Question: Which has more atoms: 1 kg of lead or 1 kg of copper? (See the Periodic Table or Appendix B.) Explain why.

The atomic mass is defined as the mass of one atom of an element. The atomic mass of any element shows us how much one atom weighs in atomic mass units.

The relationship between the unit of one atomic mass and the unit of kilograms is as follows:

\(1\;{\rm{u}} = {\rm{1}}{\rm{.6605}} \times {10^{ - 27}}\;{\rm{kg}}\)

The mass of one atom of lead is \(207\;{\rm{u}}\). This mass in kilograms can be converted as follows:

\(\begin{array}{c}207\;{\rm{u}} = \left( {207} \right)\left( {{\rm{1}}{\rm{.6605}} \times {{10}^{ - 27}}\;{\rm{kg}}} \right)\\ = 3.4372 \times {10^{ - 25}}\;{\rm{kg}}\end{array}\)

The number of atoms in 1 kg of lead can be calculated as follows:

\(\begin{array}{c}{n_{{\rm{Pb}}}} = \frac{{1\;{\rm{kg}}}}{{3.4372 \times {{10}^{ - 25}}\;{\rm{kg}}}}\\{n_{{\rm{Pb}}}} = 2.909 \times {10^{24}} \approx 3 \times {10^{24}}\end{array}\) … (i)

The mass of one atom of copper is \(64\;{\rm{u}}\). This mass in kilograms can be converted as follows:

\(\begin{array}{c}64\;{\rm{u}} = \left( {64} \right)\left( {{\rm{1}}{\rm{.6605}} \times {{10}^{ - 27}}\;{\rm{kg}}} \right)\\ = 1.0627 \times {10^{ - 25}}\;{\rm{kg}}\end{array}\)

The number of atoms in 1 kg of copper can be calculated as follows:

\(\begin{array}{c}{n_{{\rm{Cu}}}} = \frac{{1\;{\rm{kg}}}}{{1.0627 \times {{10}^{ - 25}}\;{\rm{kg}}}}\\{n_{{\rm{Cu}}}} = 9.404 \times {10^{24}} \approx 9 \times {10^{24}}\end{array}\) … (ii)

Thus, from equations (i) and (ii), it is clear that \({n_{{\rm{Cu}}}} > {n_{{\rm{Pb}}}}\). This is because the atomic mass of lead is more than the atomic mass of copper.