Example 2.4: Calculation of Average Atomic Mass

A meteorite found in central Indiana contains traces of the noble gas neon picked up from the solar wind during the meteorite’s trip through the solar system. Analysis of a sample of the gas showed that it consisted of 91.84% \(\ce{^20Ne}\) (mass 19.9924 Da), 0.47% \(\ce{^21Ne}\) (mass 20.9940 Da), and 7.69% \(\ce{^22Ne}\) (mass 21.9914 Da). What is the average mass of the neon in the solar wind?

Solution

\(f_{\mathrm{\ce{20}}}\) \(= 91.84\ \mathrm{%}\)


\(f_{\mathrm{\ce{21}}}\) \(= 0.47\ \mathrm{%}\)


\(f_{\mathrm{\ce{22}}}\) \(= 7.69\ \mathrm{%}\)


\(m_{\mathrm{\ce{20}}}\) \(= 19.9924\ \mathrm{Da}\)


\(m_{\mathrm{\ce{21}}}\) \(= 20.9940\ \mathrm{Da}\)


\(m_{\mathrm{\ce{22}}}\) \(= 21.9914\ \mathrm{Da}\)


\(m_{\mathrm{average}}\) = ?


\(m_{\mathrm{average}}\) \(= f_{\mathrm{\ce{20}}} \cdot m_{\mathrm{\ce{20}}} + f_{\mathrm{\ce{21}}} \cdot m_{\mathrm{\ce{21}}} + f_{\mathrm{\ce{22}}} \cdot m_{\mathrm{\ce{22}}}\)

\(\ \ \ =91.84\ \mathrm{%} \cdot 19.9924\ \mathrm{Da} + 0.47\ \mathrm{%} \cdot 20.9940\ \mathrm{Da} + 7.69\ \mathrm{%} \cdot 21.9914\ \mathrm{Da}\)

\(\ \ \ =18.3610\ \mathrm{Da} + 0.0987\ \mathrm{Da} + 1.6911\ \mathrm{Da}\)

\(\ \ \ =18.4597\ \mathrm{Da} + 1.6911\ \mathrm{Da}\)

\(\ \ \ =20.151\ \mathrm{Da}\)


The average mass of the neon in the solar wind is 20.151 Da. (The average mass of a terrestrial neon atom is 20.1796 Da. This result demonstrates that we may find slight differences in the natural abundance of isotopes, depending on their origin.)