On October 21,1982, the Bureau of the Mint changed the...

On October 21,1982, the Bureau of the Mint changed the composition of pennies (see Exercise 106$)$. Instead of an alloy of $95 \%$ $\mathrm{Cu}$ and $5 \%$ Zn by mass, a core of $99.2 \% \mathrm{Zn}$ and $0.8 \%$ Cu with a thin shell of copper was adopted. The overall composition of the new penny was $97.6 \% \mathrm{Zn}$ and $2.4 \%$ Cu by mass. Does this account for the difference in mass among the pennies in Exercise 106 ? Assume the volume of the individual metals that make up each penny can be added together to give the overall volume of the penny, and assume each penny is the same size. (Density of $\mathrm{Cu}=8.96 \mathrm{~g} / \mathrm{cm}^{3} ;$ density of $\mathrm{Zn}=7.14 \mathrm{~g} / \mathrm{cm}^{3} .$ )

Key Concepts

Percentage Composition by Mass

Percentage composition by mass is a method of expressing the concentration of each constituent in a mixture relative to the total mass. It is used to determine how much of each component, such as copper and zinc, is present in a sample and is essential when comparing different alloys or mixtures.

Density and Mass-Volume Relationship

Density is defined as the mass of a substance per unit volume. This concept is critical in linking the physical dimensions of an object to its overall mass, especially when the material composition is changed. Variations in the densities of the constituent metals are directly responsible for differences in the final mass for objects of the same size.

Alloy Composition

Alloy composition involves the specification of the individual components that make up a material and their relative proportions, usually expressed as a percentage by mass. Understanding how these proportions affect the overall properties of the material is crucial, as changes in the alloy's formula can lead to differences in density, durability, and other physical attributes.

Volume Additivity in Metal Alloys

Volume additivity is the assumption that the total volume of an alloy is equal to the sum of the volumes of its individual components, each calculated from their respective masses and densities. This concept simplifies the analysis of how changes in alloy composition affect the overall mass of the object, by allowing for a direct computation using the densities of the constituent materials.

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