Problem 89 - Chemistry

Question

An experiment is performed to determine if pennies are made of pure copper. The mass of 10 pennies was measured on a balance and found to be \(24.656 \mathrm{~g}\). The volume was found by dropping the 10 pennies into a graduated cylinder initially containing \(10.0 \mathrm{~mL}\) of water. The volume after the pennies were added was \(12.90 \mathrm{~mL}\). Calculate the density of the pennies. If the density of pure copper at the same temperature is \(8.96 \mathrm{~g} / \mathrm{cm}^{3}\), are the pennies made of pure copper?

Step-by-Step Solution

Answer

The pennies are not pure copper since their density is about 8.50 g/mL, less than copper's 8.96 g/cm³.

Step 1: Calculate Volume of Pennies

Determine the volume of the 10 pennies by using the water displacement method. The initial volume of the water was 10.0 mL, and it increased to 12.90 mL after the pennies were submerged. The volume of the pennies is the difference between these two measurements:\[\text{Volume of pennies} = 12.90 \text{ mL} - 10.0 \text{ mL} = 2.90 \text{ mL}\]

Step 2: Calculate Density of Pennies

Density is calculated using the formula:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]The mass of the pennies is given as 24.656 g, and the volume is 2.90 mL:\[\text{Density} = \frac{24.656 \text{ g}}{2.90 \text{ mL}} \approx 8.50 \text{ g/mL}\]

Step 3: Compare with Copper Density

The calculated density of the pennies is approximately 8.50 g/mL. Compare this with the known density of pure copper, which is 8.96 g/cm³. Since the density of the pennies is less than the density of pure copper, they are not made entirely of copper.

Key Concepts

Understanding the Water Displacement Method

The water displacement method is a straightforward and effective way to measure the volume of an irregularly shaped object, such as coins. To use this method, you begin by filling a graduated cylinder with a certain volume of water. It’s important to record this initial volume precisely.
Next, you gently add the object (or objects, like our 10 pennies) into the water. The key here is to ensure that all the objects are fully submerged and that they do not float. Once submerged, the water level in the graduated cylinder will rise. The new water level should be noted carefully.

• The difference in volume, that is: \[\text{Volume of Object} = \text{Final Water Level} - \text{Initial Water Level}\]

This difference is the volume of the submerged objects. For example, if the water initially measures 10.0 mL and rises to 12.9 mL after the pennies are added, the volume of the pennies is \[2.9 \text{ mL}\].
By understanding this process, you can accurately calculate the volume of objects that would be difficult to measure using traditional methods.

Calculating and Understanding Copper Density

Density is a measure of how much mass is contained in a given volume and is calculated using the formula:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]
For copper, this number is a known constant—8.96 g/cm³. This value tells us that copper is quite dense, which is why it feels heavy for its size. To determine the density of the pennies in the exercise, we use their mass and volume. The mass given is 24.656 g, and the volume, determined using the water displacement method, is 2.90 mL.
We substitute these into the formula:\[\text{Density of Pennies} = \frac{24.656 \text{ g}}{2.90 \text{ mL}} \approx 8.50 \text{ g/mL}\]

• If the density calculated (8.50 g/mL) is less than that of pure copper, it indicates that pennies are not made entirely of copper.
• This suggests that the pennies have a composition of materials less dense than copper.

Recognizing the density differences helps determine material composition effectively.

Importance of Accurate Mass and Volume Measurement

Accurate measurement of mass and volume is crucial in scientific experiments to ensure precise calculations. To determine the density of any object, one must first measure its mass using a balance. This device provides the weight of the object in grams or kilograms.
Next, comes measuring the object's volume, especially when irregular shapes are involved. The water displacement method, as previously explained, is ideal for this task. By achieving precise measurements:

• You can reliably calculate density, an indicator of material composition and purity.
• In our exercise, the mass of the pennies was exactly 24.656 g, a critical detail for accurate density calculation.
• Combining this mass with a precisely measured volume of 2.90 mL allows for a precise density determination.

Through correct application of these techniques, conclusions about the material properties can be drawn, determining if, in this case, the pennies are pure copper or a mix of different metals.