (amu) Percent Abundance Contribution to the Atomic Mass $^{24}_{12}Mg$ 23.99            × $\frac{78.70}{100}$                             = 18.88 amu $^{25}_{12}Mg$ 24.99            × $\frac{10.13}{100}$                             = 2.531 amu $^{26}_{12}Mg$ 25.98            × $\frac{11.17}{100}$                             = 2.902 amu