Problem 56 - Chemistry The Science in Context

Question

A student wonders whether a piece of jewelry is made of pure silver. She determines that its mass is 3.17 g. Then she drops it into a 10 mL graduated cylinder partially filled with water and determines that its volume is \(0.3 \mathrm{mL}\). Could the jewelry be made of pure silver?

Step-by-Step Solution

Answer

Answer: The calculated density of the jewelry (10.57 g/mL) is close to the known density of pure silver (10.5 g/mL), so it is possible that the jewelry is made of pure silver. However, further tests would be needed to confirm this with certainty.

Step 1: Write down the given values

The mass of the jewelry is 3.17 g, and the volume is 0.3 mL.

Step 2: Calculate the density of the jewelry

The formula to find the density is: Density = mass/volume In this case, we have: Density = 3.17 g / 0.3 mL Now calculate the density of the jewelry: Density ≈ 10.57 g/mL

Step 3: Compare the calculated density to the density of pure silver

The density of pure silver is known to be 10.5 g/mL. Our calculated density, which is 10.57 g/mL, is close to the density of pure silver.

Step 4: Conclusion

Since the calculated density of the jewelry (10.57 g/mL) is close to the known density of pure silver (10.5 g/mL), it is possible that the jewelry is made of pure silver. However, further tests would be needed to confirm this with certainty.

Key Concepts

Density of Silver

Understanding the density of silver is crucial when determining its purity in various objects like jewelry. Density is a property that describes how much mass is contained in a given volume. It is usually expressed in units like grams per milliliter (g/mL).
The density of any material, including pure silver, is calculated using the formula:

• Density = Mass/Volume

For pure silver, the density is known to be approximately 10.5 g/mL. This means that for every milliliter of silver, it has a mass of 10.5 grams.
In the context of the exercise, the calculated density of the jewelry is 10.57 g/mL, which is close to the density of pure silver. While minor discrepancies exist, this could be due to measurement errors or alloy mixtures. Nonetheless, a calculated density near 10.5 g/mL suggests that the jewelry is very likely made of silver or a silver-dominant alloy.

Graduated Cylinder

A graduated cylinder is an essential laboratory instrument used to measure the volume of a liquid. It has measurement markings along its side, making it easy to read the level of liquid inside to determine the exact volume displaced.
Using a graduated cylinder to determine the volume of an object involves a simple process:

• Partially fill the graduated cylinder with water and record the initial volume.
• Carefully drop the object into the water, making sure to avoid splashing or spilling.
• Record the new volume of water. The volume of the object is the difference between the initial and final volumes.

In the exercise, a graduated cylinder was used to measure the displaced volume of the jewelry, which was found to be 0.3 mL. This precise volume measurement is vital when calculating density.

Mass and Volume

Mass and volume are fundamental concepts in physics that go hand-in-hand when determining the density of an object.
Mass refers to the amount of matter present in an object and is typically measured in grams (g) or kilograms (kg). In the case of the jewelry mentioned, the mass was found to be 3.17 grams.
Volume is the amount of space that an object occupies and can be expressed in milliliters (mL) or liters (L). The volume of the jewelry, measured by water displacement, was 0.3 mL.
To find the density, both mass and volume are combined using the formula:

• Density = Mass/Volume

In practical terms, these measurements help to discover whether materials like the jewelry in question match expected density values, such as those of pure silver, to make educated guesses about their composition.