## Chemistry: Molecular Approach (4th Edition)

Published by Pearson

# Chapter 2 - Exercises - Page 82: 117

#### Answer

$\text{Li-6}\,=\underline{7.494\,\text{percent}}$ and $\text{Li-7}=\underline{92.506\,\text{percent}}$

#### Work Step by Step

Calculate the fraction of lithium-6 as follows: $\text{Fraction of isotope lithium-}6=\frac{\text{Relative abundance of lithium-}6}{\text{100}}$ Calculate the fraction of lithium-7 as follows: $\text{Fraction of isotope lithium-}7=\frac{\text{Relative abundance of lithium-}7}{\text{100}}$ Atomic mass is the average of the mass of isotopes. So, the atomic mass of lithium is $6.941\text{ amu}$. Calculate the relative abundance as follows: \begin{align} & \text{Atomic mass}=\left( \text{Fraction of lithium-}6\times \text{Mass of lithium-}6 \right)+ \\ & \left( \text{Fraction of lithium-}7\times \text{Mass of lithium-}7 \right) \\ & 6.941\text{ amu}=\left( \frac{\text{Relative abundance of lithium-}6}{\text{100}}\times \text{6}\text{.01512 amu} \right) \\ & +\left( \frac{\text{Relative abundance of lithium-}7}{\text{100}}\times 7.01601\text{ amu} \right) \end{align} Substitute relative abundance of lithium-7 as $100-\text{relative abundance of lithium-}6$ in the above expression as follows: \begin{align} & 6.941\text{ amu}=\left( \frac{\text{Relative abundance of lithium-}6}{\text{100}}\times \text{6}\text{.01512 amu} \right) \\ & +\left( \frac{\text{100}-\text{Relative abundance of lithium-}6}{\text{100}}\times 7.01601\text{ amu} \right) \\ & \text{Relative abundance of lithium-}6=7.494\,\text{percent} \end{align} Calculate the relative abundance of lithium-7 as follows: \begin{align} & \text{Relative abundance of lithium-}7=100\,\text{percent}-7.494\,\text{percent} \\ & =92.506\,\text{percent} \end{align} The relative abundance of lithium-6 is $\underline{7.494\,\text{percent}}$ and the relative abundance of lithium-7 is $\underline{92.506\,\text{percent}}$.

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