In 1983 , the United States began coining the cent piece out...

In 1983 , the United States began coining the cent piece out of copper-clad zinc rather than pure copper. The mass of the old copper penny is 3.083 g, while that of the new cent is 2.517 g. Calculate the percentage of zinc (by volume) in the new cent. The density of copper is 8.960 $\mathrm{g} / \mathrm{cm}^{3}$ and that of zinc is $7.133 \mathrm{g} / \mathrm{cm}^{3} .$ The new and old coins have the same volume.

Key Concepts

Percent Composition by Volume

Percent composition by volume refers to the fraction or percentage of a specific substance within a mixture, calculated based on the volume it occupies relative to the total volume. This concept is particularly useful when the overall volume is fixed and the objective is to determine the contribution of each component to that volume, using the known densities and masses of the components.

Mixture Problems

Mixture problems involve combining two or more substances with distinct properties and determining the overall properties of the mixture. In scenarios involving different densities, it is necessary to set up equations that account for the separate volumes and masses of each component to compute the composition, ensuring that conservation principles, such as constant total volume, are maintained.

Volume-Mass Relationship

Understanding the relationship between mass and volume is key to solving problems where the volume is held constant but the mass varies due to different material densities. By using the formula density = mass/volume, one can derive volume from mass and density, or vice versa, which is essential when comparing or combining materials.

Density

Density is a physical property defined as the mass of a substance per unit volume. It is crucial in comparing materials because it allows one to determine how much mass is present in a given volume, which is essential when working with composite materials or mixtures where different substances have different densities.

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