Question

In 1982 the U.S. Mint stopped making copper pennies and began phasing in pennies made of zinc plated with a thin layer of copper. If a 1990 penny weighs \(2.554 \mathrm{~g}\) and contains \(2.490 \mathrm{~g}\) zinc, what is the percent of copper in the coin?

Short answer

The penny is approximately 2.51% copper.

Step-by-step solution

Understand the Problem

We begin by identifying the known values. The total mass of a 1990 penny is given as \(2.554\, \text{g}\) and it contains \(2.490\, \text{g}\) of zinc. We are tasked with finding out the percent of copper in the penny.

Calculate the Mass of Copper

Subtract the mass of zinc from the total mass of the penny to find the mass of copper. The equation is: \(\text{mass of copper} = \text{total mass} - \text{mass of zinc}\). This gives us \(\text{mass of copper} = 2.554\, \text{g} - 2.490\, \text{g} = 0.064\, \text{g}\).

Calculate the Percent of Copper

The percentage of copper is calculated by dividing the mass of copper by the total mass of the penny and then multiplying by 100. So, \(\text{percent of copper} = \left(\frac{0.064}{2.554}\right) \times 100\).

Perform the Calculation

Perform the calculation: \(\left(\frac{0.064}{2.554}\right) \times 100 \approx 2.51\%\). This tells us that \(2.51\%\) of the penny is made of copper.

Key concepts

Mass Calculation

Mass calculation is a fundamental skill in chemistry and physical sciences. It involves determining the weight of different components within a compound or object.
For the 1990 penny, we start with the total mass and the mass of the zinc component. The total mass of the penny is given as 2.554 grams. The zinc within this penny weighs 2.490 grams.
To find the remaining mass, which is copper in this context, we simply subtract the zinc's mass from the total mass:

• Total mass = 2.554 grams
• Mass of zinc = 2.490 grams

So, the calculation is straightforward: \( \text{Mass of copper} = 2.554 - 2.490 = 0.064 \text{ grams} \).
This subtraction gives us the weight of the copper component in the penny. Understanding this step is essential because it serves as a basis for further calculations, like determining percentage composition.

Copper Content in Alloys

The copper content in alloys, such as those used in post-1982 pennies, can be quantified using the percent composition technique. This is important when analyzing the composition of various metal products.
In our example, the 1990 penny is an alloy primarily composed of zinc with a small percentage of copper. Once the mass of copper is known, which is 0.064 grams as calculated previously, determining its percentage in the overall penny is the next step.
The key formula here is:

• \( \text{Percent of copper} = \left( \frac{\text{Mass of copper}}{\text{Total mass of penny}} \right) \times 100 \)

Applying this to our numbers gives us: \( \left( \frac{0.064}{2.554} \right) \times 100 \approx 2.51\% \).
This calculation indicates that 2.51% of the penny's mass is copper. This concept helps understand the proportion of different metals in an alloy, which is crucial for various manufacturing and recycling processes.

Zinc Penny Composition

Understanding the composition of zinc pennies involves analyzing the different materials that make up these coins. Post-1982 pennies demonstrate a shift in composition due to economic reasons.
Originally made predominantly from copper, the change to zinc cores with copper plating reflected the need to reduce costs while maintaining functionality.
Zinc pennies consist of two main layers:

• A core that is largely made of zinc (making up the majority of the penny's mass).
• A thin outer layer of copper that does not significantly alter the penny's mass.

The transition from copper to zinc pennies underscored the importance of using more economical materials without sacrificing quality.
The knowledge of different metal compositions, particularly knowing that a modern penny is mostly zinc with minimal copper, helps in such calculations and adds to an understanding of shifts in material science based on economic drivers.