Problem 81 - Chemistry

Question

What is the density of lead in \(\mathrm{g} / \mathrm{cm}^{3}\) if a sample weighing \(206.77 \mathrm{~g}\) has a volume of \(15.50 \mathrm{~cm}^{3} ?\)

Step-by-Step Solution

Answer

Density of lead is approximately \(13.34 \ \mathrm{g/cm}^3\).

Step 1: Understand Density Formula

Density is defined as mass per unit volume. The formula used to calculate density is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This means you divide the mass of the object by its volume.

Step 2: Identify Given Values

From the problem, we have:- Mass \( = 206.77 \ \mathrm{g} \)- Volume \( = 15.50 \ \mathrm{cm}^3 \).

Step 3: Substitute Values into the Formula

Substitute the given mass and volume into the density formula:\[ \text{Density} = \frac{206.77 \ \mathrm{g}}{15.50 \ \mathrm{cm}^3} \].

Step 4: Perform the Calculation

Calculate the density by dividing the mass by the volume:\[ \text{Density} = \frac{206.77}{15.50} \approx 13.34 \ \mathrm{g/cm}^3 \].

Key Concepts

Density Calculation

Density is a way of showing how much mass is packed into a certain volume. It's like thinking about how many things fit into a box. For instance, if you have two boxes of the same size but filled with different materials, one might feel heavier than the other because it has more mass packed into the same volume.

To calculate density, you'll use a simple formula:

• Density is found by dividing the mass by the volume using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

By understanding this calculation, you can determine how dense a material is compared to others. For our example with the lead sample: after putting the values 206.77 g for mass and 15.50 cm³ for volume into the formula, you get approximately 13.34 g/cm³.

Mass and Volume Relationship

The mass and volume relationship is crucial to understanding density. Mass refers to the amount of matter in an object, and it's measured in grams when considering substances like lead. Volume, on the other hand, is the space that the object occupies, usually measured in cubic centimeters (cm³) for smaller objects.

When considering this relationship:

• Larger volume with similar mass means less density (think about a sponge).
• Smaller volume with the same mass means more density (like a rock).

These concepts help in figuring out how objects with the same mass can take different amounts of space, leading to various density values. Understanding this can help in predicting how an object will behave, such as whether it will float or sink in a liquid.

Density Formula

The density formula is key in solving many physics and chemistry problems as it relates mass and volume to give a complete picture of how packed a substance is. With the formula \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \], you can evaluate a material's compactness.

In our example, using the formula effectively means:

• Identifying the mass which was given as 206.77 grams.
• Noticing the volume provided was 15.50 cm³.
• Plugging these values into the formula to find the final density.

This basic formula not only calculates density but also gives insight into the object's properties compared to others, like why one metal is heavier than another despite being the same size.