Question

Before 1982 the U.S. Mint cast penny coins from a copper and zinc mixture. If a 1980 penny weighs \(3.051 \mathrm{~g}\) and contains \(0.153 \mathrm{~g}\) zinc, what is the percent of copper in the coin?

Short answer

The penny is approximately 95.00% copper.

Step-by-step solution

Identify Total Weight

The total weight of the 1980 penny is given as \(3.051 \, \text{g}\). We will use this value in subsequent calculations to determine the copper content.

Identify Zinc Weight

The weight of the zinc in the penny is given as \(0.153 \, \text{g}\). We need this to calculate the weight of the copper by subtracting the zinc weight from the total weight.

Calculate Copper Weight

Subtract the weight of zinc from the total weight to find the weight of copper: \[\text{Weight of Copper} = 3.051 \, \text{g} - 0.153 \, \text{g} = 2.898 \, \text{g}\]

Calculate Percent Copper

The percentage of copper in the penny can be calculated using the formula:\[\text{Percent Copper} = \left( \frac{\text{Weight of Copper}}{\text{Total Weight}} \right) \times 100\%\]Substituting the known values:\[\text{Percent Copper} = \left( \frac{2.898}{3.051} \right) \times 100\% \approx 95.00\%\]

Key concepts

Understanding Percent Composition

Percent composition is a way in chemistry to express the make-up of a substance by showing the percentage by mass of each component within it. It helps us understand what portion of a mixture is comprised of each ingredient. Think of it like finding out how much of a pizza's weight is attributed to cheese versus toppings!

To calculate percent composition, use the formula:
- Find the mass of each element in the compound
- Divide the mass of the element by the total mass of the compound
- Multiply by 100 to get a percentage

In our penny example, after calculating the weight of copper, we determined the percent composition of copper by dividing its weight by the total weight of the penny. Then multiplying the result by 100 to find out that approximately 95% of the penny's weight comes from copper.

Copper in the 1980 Penny

Copper is a reddish metal that is well-known for its conductivity and malleability, making it an excellent choice for coinage. In the case of pennies from 1980, copper was the primary component.

When dealing with chemical compositions like in our penny example, it's crucial to know the different roles of each metal. Copper was used in pennies because it resists corrosion effectively while maintaining its structural integrity over time. So, studying percent composition allows us to understand how much of this reliable metal was used per penny.

The calculated 95% of copper in the penny not only highlights copper's dominance in its composition but also sheds light on the economic and material factors that influence minting decisions.

Zinc's Role

Zinc is another important metal that was used alongside copper in penny production. While zinc occupies a smaller fraction of old U.S. pennies, its presence is significant because it helps in reducing costs and adjusting the penny's properties.

Zinc is less expensive than copper, so incorporating it into the alloy decreases production costs. Furthermore, it adds some desired properties to the copper alloy, such as increased strength and hardness, aiding the penny’s durability. In our scenario, pennies incorporated a small percent of zinc, around 5%, which helped keep costs down while ensuring the functionality.

Understanding the percent composition of zinc in items like pennies can highlight how varying proportions of materials serve specific purposes in product design.

The Art of Problem-Solving in Chemistry

Solving problems in chemistry often relies on systematic approaches that break down complex calculations into actionable steps. This is a powerful skill that aids in analyzing chemical compositions accurately.

When faced with a problem like determining the percent composition of a substance, you can use a stepwise method. Begin by identifying known values, calculate individual components, and finally arrive at the desired percentage by utilizing formulas efficiently.

In the context of the penny problem, we used clear steps: determining total weight and component weights, performing subtraction to find the weight of copper, and finally applying the percent composition formula. This ordered approach not only makes complex problems more manageable but also builds valuable critical thinking skills useful beyond the scope of chemistry.