Chapter 1, Problem 1.116QP

The composition of pennies has changed over the years, depending on a number of factors, including the availability of various metals. A penny minted in 1825 was pure copper; a penny minted in 1860 was 88 percent copper and 12 percent nickel; a penny minted in 1965 was 95 percent copper and 5 percent zinc; and a penny minted today is 97.5 percent zinc and 2.5 percent copper. Given that the densities of copper, nickel, and zinc are 8.92 g/cm³, 8.91 g/cm³, and 7.14 g/cm³, respectively, determine the density of each penny.

Interpretation Introduction

Interpretation: From the given data, density of each penny should be determined.

Concept introduction:

$\text{Density}\text{of}\text{penny}\text{=}{\displaystyle \sum \left(\frac{\text{percent}\text{metal}}{\text{100}}\text{×density}\text{of}\text{metal}\right)}$

Answer to Problem 1.116QP

$\begin{array}{l}1825;\\ Densityofpenny=8.92g/c{m}^3\\ 1860;\\ Densityofpenny=8.9g/c{m}^3\\ 1965;\\ Densityofpenny=8.8g/c{m}^3\\ Today;\\ Densityofpenny=7.18g/c{m}^3\end{array}$

Explanation of Solution

The density of penny minted in 1825

$\text{Density}\text{of}\text{penny=8}\text{.92}{\text{g/cm}}^{\text{3}}$

A penny minted in 1825 was pure copper. Therefore, the density of penny was that of copper. The density of copper was $\text{8}\text{.92}{\text{g/cm}}^{\text{3}}$.

The density of penny minted in 1860

$\text{Density}\text{of}\text{penny=8}\text{.9}{\text{g/cm}}^{\text{3}}$

A penny minted in 1860 was 88 percent copper and 12 percent nickel. The density of the penny can be calculated using the weight percentages of each element and the densities of element. Here in the case on 1860,

$\begin{array}{l}\text{The}\text{penny}\text{was}\text{88\%copper}\text{and}\text{12\%nickel}\text{and}\text{density}\text{of}\text{nickel}\text{is}\text{8}\text{.91}{\text{g/cm}}^{\text{3}}\\ \end{array}$

So, the density of penny can be calculated as follows;

$\text{Density}\text{of}\text{penny}\text{=}{\displaystyle \sum \left(\frac{\text{percent}\text{metal}}{\text{100}}\text{×density}\text{of}\text{metal}\right)}$

                          $\begin{array}{l}=\left(\frac{88}{100}\right)(\text{8}\text{.92}{\text{g/cm}}^{\text{3}})+\left(\frac{12}{100}\right)(\text{8}\text{.91}{\text{g/cm}}^{\text{3}})\\ =\text{8}\text{.9}{\text{g/cm}}^{\text{3}}\end{array}$

The density of penny minted in 1965

$\text{Density}\text{of}\text{penny=8}\text{.8}{\text{g/cm}}^{\text{3}}$

A penny minted in 1965 was 95 percent copper and 5 percent zinc. The density of the penny can be calculated using the weight percentages of each element and the densities of element. Here in the case on 1965,

$\text{The}\text{penny}\text{was}\text{95\%copper}\text{and}\text{5\%zinc}\text{and}\text{density}\text{of}\text{zinc}\text{is}\text{7}\text{.14}{\text{g/cm}}^{\text{3}}$

So, the density of penny can be calculated as follows;

$\text{Density}\text{of}\text{penny}\text{=}{\displaystyle \sum \left(\frac{\text{percent}\text{metal}}{\text{100}}\text{×density}\text{of}\text{metal}\right)}$

                          $\begin{array}{l}=\left(\frac{95}{100}\right)(\text{8}\text{.92}{\text{g/cm}}^{\text{3}})+\left(\frac{5}{100}\right)(7.14{\text{g/cm}}^{\text{3}})\\ =\text{8}\text{.8}{\text{g/cm}}^{\text{3}}\end{array}$

The density of penny minted today

$\text{Density}\text{of}\text{penny=7}\text{.18}{\text{g/cm}}^{\text{3}}$

A penny minted today is 97.5 percent zinc and 2.5 percent copper. The density of the penny can be calculated using the weight percentages of each element and the densities of element. Here in the case,

$\begin{array}{l}\text{The}\text{penny}\text{was}\text{97}\text{.5\%}\text{zinc}\text{and}\text{2}\text{.5\%}\text{copper}\\ \text{Density}\text{of}\text{zinc}\text{is}\text{7}\text{.14}{\text{g/cm}}^{\text{3}}\text{and}\text{density}\text{of}\text{copper}\text{is}\text{8}\text{.92}{\text{g/cm}}^{\text{3}}\end{array}$

So, the density of penny can be calculated as follows;

$\text{Density}\text{of}\text{penny}\text{=}{\displaystyle \sum \left(\frac{\text{percent}\text{metal}}{\text{100}}\text{×density}\text{of}\text{metal}\right)}$

                          $\begin{array}{l}\text{=}\left(\frac{\text{97}\text{.5}}{\text{100}}\right)\text{(7}\text{.14}{\text{g/cm}}^{\text{3}}\text{)+}\left(\frac{\text{5}}{\text{100}}\right)\text{(8}\text{.92}{\text{g/cm}}^{\text{3}}\text{)}\\ \text{=}\text{7}\text{.18}{\text{g/cm}}^{\text{3}}\end{array}$

Conclusion

From the given data, density of each penny is determined.