Chemistry: Molecular Approach (4th Edition)

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

Chapter 2 - Exercises - Page 81: 101


\[\underline{\text{207 amu}}\]

Work Step by Step

Calculate the abundance of Pb-208 as follows: \[\begin{align} & \text{Abundance of Pb-}208=\frac{100\,\text{percent}}{100\,\text{percent}+48.9\,\text{percent}+41.1\,\text{percent}}\times 100\,\text{percent} \\ & =52.63\,\text{percent} \end{align}\] Calculate the abundance of Pb-206 as follows: \[\begin{align} & \text{Abundance of Pb-}206=\frac{48.9\,\text{percent}}{100\,\text{percent}+48.9\,\text{percent}+41.1\,\text{percent}}\times 100\,\text{percent} \\ & =25.74\,\text{percent} \end{align}\] Calculate the abundance of Pb-207 as follows: \[\begin{align} & \text{Abundance of Pb-}207=\frac{41.1\,\text{percent}}{100\,\text{percent}+48.9\,\text{percent}+41.1\,\text{percent}}\times 100\,\text{percent} \\ & =21.63\,\text{percent} \end{align}\] Calculate the fraction of Pb-208 as follows: \[\begin{align} & \text{Fraction of isotope Pb-}208=\frac{52.63}{100} \\ & =0.5263 \end{align}\] Calculate the fraction of Pb-206 as follows: \[\begin{align} & \text{Fraction of isotope Pb-}206=\frac{25.74}{100} \\ & =0.2574 \end{align}\] Calculate the fraction of Pb-207 as follows: \[\begin{align} & \text{Fraction of isotope Pb-}207=\frac{21.63}{100} \\ & =0.2163 \end{align}\] Calculate the atomic mass of the element as follows: \[\begin{align} & \text{Atomic mass}=\left( \text{Fraction of Pb-}208\times \text{Mass of Pb-}208 \right)+ \\ & \left( \text{Fraction of Pb-}206\times \text{Mass of Pb-}206 \right)+ \\ & \left( \text{Fraction of Pb-}207\times \text{Mass of Pb-}207 \right) \\ & =\left( 0.5263\times 208\text{ amu} \right)+\left( 0.2574\times 206\text{ amu} \right) \\ & +\left( 0.2163\times 207\text{ amu} \right) \\ & =109.47\text{ amu}+53.02\text{ amu}+44.77\text{ amu} \\ & =207.26\text{ amu} \end{align}\] The atomic mass of lead is \[\underline{\text{207 amu}}\].
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