Problem 70 - Chemistry: An Atoms-Focused Approach

Question

A student wonders whether a piece of jewelry is made of pure silver. She determines that its mass is \(3.17 \mathrm{g} .\) 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

Explain your answer.

Step 1: Find the density of the material

To find the density of the material we will use the formula: Density = \(\frac{Mass}{Volume}\) Given the mass and volume of the jewelry, we can find its density.

Step 2: Calculate the density of the jewelry

We have the mass of the jewelry as \(3.17 \mathrm{g}\) and its volume as \(0.3 \mathrm{mL}\). Substitute these values into the density formula. Density = \(\frac{3.17}{0.3} = 10.57 \mathrm{\frac{g}{mL}}\) So, the density of this jewelry is \(10.57 \mathrm{\frac{g}{mL}}\).

Step 3: Compare the density with the density of pure silver

The density of pure silver is \(10.49 \mathrm{\frac{g}{mL}}\). Compare this value with the calculated density of the jewelry, which is \(10.57 \mathrm{\frac{g}{mL}}\). We can see that the density of the jewelry is slightly higher than the density of pure silver. This means that the jewelry could contain a metal with a higher density than silver or that it is an alloy.

Step 4: Conclusion:

Based on the comparison between the density of the jewelry and the density of pure silver, we cannot conclusively say that the jewelry is made of pure silver. It could be an alloy or a different material altogether.

Key Concepts

Mass

When discussing the concept of mass, we are referring to the amount of matter within an object. In the context of our example, the mass of the jewelry in question is given as \(3.17\, \text{g}\). Mass is usually measured in grams (g) or kilograms (kg) depending on the context.
Understanding mass is crucial because it is a fundamental measurement in physics and chemistry.

• Mass is consistent regardless of location. This means that the mass of the piece of jewelry would remain \(3.17\, \text{g}\) whether on Earth or in space.
• Mass is often confused with weight, but they are not the same. Weight is the force exerted by gravity on an object.

In calculation of density, the mass of the object is a pivotal component of the formula.

Volume

Volume is the amount of space that an object occupies. For our jewelry piece, its volume is determined to be \(0.3\, \text{mL}\). Volume can be measured in various units like cubic centimeters (cm³), milliliters (mL), or liters (L), depending on the object.

Seeing volume in a new light helps when deciphering how matter surrounds us.

• Accurate measurement of volume is crucial when calculating density.
• In our example, a graduated cylinder was used to find the displacement caused by the jewelry - a common method for irregular objects.

By knowing how to measure volume, we can begin to understand how it factors into larger concepts, such as density.

Density of Silver

The concept of density combines both mass and volume to describe how compact an object is. It is given by the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). For pure silver, its known density is \(10.49\, \text{g/mL}\).

In the exercise, by calculating the density of the jewelry as \(10.57\, \text{g/mL}\), we can draw comparisons:

• Density measures how much mass is packed into a given volume.
• This small difference suggests the jewelry might not be pure silver, as other metals could be present. This would change the calculated density.

Knowing the density of silver allows us to make educated guesses about the composition of different metallic objects. It's a tool for verification and hypothesis beyond surface characteristics.