Chemistry: Molecular Approach (4th Edition)

Published by Pearson
ISBN 10: 0134112830
ISBN 13: 978-0-13411-283-1

Chapter 2 - Exercises - Page 80: 78


\[\underline{\text{29}\text{.96 amu}}\] and \[\underline{\text{3}\text{.13}\,\text{percent}\,}\]

Work Step by Step

Calculate the Si-28 fraction as follows: \[\begin{align} & \text{Fraction Si-}28=\frac{92.2}{100} \\ & =0.922 \end{align}\] Calculate the Si-29 fraction as follows: \[\begin{align} & \text{Fraction Si-}29=\frac{4.67}{100} \\ & =0.0467 \end{align}\] Calculate the Si-30 natural abundance as follows: \[\begin{align} & \text{Natural abundance}=100\,\text{percent}\,-\left( \text{Natural abundance Si-}28+\text{Natural abundance Si-}29 \right) \\ & =100\,\text{percent}\,-\left( 92.2\,\text{percent}\,+4.67\,\text{percent}\, \right) \\ & =3.13\,\text{percent}\, \end{align}\] Calculate the Si-30 fraction as follows: \[\begin{align} & \text{Fraction isotope Si-}30=\frac{3.13}{100} \\ & =0.0313 \end{align}\] Calculate the atomic mass of the element as follows: \[\begin{align} & \text{Atomic mass}=\left( \text{fraction of Si-}28\times \text{mass of Si-}28 \right)+ \\ & \left( \text{fraction of Si-}29\times \text{mass of Si-}29 \right)+ \\ & \left( \text{fraction of Si-}30\times \text{mass of Si-}30 \right) \\ & \text{28}\text{.09 amu}=\left( 0.922\times 27.9769\text{ amu} \right)+\left( 0.0467\times 28.9765\text{ amu} \right)+\left( 0.0313\times \text{mass of Si-}30 \right) \end{align}\] Rearrange the above expression as follows: \[\begin{align} & \left( 0.0313\times \text{mass of Si-}30 \right)=0.93763768\text{ amu} \\ & \text{mass of Si-}30=29.96\text{ amu} \end{align}\] The mass of Si-30 is \[\underline{\text{29}\text{.96 amu}}\] and the natural abundance is \[\underline{\text{3}\text{.13}\,\text{percent}\,}\].
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