Problem 12 - Chemistry and Chemical Reactivity

Question

A piece of silver metal has a mass of \(2.365 \mathrm{g} .\) If the density of silver is \(10.5 \mathrm{g} / \mathrm{cm}^{3},\) what is the volume of the silver?

Step-by-Step Solution

Answer

The volume of the silver is approximately 0.225 cm³.

Step 1: Understanding the Problem

We are given a mass of silver which is 2.365 grams and we know the density of silver is 10.5 grams per cubic centimeter. We need to find the volume of the silver piece.

Step 2: Setting Up the Formula

Density is defined as mass per unit volume. The formula for density is given by \( \text{density} = \frac{\text{mass}}{\text{volume}} \). We can rearrange this formula to find volume, \( \text{volume} = \frac{\text{mass}}{\text{density}} \).

Step 3: Plug in the Values

Now that we have the formula \( \text{volume} = \frac{\text{mass}}{\text{density}} \), we can substitute the given values into this formula to find the volume: \( \text{volume} = \frac{2.365 \text{ g}}{10.5 \text{ g/cm}^3} \).

Step 4: Calculate the Volume

Divide the mass by the density to find the volume: \[ \text{volume} = \frac{2.365}{10.5} \approx 0.225 cm^3 \].

Step 5: Conclusion

The volume of the silver piece is approximately 0.225 cubic centimeters.

Key Concepts

Understanding Mass

Mass is a fundamental concept that represents the amount of matter in an object. It's often measured in grams (g) or kilograms (kg) in the metric system. Mass does not change based on location; for example, your mass remains the same whether you're on Earth or the Moon.
In our problem, the mass of the silver piece is given as 2.365 grams. This is a fixed amount, representing how much silver is present. This measurement is crucial when calculating other properties like density and volume. Understanding mass helps predict how objects will behave in different physical situations, like inertia in motion or gravitational force attraction.
When dealing with chemical reactions or physical changes, knowing the mass of each component helps in making precise calculations, ensuring the right amount of substance is used.

Calculating Volume

Volume indicates how much space an object occupies. It's often measured in cubic centimeters (cm³) or liters (L). In the context of solids like a piece of silver, volume gives us a clear idea about the size and shape related characteristics.
To find the volume of an object when its mass and density are known, you can use the rearranged formula of density: \[ \text{volume} = \frac{\text{mass}}{\text{density}} \] For the silver piece, we have: \[ \text{volume} = \frac{2.365 \text{ g}}{10.5 \text{ g/cm}^3} \approx 0.225 \text{ cm}^3 \]
This calculation shows that our silver piece occupies about 0.225 cubic centimeters of space. Volume measurements help in understanding capacity, container size, and how materials interact when packed together.

Properties of Silver

Silver is a chemical element known for its shiny appearance and excellent conductivity. As a metal, it's highly valued in various industries for its properties. It is often used in jewelry, electronics, and as currency.
Key characteristics of silver include:

• Density: Silver has a density of 10.5 grams per cubic centimeter, which means it is quite dense and heavy for its size compared to other materials.
• Conductivity: Silver is the best natural conductor of electricity, surpassing even copper, which is why it is highly sought after in the electronics industry.
• Tarnishing: While silver may tarnish when exposed to air due to it reacting with sulfur compounds, its luster can be easily restored.

Understanding these properties of silver not only helps in identifying and using the metal for practical purposes but also adds value to experiments and projects where precise material characteristics are required.