Chapter 2 - Exercises - Page 81: 102

\[\underline{\text{201 amu}}\]

Calculate the abundance of Hg-196 as follows: \[\begin{align} & \text{Abundance of Hg-}196=\frac{1.0\,\text{percent}}{\left( 1.0+32.5+57.5+76.1+32.5+100+23.4 \right)\,\,\text{percent}}\times 100\,\text{percent} \\ & =\frac{1\,\text{percent}}{323\,\text{percent}}\times 100\,\text{percent} \\ & =0.31\,\text{percent} \end{align}\] Calculate the abundance of Hg-198 as follows: \[\begin{align} & \text{Abundance of Hg-}198=\frac{32.5\,\text{percent}}{\left( 1.0+32.5+57.5+76.1+32.5+100+23.4 \right)\,\text{percent}}\times 100\,\text{percent} \\ & =\frac{32.5\,\text{percent}}{323\,\text{percent}}\times 100\,\text{percent} \\ & =10.06\,\text{percent} \end{align}\] Calculate the abundance of Hg-199 as follows: \[\begin{align} & \text{Abundance of Hg-}199=\frac{57.5\,\text{percent}}{\left( 1.0+32.5+57.5+76.1+32.5+100+23.4 \right)\,\text{percent}}\times 100\,\text{percent} \\ & =\frac{57.5\,\text{percent}}{323\,\text{percent}}\times 100\,\text{percent} \\ & =17.80\,\text{percent} \end{align}\] Calculate the abundance of Hg-200 as follows: \[\begin{align} & \text{Abundance of Hg-}200=\frac{76.1\,\text{percent}}{\left( 1.0+32.5+57.5+76.1+32.5+100+23.4 \right)\,\text{percent}}\times 100\,\text{percent} \\ & =\frac{76.1\,\text{percent}}{323\,\text{percent}}\times 100\,\text{percent} \\ & =23.56\,\text{percent} \end{align}\] Calculate the abundance of Hg-201 as follows: \[\begin{align} & \text{Abundance of Hg-}201=\frac{32.5\,\text{percent}}{\left( 1.0+32.5+57.5+76.1+32.5+100+23.4 \right)\,\text{percent}}\times 100\,\text{percent} \\ & =\frac{32.5\,\text{percent}}{323\,\text{percent}}\times 100\,\text{percent} \\ & =10.06\,\text{percent} \end{align}\] Calculate the abundance of Hg-202 as follows: \[\begin{align} & \text{Abundance of Hg-}202=\frac{100\,\text{percent}}{\left( 1.0+32.5+57.5+76.1+32.5+100+23.4 \right)\,\text{percent}}\times 100\,\text{percent} \\ & =\frac{100\,\text{percent}}{323\,\text{percent}}\times 100\,\text{percent} \\ & =30.96\,\text{percent} \end{align}\] Calculate the abundance of Hg-204 as follows: \[\begin{align} & \text{Abundance of Hg-}204=\frac{23.4\,\text{percent}}{\left( 1.0+32.5+57.5+76.1+32.5+100+23.4 \right)\,\text{percent}}\times 100\,\text{percent} \\ & =\frac{23.4\,\text{percent}}{323\,\text{percent}}\times 100\,\text{percent} \\ & =7.24\,\text{percent} \end{align}\] Calculate the fraction of Hg-196 as follows: \[\begin{align} & \text{Fraction of isotope Hg-}196=\frac{0.31}{100} \\ & =0.0031 \end{align}\] Calculate the fraction of Hg-198 as follows: \[\begin{align} & \text{Fraction of isotope Hg-}198=\frac{10.06}{100} \\ & =0.1006 \end{align}\] Calculate the fraction of Hg-199 as follows: \[\begin{align} & \text{Fraction of isotope Hg-}199=\frac{17.80}{100} \\ & =0.178 \end{align}\] Calculate the fraction of Hg-200 as follows: \[\begin{align} & \text{Fraction of isotope Hg-}200=\frac{23.56}{100} \\ & =0.2356 \end{align}\] Calculate the fraction of Hg-201 as follows: \[\begin{align} & \text{Fraction of isotope Hg-}201=\frac{10.06}{100} \\ & =0.1006 \end{align}\] Calculate the fraction of Hg-202 as follows: \[\begin{align} & \text{Fraction of isotope Hg-}202=\frac{30.96}{100} \\ & =0.3096 \end{align}\] Calculate the fraction of Hg-204 as follows: \[\begin{align} & \text{Fraction of isotope Hg-}204=\frac{7.24}{100} \\ & =0.0724 \end{align}\] Calculate the atomic mass of element as follows: \[\begin{align} & \text{Atomic mass}=\left( \text{Fraction of Hg-}196\times \text{Mass of Hg-}196 \right)+ \\ & \left( \text{Fraction of Hg-}198\times \text{Mass of Hg-}198 \right)+ \\ & \left( \text{Fraction of Hg-}199\times \text{Mass of Hg-}199 \right)+ \\ & \left( \text{Fraction of Hg-}200\times \text{Mass of Hg-}200 \right)+ \\ & \left( \text{Fraction of Hg-}201\times \text{Mass of Hg-}201 \right)+ \\ & \left( \text{Fraction of Hg-}202\times \text{Mass of Hg-}202 \right)+ \\ & \left( \text{Fraction of Hg-}204\times \text{Mass of Hg-}204 \right) \\ & =\left( 0.0031\times 196\text{ amu} \right)+\left( 0.1006\times 198\text{ amu} \right)+ \\ & \left( 0.178\times 199\text{ amu} \right)+\left( 0.2356\times 200\text{ amu} \right)+ \\ & \left( 0.1006\times 201\text{ amu} \right)+\left( 0.3096\times 202\text{ amu} \right)+ \\ & \left( 0.0724\times 204\text{ amu} \right) \\ & =0.6076\text{ amu}+19.9188\text{ amu}+35.422\text{ amu}+47.12\text{ amu} \\ & +20.2206\text{ amu}+62.5392\text{ amu}+14.77\text{ amu} \\ & =200.598\text{ amu} \end{align}\] The atomic mass of mercury is \[\underline{\text{201 amu}}\].